python3 -c " import pdfplumber with pdfplumber.open('/tmp/workspace/attachments/0a131397-8a21-4668-8cce-daf4c51b9a02/157759.pdf') as pdf: print(f'Pages: {len(pdf.pages)}') for i, page in enumerate(pdf.pages): text = page.extract_text() print(f'--- PAGE {i+1} ---') print(text) print() "

python3 -c " from pypdf import PdfReader reader = PdfReader('/tmp/workspace/attachments/0a131397-8a21-4668-8cce-daf4c51b9a02/157759.pdf') print(f'Pages: {len(reader.pages)}') # Try extracting text with pypdf for i, page in enumerate(reader.pages): text = page.extract_text() if text and text.strip(): print(f'--- PAGE {i+1} ---') print(text[:2000]) print() # Check annotations for i, page in enumerate(reader.pages): if '/Annots' in page: print(f'Page {i+1} has annotations') annots = page['/Annots'] for annot in annots: obj = annot.get_object() print(obj) "

python3 -c " from pypdf import PdfReader import subprocess, sys # Check what's inside the PDF - images? reader = PdfReader('/tmp/workspace/attachments/0a131397-8a21-4668-8cce-daf4c51b9a02/157759.pdf') page = reader.pages[0] print('Page keys:', list(page.keys())) print('Resources:', page.get('/Resources', 'None')) # Check if there are XObjects (images) resources = page.get('/Resources') if resources: res_obj = resources.get_object() if hasattr(resources, 'get_object') else resources print('Resource keys:', list(res_obj.keys()) if res_obj else 'None') xobj = res_obj.get('/XObject') if xobj: xobj_obj = xobj.get_object() if hasattr(xobj, 'get_object') else xobj print('XObjects:', list(xobj_obj.keys()) if xobj_obj else 'None') "

python3 -c " from pypdf import PdfReader import io reader = PdfReader('/tmp/workspace/attachments/0a131397-8a21-4668-8cce-daf4c51b9a02/157759.pdf') # Extract the image from page 1 page = reader.pages[0] resources = page['/Resources'].get_object() xobj = resources['/XObject'].get_object() img_obj = xobj['/X0'].get_object() print('Image subtype:', img_obj.get('/Subtype')) print('Filter:', img_obj.get('/Filter')) print('Width:', img_obj.get('/Width')) print('Height:', img_obj.get('/Height')) print('ColorSpace:', img_obj.get('/ColorSpace')) print('BitsPerComponent:', img_obj.get('/BitsPerComponent')) # Save the raw image data data = img_obj.get_data() print('Data size:', len(data)) with open('/tmp/workspace/page1_raw.bin', 'wb') as f: f.write(data) print('Saved raw data') "

python3 -c " from pypdf import PdfReader import os reader = PdfReader('/tmp/workspace/attachments/0a131397-8a21-4668-8cce-daf4c51b9a02/157759.pdf') os.makedirs('/tmp/workspace/pdf_pages', exist_ok=True) for i, page in enumerate(reader.pages): resources = page['/Resources'].get_object() xobj = resources.get('/XObject') if not xobj: print(f'Page {i+1}: no XObject') continue xobj_obj = xobj.get_object() for key in xobj_obj: img_obj = xobj_obj[key].get_object() if img_obj.get('/Subtype') == '/Image': data = img_obj.get_data() fname = f'/tmp/workspace/pdf_pages/page_{i+1:02d}.jpg' with open(fname, 'wb') as f: f.write(data) print(f'Page {i+1}: saved {len(data)} bytes -> {fname}') break print('Done') "

mkdir -p /tmp/workspace/atomic_structure_clean && python3 << 'PYEOF' from reportlab.lib.pagesizes import A4 from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle from reportlab.lib.units import mm, cm from reportlab.lib import colors from reportlab.platypus import (SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle, HRFlowable, KeepTogether) from reportlab.lib.enums import TA_LEFT, TA_CENTER, TA_JUSTIFY from reportlab.platypus import Flowable W, H = A4 doc = SimpleDocTemplate( '/tmp/workspace/atomic_structure_clean/Atomic_Structure_NEET_Clean.pdf', pagesize=A4, leftMargin=18*mm, rightMargin=18*mm, topMargin=15*mm, bottomMargin=15*mm ) styles = getSampleStyleSheet() # Custom styles title_style = ParagraphStyle('TitleStyle', parent=styles['Normal'], fontSize=22, fontName='Helvetica-Bold', alignment=TA_CENTER, spaceAfter=4, textColor=colors.black) subtitle_style = ParagraphStyle('SubtitleStyle', parent=styles['Normal'], fontSize=10, fontName='Helvetica', alignment=TA_CENTER, spaceAfter=2, textColor=colors.black) sec_style = ParagraphStyle('SecStyle', parent=styles['Normal'], fontSize=11, fontName='Helvetica-Bold', alignment=TA_LEFT, spaceBefore=6, spaceAfter=3, textColor=colors.white, backColor=colors.black, leftIndent=4, rightIndent=4, leading=16) subsec_style = ParagraphStyle('SubSecStyle', parent=styles['Normal'], fontSize=10, fontName='Helvetica-Bold', alignment=TA_LEFT, spaceBefore=4, spaceAfter=2, textColor=colors.black, borderPad=3, borderWidth=1, borderColor=colors.black, leading=14) body_style = ParagraphStyle('BodyStyle', parent=styles['Normal'], fontSize=9, fontName='Helvetica', alignment=TA_LEFT, spaceBefore=1, spaceAfter=1, leading=13, leftIndent=4) trap_style = ParagraphStyle('TrapStyle', parent=styles['Normal'], fontSize=8.5, fontName='Helvetica', alignment=TA_LEFT, spaceBefore=1, spaceAfter=1, leading=12, leftIndent=4, textColor=colors.HexColor('#333333')) bold_body = ParagraphStyle('BoldBody', parent=body_style, fontName='Helvetica-Bold') def sec(t): return Paragraph(f'<b> {t} </b>', sec_style) def sub(t): return Paragraph(f'<b>{t}</b>', subsec_style) def p(t, style=None): if style is None: style = body_style return Paragraph(t, style) def trap(t): return Paragraph(t, trap_style) def sp(h=3): return Spacer(1, h*mm) def hr(): return HRFlowable(width='100%', thickness=0.5, color=colors.black) # Table helper def make_table(data, col_widths=None, header_bg=colors.black, header_fg=colors.white): if col_widths is None: col_widths = None t = Table(data, colWidths=col_widths, repeatRows=1 if len(data)>2 else 0) n_rows = len(data) style_cmds = [ ('BACKGROUND', (0,0), (-1,0), header_bg), ('TEXTCOLOR', (0,0), (-1,0), header_fg), ('FONTNAME', (0,0), (-1,0), 'Helvetica-Bold'), ('FONTSIZE', (0,0), (-1,-1), 8.5), ('FONTNAME', (0,1), (-1,-1), 'Helvetica'), ('GRID', (0,0), (-1,-1), 0.5, colors.black), ('VALIGN', (0,0), (-1,-1), 'TOP'), ('LEFTPADDING', (0,0), (-1,-1), 4), ('RIGHTPADDING', (0,0), (-1,-1), 4), ('TOPPADDING', (0,0), (-1,-1), 2), ('BOTTOMPADDING', (0,0), (-1,-1), 2), ] t.setStyle(TableStyle(style_cmds)) return t def formula_table(data, col_widths=None): """2-col formula table: left=label, right=formula (bold)""" if col_widths is None: col_widths = [80*mm, 90*mm] rows = [] for label, formula in data: rows.append([ Paragraph(label, ParagraphStyle('fl', parent=body_style, fontSize=8.5)), Paragraph(f'<b>{formula}</b>', ParagraphStyle('fr', parent=body_style, fontSize=8.5, fontName='Helvetica-Bold')) ]) t = Table(rows, colWidths=col_widths) t.setStyle(TableStyle([ ('GRID', (0,0), (-1,-1), 0.5, colors.black), ('VALIGN', (0,0), (-1,-1), 'TOP'), ('LEFTPADDING', (0,0), (-1,-1), 4), ('RIGHTPADDING', (0,0), (-1,-1), 4), ('TOPPADDING', (0,0), (-1,-1), 2), ('BOTTOMPADDING', (0,0), (-1,-1), 2), ])) return t story = [] # ============================================================ # TITLE # ============================================================ story.append(sp(4)) story.append(Paragraph('<b>ATOMIC STRUCTURE</b>', title_style)) story.append(Paragraph('Class 11 | Complete NEET Formula, Notes &amp; Revision Sheet', subtitle_style)) story.append(Paragraph('Every Formula • Full Notes • All NEET Traps • Zero Omissions', subtitle_style)) story.append(hr()) story.append(sp(2)) # ============================================================ # SECTION 1 # ============================================================ story.append(sec('1. DISCOVERY EXPERIMENTS &amp; FUNDAMENTAL PARTICLES')) story.append(sp(1)) story.append(sub('1A. Cathode Ray Discharge Tube Experiment (J.J. Thomson, 1897)')) for line in [ '• A gas-discharge tube at very low pressure with high voltage produces CATHODE RAYS from the negative electrode (cathode).', '• Cathode rays travel in a STRAIGHT LINE from cathode to anode.', '• They are deflected by BOTH electric and magnetic fields (towards +ve plate) → they are NEGATIVELY charged.', '• The properties of cathode rays are INDEPENDENT of the nature of the gas or electrode material used.', '• This proved electrons exist in ALL atoms and are UNIVERSAL particles.', '• J.J. Thomson measured charge-to-mass ratio: e/m = 1.758 × 10<super>11</super> C kg<super>−1</super>.', '• Thomson\'s value of e/m showed electrons are ~1836× lighter than protons.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('1B. Anode Ray / Canal Ray Experiment (Goldstein, 1886)')) for line in [ '• When cathode has holes (perforations), rays pass through in OPPOSITE direction — called canal rays or anode rays.', '• These are positively charged particles (atoms minus electrons = cations).', '• The mass and e/m ratio of canal rays DEPEND on the gas used.', '• For hydrogen gas, the lightest positive ray is obtained — this particle is the PROTON (named by Rutherford, 1920).', '• Proton charge: +1.602 × 10<super>−19</super> C. Mass: 1.673 × 10<super>−27</super> kg = 1 amu.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('1C. Millikan\'s Oil Drop Experiment (1909)')) for line in [ '• Tiny oil droplets were charged by X-rays and suspended between charged plates.', '• Measured the minimum charge on any drop → charge of one electron = 1.602 × 10<super>−19</super> C.', '• Combined with Thomson\'s e/m ratio: mass of electron = 9.109 × 10<super>−31</super> kg.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('1D. Discovery of Neutron (James Chadwick, 1932)')) for line in [ '• Chadwick bombarded Beryllium with alpha particles: ⁴He + ⁹Be → ¹²C + ¹n', '• The emitted neutral particles (mass ≈ 1 amu, charge = 0) were named NEUTRONS.', '• Neutron mass = 1.675 × 10<super>−27</super> kg ≈ 1.008 amu.', '• NEET: Neutrons were discovered LAST among the three fundamental particles.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('1E. Fundamental Particle Data Table')) particle_data = [ ['Particle', 'Symbol', 'Charge (C)', 'Mass (kg)', 'Mass (amu)', 'Discoverer'], ['Electron', 'e⁻', '−1.602×10⁻¹⁹', '9.109×10⁻³¹', '0.000549 (~0)', 'J.J. Thomson (1897)'], ['Proton', 'p⁺', '+1.602×10⁻¹⁹', '1.673×10⁻²⁷', '1.007276 (~1)', 'Goldstein/Rutherford'], ['Neutron', 'n', '0', '1.675×10⁻²⁷', '1.008665 (~1)', 'Chadwick (1932)'], ] story.append(make_table(particle_data, col_widths=[28*mm,20*mm,30*mm,28*mm,28*mm,36*mm])) story.append(sp(2)) for line in [ '[ TRAP ] Cathode rays properties are SAME regardless of gas/electrode — electrons are universal.', '[ TRAP ] Proton is ~1836 times heavier than electron. Mass ratio mₚ/mₑ = 1836.', '[ TRAP ] e/m ratio for cathode rays is SAME for all gases → electrons are identical in all atoms.', '[ TRAP ] Canal ray e/m ratio VARIES with gas → positive particles differ with gas.', '[ TRAP ] Neutron discovered by Chadwick in 1932 — it was the LAST of the three to be found.', '[ TRAP ] Charge of electron = charge of proton in magnitude. Both = 1.602 × 10<super>−19</super> C.', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 2 # ============================================================ story.append(sec('2. ATOMIC MODELS')) story.append(sp(1)) story.append(sub('2A. Thomson\'s Plum Pudding Model (1904)')) for line in [ '• Atom is a sphere of UNIFORM POSITIVE CHARGE with electrons embedded like plums in a pudding.', '• Total positive charge = total negative charge → atom is electrically neutral.', '• FAILURE: Could NOT explain Rutherford\'s alpha-scattering results (most alpha particles passed straight through).', '• Could NOT explain line spectra of elements.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('2B. Rutherford\'s Nuclear Model — Alpha Scattering Experiment (1911)')) for line in [ '• Thin gold foil (thickness ~100 nm) bombarded with a beam of fast-moving alpha (α) particles.', '• Alpha particles: ⁴He nucleus, charge +2, mass 4 amu.', '• OBSERVATIONS:', ' - Most α-particles passed STRAIGHT through (atom is mostly empty space).', ' - A few were deflected at small angles.', ' - Very few (~1 in 20,000) bounced back at angles > 90° (large deflection).', ' - About 1 in 10,000 bounced STRAIGHT back (180° deflection).', '• CONCLUSIONS:', ' - Atom is mostly empty space.', ' - All positive charge and nearly all mass is concentrated in a very small, dense region called the NUCLEUS.', ' - Electrons revolve around the nucleus in circular orbits.', ' - Nuclear radius ≈ 10<super>−15</super> m (1 fm). Atomic radius ≈ 10<super>−10</super> m (1 Å). Ratio ≈ 10⁵.', ]: story.append(p(line)) story.append(sp(2)) rutherford_formulas = [ ('Nuclear radius formula', 'r = r₀ × A^(1/3) r₀ = 1.2 × 10⁻¹⁵ m = 1.2 fm'), ('Atomic radius', '~10⁻¹⁰ m = 1 Å = 100 pm'), ('Nuclear radius', '~10⁻¹⁵ m = 1 fm (femtometre)'), ('Atom : Nucleus size ratio', 'Atomic radius / Nuclear radius ≈ 10⁵'), ('Nuclear volume', 'V ∝ A (proportional to mass number)'), ('Nuclear density', 'ρ_nucleus ≈ 10¹⁷ kg/m³ (extremely high, same for all nuclei)'), ] story.append(formula_table(rutherford_formulas)) story.append(sp(2)) p_failr = [ '• FAILURES OF RUTHERFORD\'S MODEL:', ' - An electron revolving in circular orbit is continuously ACCELERATING → it should radiate energy → orbit should shrink → atom should collapse in ~10⁻⁸ s. This DOES NOT happen (atom is stable). — This is the classical collapse problem.', ' - Could NOT explain the LINE SPECTRA of hydrogen (why only specific wavelengths?).', ' - Could not explain why electrons don\'t fall into the nucleus.', ] for line in p_failr: story.append(p(line)) story.append(sp(2)) for line in [ '[ TRAP ] Rutherford\'s model FAILED because accelerating charges radiate — atom should spiral and collapse.', '[ TRAP ] Gold was chosen for the foil because it can be beaten into very thin sheets.', '[ TRAP ] r = r₀A^(1/3): nuclear radius depends on mass number A, NOT on atomic number Z.', '[ TRAP ] Nuclear density is approximately CONSTANT for all nuclei (same r₀ for all).', '[ TRAP ] Large deflection (> 90°) occurs only when α-particle passes very close to the nucleus.', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 3 # ============================================================ story.append(sec('3. BOHR\'S MODEL OF HYDROGEN ATOM (1913)')) story.append(sp(1)) story.append(sub('3A. Bohr\'s Four Postulates')) for line in [ '• POSTULATE 1 — Stationary Orbits: Electrons revolve in specific circular orbits (shells) around the nucleus without radiating energy. These are called STATIONARY STATES or ALLOWED ORBITS.', '• POSTULATE 2 — Quantisation of Angular Momentum: The angular momentum of an electron in an allowed orbit is an integral multiple of h/2π. mvr = nh/2π where n = 1, 2, 3, … (principal quantum number).', '• POSTULATE 3 — Energy Radiation (Quantum Jump): An electron can jump between orbits by absorbing or emitting a photon. Energy of photon = difference in energy between orbits. hν = E₂ − E₁', '• POSTULATE 4 — Ground State: The orbit with lowest energy (n=1) is the ground state. Electron normally resides in this state.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('3B. Bohr\'s Model — All Formulas')) bohr_formulas = [ ('Angular momentum', 'mvr = n·h / 2π (n = 1, 2, 3, …)'), ('Radius of nth orbit', 'rₙ = 0.529 × n² / Z Å = a₀ × n²/Z'), ('Radius of nth orbit (in m)', 'rₙ = 5.29 × 10⁻¹¹ × n²/Z m'), ('Bohr radius a₀', 'a₀ = 0.529 Å = 52.9 pm = 5.29 × 10⁻¹¹ m'), ('Velocity of electron', 'vₙ = 2.18 × 10⁶ × Z / n m/s'), ('Velocity in terms of c', 'vₙ = (Z/n) × (e²/2ε₀h) ≈ (Z/n) × c/137'), ('Energy of nth orbit (eV)', 'Eₙ = −13.6 × Z² / n² eV'), ('Energy of nth orbit (J)', 'Eₙ = −2.18 × 10⁻¹⁸ × Z² / n² J'), ('Kinetic energy (KE)', 'KE = −Eₙ = +13.6 Z²/n² eV (always positive)'), ('Potential energy (PE)', 'PE = 2Eₙ = −27.2 Z²/n² eV (always negative)'), ('Relationship: KE, PE, TE', 'TE = KE + PE = −KE = PE/2'), ('Ionisation energy (from n)', 'IE = 0 − Eₙ = +13.6 Z²/n² eV'), ('IE of H from ground state', 'IE = 13.6 eV = 1312 kJ/mol = 2.18 × 10⁻¹⁸ J'), ('Energy gap (n₁ → n₂)', 'ΔE = 13.6 Z² (1/n₁² − 1/n₂²) eV [n₂ > n₁]'), ('Frequency of emitted photon', 'ν = ΔE / h = (13.6 Z² / h)(1/n₁² − 1/n₂²)'), ('Rydberg equation', '1/λ = R_H × Z² × (1/n₁² − 1/n₂²)'), ('Rydberg constant R_H', 'R_H = 1.097 × 10⁷ m⁻¹ = 109677 cm⁻¹'), ('Time period of revolution', 'Tₙ ∝ n³ / Z² (Tₙ = 2πrₙ/vₙ)'), ('Frequency of revolution', 'νₙ ∝ Z² / n³'), ('Number of revolutions/sec', 'νₙ = vₙ / (2πrₙ)'), ('For H-like ions (any Z)', 'Same formulas with Z substituted (Z=1 for H, Z=2 for He⁺, Z=3 for Li²⁺…)'), ] story.append(formula_table(bohr_formulas)) story.append(sp(2)) story.append(sub('3C. Spectral Series of Hydrogen — Complete Table')) spectral_data = [ ['Series', 'n₁', 'n₂ (starts)', 'Region', 'Series Limit λ', 'First Line (n₂=n₁+1) wavelength'], ['Lyman', '1', '2, 3, 4…', 'UV', '91.2 nm', 'H-Lα = 121.6 nm'], ['Balmer', '2', '3, 4, 5…', 'Visible/UV', '364.7 nm', 'H-α=656.3 nm (red), H-β=486.1 nm (blue-green)'], ['Paschen', '3', '4, 5, 6…', 'Near IR', '820.4 nm', '1875.1 nm'], ['Brackett', '4', '5, 6, 7…', 'IR', '1458.0 nm', '4051.3 nm'], ['Pfund', '5', '6, 7, 8…', 'Far IR', '2278.9 nm', '7459.9 nm'], ['Humphreys', '6', '7, 8, 9…', 'Far IR', '3281.9 nm', '12371.9 nm'], ] story.append(make_table(spectral_data, col_widths=[22*mm,12*mm,22*mm,22*mm,24*mm,64*mm])) story.append(sp(2)) for line in [ '• Series limit (convergence limit): when n₂ → ∞. Formula: 1/λ_limit = R_H Z²/n₁²', '• First line (longest wavelength in each series) corresponds to transition from (n₁+1) → n₁.', '• Shortest wavelength in each series corresponds to the SERIES LIMIT (n₂ → ∞).', '• Longest wavelength in each series has MINIMUM energy (smallest ΔE transition).', '• Number of spectral lines when electron falls from nth level to ground state: L = n(n-1)/2', '• Number of spectral lines when electron falls from n₂ to n₁ (n₂ > n₁): L = (n₂−n₁)(n₂−n₁+1)/2', '• At room temperature, H atoms are in ground state → only LYMAN series visible in ABSORPTION.', '• EMISSION spectrum shows all series (atoms excited to multiple levels).', ]: story.append(p(line)) story.append(sp(2)) for line in [ '[ TRAP ] Lyman is ULTRAVIOLET — NOT visible. Balmer is partially visible (400-700 nm range only).', '[ TRAP ] H-alpha (656.3 nm, RED): n=3→2. H-beta (486.1 nm, BLUE-GREEN): n=4→2.', '[ TRAP ] PE = 2 × TE. KE = -TE. Therefore PE = -2 × KE. These relations are CRITICAL.', '[ TRAP ] Bohr model is valid ONLY for H-like species (one electron): H, He⁺, Li²⁺, Be³⁺…', '[ TRAP ] For He⁺ (Z=2): Energy = 4 × H energy; Radius = H radius / 2.', '[ TRAP ] Increasing n → less negative energy → higher total energy → less stable (weakly bound).', '[ TRAP ] The most negative energy = GROUND STATE = MOST STABLE state.', '[ TRAP ] Time period Tₙ ∝ n³/Z². Frequency νₙ ∝ Z²/n³. These are often asked in MCQs.', '[ TRAP ] Energy is NEGATIVE (bound state). If E = 0, electron is free (ionised).', '[ TRAP ] Series limit has MAXIMUM FREQUENCY and MINIMUM WAVELENGTH in that series.', '[ TRAP ] Rydberg equation: 1/λ NOT ν. n₁ < n₂ always (electron drops from n₂ to n₁).', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 4 # ============================================================ story.append(sec('4. ELECTROMAGNETIC RADIATION &amp; PLANCK\'S QUANTUM THEORY')) story.append(sp(1)) story.append(sub('4A. Wave Properties of EM Radiation')) em_formulas = [ ('Speed of light (c)', 'c = ν × λ = 3 × 10⁸ m/s (in vacuum)'), ('Wave number (ν̃)', 'ν̃ = 1/λ unit: m⁻¹ or cm⁻¹'), ('Frequency from wavelength', 'ν = c/λ (inversely proportional)'), ('Relation: ν, λ, ν̃', 'ν = c × ν̃ so ν̃ = ν/c'), ('Time period (T)', 'T = 1/ν unit: seconds'), ('Amplitude (A)', 'Height of wave crest — determines INTENSITY (brightness) of radiation'), ] story.append(formula_table(em_formulas)) story.append(sp(2)) story.append(sub('4B. EM Spectrum (Increasing Frequency / Decreasing Wavelength)')) em_spectrum = [ ['Radiation', 'Wavelength Range', 'Frequency Range (Hz)', 'Source / Use'], ['Radio waves', '> 0.1 m', '< 3 × 10⁹', 'Radio, TV broadcasting'], ['Microwaves', '0.1 m – 1 mm', '3×10⁹ – 3×10¹¹', 'Radar, microwave oven'], ['Infrared (IR)', '1 mm – 700 nm', '3×10¹¹ – 4.3×10¹⁴', 'Heat, night vision'], ['Visible light', '700 – 400 nm', '4.3×10¹⁴ – 7.5×10¹⁴', 'VIBGYOR: V=400nm, R=700nm'], ['Ultraviolet (UV)', '400 – 10 nm', '7.5×10¹⁴ – 3×10¹⁷', 'Sun lamps, sterilisation'], ['X-rays', '10 nm – 0.01 nm', '3×10¹⁷ – 3×10¹⁹', 'Medical imaging'], ['Gamma rays (γ)', '< 0.01 nm', '> 3×10¹⁹', 'Nuclear reactions, cancer therapy'], ] story.append(make_table(em_spectrum, col_widths=[28*mm,32*mm,40*mm,60*mm])) story.append(sp(2)) story.append(sub('4C. Planck\'s Quantum Theory')) for line in [ '• Energy is NOT emitted or absorbed continuously but in DISCRETE packets called QUANTA (singular: quantum). For light, a quantum is called a PHOTON.', '• Energy of one photon: E = hν = hc/λ = hcν̃', '• Energy of n photons: E = nhν', '• Energy is directly proportional to frequency: E ∝ ν', '• Energy is inversely proportional to wavelength: E ∝ 1/λ', '• Planck\'s constant h = 6.626 × 10⁻³⁴ J·s = 6.626 × 10⁻³⁴ kg·m²·s⁻¹', '• 1 eV = 1.602 × 10⁻¹⁹ J. So E(eV) = hν / (1.602 × 10⁻¹⁹)', ]: story.append(p(line)) story.append(sp(2)) planck_formulas = [ ('Energy of one photon', 'E = hν = hc/λ = hcν̃'), ('Energy in electron volts', 'E(eV) = 1240 / λ(nm) [useful shortcut]'), ('n photons of frequency ν', 'E_total = nhν'), ('Planck\'s constant h', '6.626 × 10⁻³⁴ J·s'), ('Momentum of photon', 'p = hν/c = h/λ = E/c'), ('Mass equivalent of photon', 'm_eff = E/c² = hν/c² = h/λc (photon has NO rest mass)'), ] story.append(formula_table(planck_formulas)) story.append(sp(2)) for line in [ '[ TRAP ] ν and λ are INVERSELY proportional. Higher frequency → shorter wavelength → higher energy.', '[ TRAP ] E ∝ ν (NOT λ). So infrared photons have LESS energy than UV photons.', '[ TRAP ] Wave number ν̃ = 1/λ. It is NOT ν/c. Units: cm⁻¹ (in spectroscopy) or m⁻¹ (SI).', '[ TRAP ] Visible light: VIBGYOR. Violet ≈ 400 nm (highest frequency, most energy in visible). Red ≈ 700 nm.', '[ TRAP ] Shortcut: E(eV) = 1240/λ(nm). For λ=400 nm: E = 3.1 eV. For λ=700 nm: E = 1.77 eV.', '[ TRAP ] Photon has ZERO rest mass but HAS momentum (p = h/λ) and energy (E = hν).', '[ TRAP ] Gamma rays have HIGHEST frequency/energy. Radio waves have LOWEST.', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 5 # ============================================================ story.append(sec('5. PHOTOELECTRIC EFFECT (Einstein, 1905)')) story.append(sp(1)) for line in [ '• When light of sufficiently high frequency falls on a metal surface, electrons are EJECTED from the surface. These are called photoelectrons.', '• THRESHOLD FREQUENCY (ν₀): The minimum frequency of light needed to eject electrons. Below ν₀, no electrons are ejected regardless of intensity.', '• WORK FUNCTION (φ or W): Minimum energy needed to remove an electron from the metal surface. φ = hν₀.', '• OBSERVATIONS:', ' - Photoelectric effect is INSTANTANEOUS (no time lag).', ' - Number of electrons emitted ∝ INTENSITY of light.', ' - Kinetic energy of electrons depends ONLY on FREQUENCY, NOT intensity.', ' - Below threshold frequency, no electrons emitted even with very high intensity.', '• Einstein\'s explanation: Light consists of photons. One photon ejects one electron.', '• Energy of photon = Work function + Kinetic energy of ejected electron.', '• This proved the PARTICLE NATURE of light.', ]: story.append(p(line)) story.append(sp(2)) photo_formulas = [ ('Einstein\'s photoelectric equation', 'hν = φ + ½mₑv² = φ + KE_max'), ('Work function', 'φ = hν₀ (ν₀ = threshold frequency)'), ('Kinetic energy of photoelectron', 'KE = hν − φ = h(ν − ν₀) = ½mₑv²'), ('Maximum velocity of electron', 'v_max = √[2h(ν − ν₀) / mₑ]'), ('Stopping potential (V₀)', 'eV₀ = KE_max = hν − φ'), ('Stopping potential (alternate)', 'V₀ = (h/e)(ν − ν₀) [slope = h/e]'), ('Threshold wavelength (λ₀)', 'λ₀ = hc / φ = c / ν₀'), ('Number of photons (intensity I)', 'n_photons = I / hν = I·λ / hc'), ('Photoelectric current', 'I_photo ∝ Intensity ∝ n_photons'), ('Saturation current', 'Max photocurrent when all ejected electrons are collected'), ] story.append(formula_table(photo_formulas)) story.append(sp(2)) for line in [ '[ TRAP ] Intensity of light = number of photons per unit area per second. More photons = more electrons, NOT more KE.', '[ TRAP ] KE of photoelectrons depends ONLY on frequency (ν), NOT on intensity.', '[ TRAP ] If ν < ν₀: NO photoelectric effect, no matter how intense the light.', '[ TRAP ] Stopping potential V₀ depends on ν only: V₀ = (h/e)ν − φ/e. Slope of V₀ vs ν graph = h/e.', '[ TRAP ] Photoelectric effect proves PARTICLE nature of light. Diffraction/interference proves WAVE nature.', '[ TRAP ] The effect is INSTANTANEOUS (no time delay, even at low intensity).', '[ TRAP ] Compton effect (X-ray scattering by electron) also proves particle nature of light.', '[ TRAP ] Different metals have different work functions (φ): Na = 2.3 eV, Al = 4.3 eV, Pt = 5.6 eV.', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 6 # ============================================================ story.append(sec('6. DUAL NATURE OF MATTER — de BROGLIE &amp; HEISENBERG')) story.append(sp(1)) story.append(sub('6A. de Broglie Hypothesis (1924)')) for line in [ '• de Broglie proposed that just as radiation has dual nature (wave + particle), MATTER also has dual nature.', '• Every moving particle with mass m and velocity v is associated with a wave (matter wave / de Broglie wave) of wavelength λ.', '• This wave nature is significant only for microscopic particles (electrons, protons). For macroscopic objects, λ is negligibly small and undetectable.', '• Davisson-Germer experiment (1927): electron diffraction through nickel crystal confirmed de Broglie hypothesis. Electrons showed wave-like DIFFRACTION — proof of wave nature of matter.', '• G.P. Thomson experiment: electron diffraction through thin gold films — independent confirmation.', ]: story.append(p(line)) story.append(sp(2)) broglie_formulas = [ ('de Broglie wavelength', 'λ = h / mv = h / p [p = momentum]'), ('In terms of kinetic energy', 'λ = h / √(2m·KE)'), ('For particle accelerated through V', 'λ = h / √(2mqV) = h / √(2meV) [for electron]'), ('For electron (λ in Å, V in volts)', 'λ = 12.27 / √V Å'), ('For proton (λ in Å, V in volts)', 'λ = 0.286 / √V Å'), ('For neutron at temp T', 'λ = h / √(3mkT) [k = 1.38×10⁻²³ J/K]'), ('Relation: λ and KE', 'λ = h / √(2m·KE) → λ ∝ 1/√KE'), ('Relation: λ and momentum', 'λ = h/p → λ ∝ 1/p → λ ∝ 1/v (for same m)'), ('Photon\'s de Broglie λ', 'λ = h/p = hc/E = c/ν (same as wave λ — consistent)'), ] story.append(formula_table(broglie_formulas)) story.append(sp(2)) story.append(sub('6B. Heisenberg\'s Uncertainty Principle (1927)')) for line in [ '• It is FUNDAMENTALLY IMPOSSIBLE to determine simultaneously the EXACT position (x) and EXACT momentum (p) of a microscopic particle.', '• The more precisely we know the position, the less precisely we know the momentum, and vice versa.', '• This is NOT about instrument error or experimental limitation — it is a fundamental property of matter arising from wave-particle duality.', '• Consequence: The concept of a DEFINITE ORBIT for an electron is invalid. We can only speak of PROBABILITY of finding an electron at a given location.', '• This led to the concept of ORBITALS (regions of space where probability of finding an electron is high) replacing Bohr\'s definite orbits.', ]: story.append(p(line)) story.append(sp(2)) heisenberg_formulas = [ ('Position-momentum uncertainty', 'Δx · Δp ≥ h/4π'), ('In terms of velocity', 'Δx · mΔv ≥ h/4π → Δx · Δv ≥ h/(4πm)'), ('Minimum uncertainty product', 'Δx · Δp = h/4π (minimum value, often written as ℏ/2)'), ('Energy-time uncertainty', 'ΔE · Δt ≥ h/4π'), ('Uncertainty using ℏ = h/2π', 'Δx · Δp ≥ ℏ/2'), ('If Δx → 0 (exact position)', 'Δp → ∞ (completely unknown momentum)'), ('If Δp → 0 (exact momentum)', 'Δx → ∞ (completely unknown position)'), ] story.append(formula_table(heisenberg_formulas)) story.append(sp(2)) for line in [ '[ TRAP ] ℏ = h/2π = 1.055 × 10⁻³⁴ J·s. The uncertainty is ≥ ℏ/2 (same as h/4π).', '[ TRAP ] This principle makes Bohr\'s model fundamentally incorrect for multi-electron atoms.', '[ TRAP ] Heisenberg\'s principle does NOT say we cannot measure precisely — it says nature itself doesn\'t allow simultaneous precision.', '[ TRAP ] For macroscopic objects (e.g. cricket ball, mass 0.1 kg), the uncertainty is negligible (~10⁻³³ m) — irrelevant practically.', '[ TRAP ] de Broglie λ ∝ 1/√V (for accelerated electrons). Higher voltage → smaller wavelength.', '[ TRAP ] de Broglie λ is larger for lighter particles (smaller mass) at same velocity.', '[ TRAP ] Davisson-Germer proved wave nature of ELECTRONS using diffraction — Nobel Prize 1937.', '[ TRAP ] Minimum Δx·Δp = h/4π (NOT h/2π, NOT h, NOT ℏ alone).', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 7 # ============================================================ story.append(sec('7. QUANTUM MECHANICAL MODEL OF ATOM')) story.append(sp(1)) for line in [ '• Quantum mechanics (Schrodinger, 1926) treats electron as a 3D WAVE (combining de Broglie + Heisenberg).', '• Schrodinger wave equation: Ĥψ = Eψ (operator form). Solutions are wave functions ψ.', '• ψ (psi) = wave function. ψ² = probability density of finding the electron at a given point.', '• An ORBITAL is a three-dimensional region in space around the nucleus where the probability of finding an electron is maximum (usually defined as 90% or 95% probability region).', '• Orbitals are characterised by THREE quantum numbers: n, l, mₗ. The spin quantum number mₛ describes the electron.', '• A node is a surface where ψ = 0 (probability of finding electron = 0).', ]: story.append(p(line)) story.append(sp(3)) # ============================================================ # SECTION 8 # ============================================================ story.append(sec('8. QUANTUM NUMBERS — COMPLETE DETAIL')) story.append(sp(1)) story.append(sub('8A. Principal Quantum Number (n)')) for line in [ '• n = 1, 2, 3, 4, 5, 6, 7 … (positive integers only).', '• Determines the ENERGY and SIZE of the orbital (distance from nucleus).', '• Higher n → higher energy → larger orbital → electron is farther from nucleus.', '• Number of orbitals in nth shell = n².', '• Maximum electrons in nth shell = 2n².', '• n = 1: K shell; n = 2: L shell; n = 3: M shell; n = 4: N shell.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('8B. Azimuthal Quantum Number / Angular Momentum Quantum Number (l)')) for line in [ '• l = 0, 1, 2, 3, … (n−1). l can take n different values for a given n.', '• Determines the SHAPE of the orbital and the subshell.', '• l = 0 → s subshell (sphere).', '• l = 1 → p subshell (dumbbell / figure-eight).', '• l = 2 → d subshell (double dumbbell / cloverleaf).', '• l = 3 → f subshell (complex multi-lobed shapes).', '• Angular momentum of electron: L = √[l(l+1)] × h/2π = √[l(l+1)] × ℏ', '• For s: L = 0. For p: L = √2 × ℏ. For d: L = √6 × ℏ.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('8C. Magnetic Quantum Number (mₗ)')) for line in [ '• mₗ = −l, −(l−1), …, 0, …, (l−1), +l. Total values = (2l + 1).', '• Determines the ORIENTATION of the orbital in space.', '• For s (l=0): mₗ = 0 → 1 orbital.', '• For p (l=1): mₗ = −1, 0, +1 → 3 orbitals (pₓ, p_y, p_z).', '• For d (l=2): mₗ = −2, −1, 0, +1, +2 → 5 orbitals.', '• For f (l=3): mₗ = −3, −2, −1, 0, +1, +2, +3 → 7 orbitals.', '• z-component of angular momentum: L_z = mₗ × ℏ.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('8D. Spin Quantum Number (mₛ)')) for line in [ '• mₛ = +½ (spin up, ↑) or −½ (spin down, ↓). Only these TWO values.', '• Represents the intrinsic spin angular momentum of the electron.', '• Spin angular momentum: S = √[s(s+1)] × ℏ = (√3/2) × ℏ.', '• Two electrons in the same orbital MUST have opposite spins (one +½, one −½).', '• This follows from Pauli\'s exclusion principle.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('8E. Quantum Number Summary Table')) qn_table = [ ['n', 'l (values)', 'Subshells', 'mₗ values', 'Orbitals/subshell', 'Max e⁻/subshell', 'Total orbitals', 'Max e⁻'], ['1', '0', '1s', '0', '1', '2', '1', '2'], ['2', '0,1', '2s, 2p', '0; −1,0,+1', '1,3', '2,6', '4', '8'], ['3', '0,1,2', '3s,3p,3d', '0;−1,0,+1;−2,−1,0,+1,+2', '1,3,5', '2,6,10', '9', '18'], ['4', '0,1,2,3', '4s,4p,4d,4f', '0;…;…;−3to+3', '1,3,5,7', '2,6,10,14', '16', '32'], ] story.append(make_table(qn_table, col_widths=[10*mm,18*mm,22*mm,36*mm,22*mm,22*mm,20*mm,16*mm])) story.append(sp(2)) qn_formulas = [ ('Number of orbitals in nth shell', 'n²'), ('Max electrons in nth shell', '2n²'), ('Number of subshells in nth shell', 'n (l = 0, 1, 2, …, n−1)'), ('Number of orbitals in subshell l', '2l + 1'), ('Max electrons in subshell l', '2(2l + 1)'), ('Angular momentum', 'L = √[l(l+1)] × ℏ'), ('Spin angular momentum', 'S = √[s(s+1)] × ℏ = (√3/2) × ℏ [s = 1/2]'), ('z-component of L', 'L_z = mₗ × ℏ'), ] story.append(formula_table(qn_formulas)) story.append(sp(2)) for line in [ '[ TRAP ] l goes from 0 to (n−1) ONLY. For n=2: l = 0, 1 only. For n=3: l = 0, 1, 2 only.', '[ TRAP ] mₗ has (2l+1) values. For l=3: 2(3)+1 = 7 values (−3 to +3).', '[ TRAP ] mₛ = +½ or −½ ONLY. No other values exist.', '[ TRAP ] Each orbital holds MAXIMUM 2 electrons (opposite spins — Pauli exclusion principle).', '[ TRAP ] 4s orbital: n=4, l=0. 3d orbital: n=3, l=2. 2p orbital: n=2, l=1.', '[ TRAP ] Angular momentum of s orbital = 0 (NOT ℏ, NOT h/2π — it is ZERO for s orbital).', '[ TRAP ] 4th shell: 16 orbitals, max 32 electrons. Subshells: 4s, 4p, 4d, 4f.', '[ TRAP ] For n=3: total orbitals = 9 (1s + 3p + 5d = 9). Max electrons = 18.', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 9 # ============================================================ story.append(sec('9. SHAPES OF ORBITALS &amp; NODES')) story.append(sp(1)) story.append(sub('9A. Node Formulas')) node_formulas = [ ('Radial (spherical) nodes', 'n − l − 1'), ('Angular (planar/conical) nodes', 'l'), ('Total nodes', 'n − 1'), ('Example: 1s', 'n=1, l=0: Radial=0, Angular=0, Total=0'), ('Example: 2s', 'n=2, l=0: Radial=1, Angular=0, Total=1'), ('Example: 2p', 'n=2, l=1: Radial=0, Angular=1, Total=1'), ('Example: 3s', 'n=3, l=0: Radial=2, Angular=0, Total=2'), ('Example: 3p', 'n=3, l=1: Radial=1, Angular=1, Total=2'), ('Example: 3d', 'n=3, l=2: Radial=0, Angular=2, Total=2'), ('Example: 4s', 'n=4, l=0: Radial=3, Angular=0, Total=3'), ('Example: 4p', 'n=4, l=1: Radial=2, Angular=1, Total=3'), ('Example: 4d', 'n=4, l=2: Radial=1, Angular=2, Total=3'), ('Example: 4f', 'n=4, l=3: Radial=0, Angular=3, Total=3'), ] story.append(formula_table(node_formulas)) story.append(sp(2)) story.append(sub('9B. Orbital Shapes — Detailed Notes')) for line in [ '• s ORBITAL (l=0):', ' - Spherically symmetrical — same probability in all directions from nucleus.', ' - 1s: single sphere centred at nucleus. 2s: two concentric spheres (1 radial node between them — a spherical shell where ψ = 0). 3s: three regions separated by 2 radial nodes.', ' - All s orbitals have NON-ZERO electron density at nucleus (ψ ≠ 0 at r = 0).', ' - Only ONE orientation (mₗ = 0 only).', '', '• p ORBITALS (l=1):', ' - Dumbbell (figure-of-eight / double-lobed) shape along an axis.', ' - THREE p orbitals: pₓ (along x-axis), p_y (along y-axis), p_z (along z-axis).', ' - All three are degenerate (same energy) in absence of external field.', ' - Each p orbital has ONE angular node: a plane through the nucleus perpendicular to the orbital axis. (pₓ: xy-plane is node; p_z: yz-plane; p_y: xz-plane).', ' - p orbitals have ZERO electron density at the nucleus.', ' - 2p: 0 radial nodes. 3p: 1 radial node. 4p: 2 radial nodes.', '', '• d ORBITALS (l=2):', ' - FIVE d orbitals: d_xy, d_yz, d_xz, d_x²-y², dz².', ' - d_xy, d_yz, d_xz: four-leaf clover/double dumbbell shape between axes.', ' - d_x²-y²: four-leaf clover along x and y axes.', ' - dz²: UNIQUE — dumbbell along z-axis WITH a doughnut (torus) ring in xy-plane.', ' - All five d orbitals are degenerate (same energy in free atom) — 2 angular nodes each.', ' - 3d: 0 radial nodes. 4d: 1 radial node. 5d: 2 radial nodes.', '', '• f ORBITALS (l=3):', ' - SEVEN f orbitals — complex, multi-lobed shapes. 3 angular nodes each.', ' - 4f: 0 radial nodes. 5f: 1 radial node.', ' - f orbitals involved in lanthanides (4f) and actinides (5f) filling.', ]: story.append(p(line)) story.append(sp(2)) for line in [ '[ TRAP ] Radial nodes = n−l−1. For 3d (n=3, l=2): 3−2−1 = 0 radial nodes. ZERO, not 1.', '[ TRAP ] Angular nodes = l. For p (l=1): 1 angular node. For d (l=2): 2 angular nodes.', '[ TRAP ] Total nodes = n−1 ALWAYS. Verify: 3p has 1 radial + 1 angular = 2 total = 3−1 = 2. Correct.', '[ TRAP ] 2s and 2p have the SAME total nodes (1 each), but different types (radial vs angular).', '[ TRAP ] dz² is unique in shape but HAS SAME ENERGY as other 4 d orbitals (degenerate).', '[ TRAP ] s orbital has NON-ZERO density at nucleus. p, d, f orbitals have ZERO density at nucleus.', '[ TRAP ] 3d orbital: n=3, l=2 → radial nodes = 3−2−1 = 0. ZERO radial nodes. Angular nodes = 2.', '[ TRAP ] 2s and 2p both have 1 total node. But 2s has 1 RADIAL node, 2p has 1 ANGULAR node.', '[ TRAP ] s orbital (l=0): angular momentum L = 0 (ZERO, not ℏ). Only p,d,f have nonzero L.', '[ TRAP ] dz² shape is unique (dumbbell + torus ring) but has SAME ENERGY as dxy, dxz, dyz, dx²-y².', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 10 # ============================================================ story.append(sec('10. ELECTRONIC CONFIGURATION — RULES &amp; PRINCIPLES')) story.append(sp(1)) story.append(sub('10A. Aufbau Principle — Filling Order')) for line in [ '• Orbitals are filled in order of INCREASING ENERGY (increasing n+l value).', '• If two orbitals have the SAME (n+l) value, fill the one with LOWER n first.', '• This determines the order: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p', ]: story.append(p(line)) story.append(sp(2)) aufbau_data = [ ['Orbital', 'n', 'l', 'n+l', 'Filling Order'], ['1s', '1', '0', '1', '1st'], ['2s', '2', '0', '2', '2nd'], ['2p', '2', '1', '3', '3rd (same n+l as 3s, but n=2 < 3)'], ['3s', '3', '0', '3', '4th'], ['3p', '3', '1', '4', '5th (same n+l as 4s, n=3 < 4)'], ['4s', '4', '0', '4', '6th'], ['3d', '3', '2', '5', '7th (same n+l as 4p, n=3 < 4)'], ['4p', '4', '1', '5', '8th'], ['5s', '5', '0', '5', '9th'], ['4d', '4', '2', '6', '10th (same n+l as 5p, n=4 < 5)'], ['5p', '5', '1', '6', '11th'], ['6s', '6', '0', '6', '12th'], ['4f', '4', '3', '7', '13th (same n+l as 5d, n=4 < 5)'], ['5d', '5', '2', '7', '14th'], ['6p', '6', '1', '7', '15th'], ['7s', '7', '0', '7', '16th'], ] story.append(make_table(aufbau_data, col_widths=[20*mm,15*mm,12*mm,15*mm,105*mm])) story.append(sp(2)) story.append(sub('10B. Pauli\'s Exclusion Principle')) for line in [ '• No two electrons in an atom can have all FOUR quantum numbers (n, l, mₗ, mₛ) identical.', '• Each orbital is characterised by a UNIQUE set of (n, l, mₗ). Two electrons can share the same orbital only if their SPIN is opposite (+½ and −½).', '• Maximum 2 electrons per orbital.', '• Maximum electrons in a subshell: 2(2l+1). s: 2, p: 6, d: 10, f: 14.', '• Maximum electrons in nth shell: 2n². K: 2, L: 8, M: 18, N: 32.', '• Example: In 2p, all 6 electrons have n=2, l=1, mₗ = −1/0/+1 (2 each), mₛ = ±½.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('10C. Hund\'s Rule of Maximum Multiplicity')) for line in [ '• When filling DEGENERATE orbitals (same energy, e.g. three 2p or five 3d), electrons occupy each orbital SINGLY with PARALLEL SPINS (same mₛ) before pairing begins.', '• The state with maximum unpaired electrons has MAXIMUM SPIN MULTIPLICITY and is the ground state.', '• Spin multiplicity = 2S + 1 where S = total spin = (no. of unpaired electrons) × ½.', '• Half-filled (p³, d⁵, f⁷) and fully-filled (p⁶, d¹⁰, f¹⁴) subshells are EXTRA STABLE due to:', ' - (a) Symmetrical distribution of electron density.', ' - (b) Maximum exchange energy (more electrons with parallel spins = more stability).', '• Examples: N: 2p³ (all 3 p orbitals singly filled, ↑ ↑ ↑). O: 2p⁴ (↑↓ ↑ ↑). Cr: 3d⁵4s¹. Cu: 3d¹⁰4s¹.', ]: story.append(p(line)) story.append(sp(2)) for line in [ '[ TRAP ] 4s fills BEFORE 3d (Aufbau) but 4s is IONISED (removed) BEFORE 3d when forming cations.', '[ TRAP ] This is because in cations, 3d is lower in energy than 4s.', '[ TRAP ] Fe: [Ar]3d⁶4s². Fe²⁺: [Ar]3d⁶ (removed both 4s). Fe³⁺: [Ar]3d⁵ (removed 2 from 4s, 1 from 3d).', '[ TRAP ] Cr (Z=24): [Ar]3d⁵4s¹ — NOT [Ar]3d⁴4s². Half-filled 3d⁵ is extra stable.', '[ TRAP ] Cu (Z=29): [Ar]3d¹⁰4s¹ — NOT [Ar]3d⁹4s². Fully-filled 3d¹⁰ is extra stable.', '[ TRAP ] Hund\'s rule: electrons in p subshell fill as ↑_ ↑_ ↑_ then pair: ↑↓ ↑_ ↑_.', '[ TRAP ] Spin multiplicity formula: 2S+1. For N (3 unpaired e⁻): S=3/2, multiplicity=4.', '[ TRAP ] Exchange energy: more parallel-spin pairs = more exchange energy = more stability.', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 11 # ============================================================ story.append(sec('11. ELECTRONIC CONFIGURATIONS — ALL NEET-IMPORTANT ELEMENTS')) story.append(sp(1)) story.append(sub('11A. Elements Z = 1 to 30')) z1_30 = [ ['Z', 'Element', 'Configuration', 'Unpaired e⁻'], ['1', 'H (Hydrogen)', '1s¹', '1'], ['2', 'He (Helium)', '1s²', '0 (noble gas)'], ['3', 'Li (Lithium)', '[He] 2s¹', '1'], ['4', 'Be (Beryllium)', '[He] 2s²', '0'], ['5', 'B (Boron)', '[He] 2s² 2p¹', '1'], ['6', 'C (Carbon)', '[He] 2s² 2p²', '2'], ['7', 'N (Nitrogen)', '[He] 2s² 2p³', '3 (half-filled 2p)'], ['8', 'O (Oxygen)', '[He] 2s² 2p⁴', '2'], ['9', 'F (Fluorine)', '[He] 2s² 2p⁵', '1'], ['10', 'Ne (Neon)', '[He] 2s² 2p⁶', '0 (noble gas)'], ['11', 'Na (Sodium)', '[Ne] 3s¹', '1'], ['12', 'Mg (Magnesium)', '[Ne] 3s²', '0'], ['13', 'Al (Aluminium)', '[Ne] 3s² 3p¹', '1'], ['14', 'Si (Silicon)', '[Ne] 3s² 3p²', '2'], ['15', 'P (Phosphorus)', '[Ne] 3s² 3p³', '3 (half-filled 3p)'], ['16', 'S (Sulphur)', '[Ne] 3s² 3p⁴', '2'], ['17', 'Cl (Chlorine)', '[Ne] 3s² 3p⁵', '1'], ['18', 'Ar (Argon)', '[Ne] 3s² 3p⁶', '0 (noble gas)'], ['19', 'K (Potassium)', '[Ar] 4s¹', '1'], ['20', 'Ca (Calcium)', '[Ar] 4s²', '0'], ['21', 'Sc (Scandium)', '[Ar] 3d¹ 4s²', '1'], ['22', 'Ti (Titanium)', '[Ar] 3d² 4s²', '2'], ['23', 'V (Vanadium)', '[Ar] 3d³ 4s²', '3'], ['24', 'Cr (Chromium)', '[Ar] 3d⁵ 4s¹ (EXCEPTION)', '6 (all unpaired)'], ['25', 'Mn (Manganese)', '[Ar] 3d⁵ 4s²', '5'], ['26', 'Fe (Iron)', '[Ar] 3d⁶ 4s²', '4'], ['27', 'Co (Cobalt)', '[Ar] 3d⁷ 4s²', '3'], ['28', 'Ni (Nickel)', '[Ar] 3d⁸ 4s²', '2'], ['29', 'Cu (Copper)', '[Ar] 3d¹⁰ 4s¹ (EXCEPTION)', '1'], ['30', 'Zn (Zinc)', '[Ar] 3d¹⁰ 4s²', '0'], ] story.append(make_table(z1_30, col_widths=[12*mm,36*mm,62*mm,56*mm])) story.append(sp(2)) story.append(sub('11B. Important Ions &amp; More Elements')) ions_data = [ ['Species', 'Configuration', 'Notes'], ['Fe²⁺ (Z=26)', '[Ar] 3d⁶', 'Remove 4s² first, then nothing from 3d'], ['Fe³⁺ (Z=26)', '[Ar] 3d⁵', 'Remove 4s² + 1 from 3d; half-filled 3d⁵ is stable'], ['Cu⁺ (Z=29)', '[Ar] 3d¹⁰', 'Remove 4s¹; get fully-filled 3d¹⁰ — stable'], ['Cu²⁺ (Z=29)', '[Ar] 3d⁹', 'Remove 4s¹ + 1 from 3d'], ['Zn²⁺ (Z=30)', '[Ar] 3d¹⁰', 'Remove 4s², keep 3d¹⁰'], ['Cr³⁺ (Z=24)', '[Ar] 3d³', 'Remove 4s¹ + 2 from 3d'], ['Mn²⁺ (Z=25)', '[Ar] 3d⁵', 'Remove 4s²; half-filled 3d — extra stable'], ['Pd (Z=46)', '[Kr] 4d¹⁰', 'EXCEPTION: no 5s electrons at all'], ['Ag (Z=47)', '[Kr] 4d¹⁰ 5s¹', 'EXCEPTION: fully-filled 4d¹⁰'], ['Mo (Z=42)', '[Kr] 4d⁵ 5s¹', 'EXCEPTION: half-filled 4d⁵'], ['Gd (Z=64)', '[Xe] 4f⁷ 5d¹ 6s²', 'Half-filled 4f⁷ promotes one e⁻ to 5d'], ['Au (Z=79)', '[Xe] 4f¹⁴ 5d¹⁰ 6s¹', 'EXCEPTION: fully-filled 5d¹⁰'], ['Pt (Z=78)', '[Xe] 4f¹⁴ 5d⁹ 6s¹', 'EXCEPTION'], ] story.append(make_table(ions_data, col_widths=[30*mm,50*mm,86*mm])) story.append(sp(2)) for line in [ '[ TRAP ] 4s is always EMPTIED before 3d when forming transition metal cations.', '[ TRAP ] Cr: [Ar]3d⁵4s¹ has 6 unpaired electrons — maximum paramagnetism for Period 4 TMs.', '[ TRAP ] Mn²⁺ = [Ar]3d⁵: half-filled 3d is VERY stable (also highest paramagnetism among 2+ ions of Period 4).', '[ TRAP ] Pd (Z=46) has NO s electrons at all in valence shell: [Kr]4d¹⁰. A common trick question.', '[ TRAP ] Cu⁺ has [Ar]3d¹⁰ — fully filled — DIAMAGNETIC. Cu²⁺ has [Ar]3d⁹ — PARAMAGNETIC.', '[ TRAP ] Zn, Cd, Hg: always have 3d¹⁰ (or 4d¹⁰, 5d¹⁰) and are DIAMAGNETIC (no unpaired e⁻).', '[ TRAP ] Species with all electrons paired = DIAMAGNETIC. With unpaired = PARAMAGNETIC.', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 12 # ============================================================ story.append(sec('12. ISOTOPES, ISOBARS, ISOTONES &amp; ISOELECTRONIC SPECIES')) story.append(sp(1)) iso_data = [ ['Term', 'Definition', 'Examples'], ['Atomic Number (Z)', 'Z = Number of protons = Number of electrons (neutral atom)', ''], ['Mass Number (A)', 'A = Z + N where N = number of neutrons', ''], ['Number of neutrons', 'N = A − Z', ''], ['Isotopes', 'Same Z, different A (same element, different mass)', '¹H, ²H(D), ³H(T); ¹²C, ¹³C, ¹⁴C; ³⁵Cl, ³⁷Cl'], ['Isobars', 'Same A, different Z (different elements)', '⁴⁰₁₈Ar and ⁴⁰₂₀Ca; ³¹₁₅P and ³¹₁₆S'], ['Isotones', 'Same N, different Z', '¹⁴C and ¹⁴N (both N=8); ³¹P and ³²S (both N=16)'], ['Isoelectronic species', 'Same number of electrons', 'N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺, Al³⁺ (all 10 e⁻)'], ['More isoelectronic', 'CO and N₂ (14 e⁻ each); NO⁺ and N₂ and CO (10 valence e⁻); CN⁻, N₂, CO (10 e⁻)', ''], ['Isostructural', 'Same structure/shape', 'SO₄²⁻ and PO₄³⁻ (both tetrahedral)'], ] story.append(make_table(iso_data, col_widths=[35*mm,82*mm,49*mm])) story.append(sp(2)) for line in [ '[ TRAP ] Isotopes: SAME chemical properties (same Z = same electrons = same chemistry), DIFFERENT physical properties.', '[ TRAP ] Isobars: DIFFERENT elements → different chemical properties entirely.', '[ TRAP ] Isotones are often confused with isotopes — remember: isotones = same NEUTRON count.', '[ TRAP ] N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺, Al³⁺ are all isoelectronic (10 electrons each) — VERY common NEET question.', '[ TRAP ] CO and N₂ are isoelectronic AND isostructural (both have triple bond, same bond order 3).', '[ TRAP ] For ¹H: A=1, Z=1, N=0 (no neutrons). Protium has ZERO neutrons.', '[ TRAP ] Deuterium (²H = D): 1 proton + 1 neutron. Tritium (³H = T): 1 proton + 2 neutrons.', ]: story.append(trap(line)) story.append(sp(3)) # ============================================================ # SECTION 13 # ============================================================ story.append(sec('13. FAILURES OF BOHR\'S MODEL')) story.append(sp(1)) for line in [ '• ZEEMAN EFFECT: Could not explain splitting of spectral lines in a magnetic field.', '• STARK EFFECT: Could not explain splitting of spectral lines in an electric field.', '• FINE STRUCTURE: Could not explain the fine structure of spectral lines (closely spaced doublets/triplets).', '• MULTI-ELECTRON ATOMS: Completely failed for atoms with more than one electron (He, Li, etc.).', '• DE BROGLIE WAVE NATURE: Did not account for the wave nature of the electron.', '• HEISENBERG UNCERTAINTY: Violated the uncertainty principle by assigning definite paths (orbits) to electrons.', '• 3D STRUCTURE OF MOLECULES: Could not explain why atoms form molecules with specific 3D shapes.', '• INTENSITY OF SPECTRAL LINES: Could not predict relative intensities of spectral lines.', ]: story.append(p(line)) story.append(sp(3)) # ============================================================ # SECTION 14 # ============================================================ story.append(sec('14. IMPORTANT CONSTANTS &amp; VALUES (Memorise All)')) story.append(sp(1)) constants_data = [ ['Constant / Quantity', 'Value'], ['Planck\'s constant h', '6.626 × 10⁻³⁴ J·s = 6.626 × 10⁻³⁴ kg·m²·s⁻¹'], ['ℏ = h/2π', '1.055 × 10⁻³⁴ J·s'], ['Speed of light c', '2.998 × 10⁸ m/s ≈ 3 × 10⁸ m/s'], ['Mass of electron mₑ', '9.109 × 10⁻³¹ kg = 0.000549 amu'], ['Mass of proton mₚ', '1.673 × 10⁻²⁷ kg = 1.007276 amu'], ['Mass of neutron mₙ', '1.675 × 10⁻²⁷ kg = 1.008665 amu'], ['Charge of electron e', '1.602 × 10⁻¹⁹ C'], ['e/m ratio of electron', '1.758 × 10¹¹ C/kg'], ['Rydberg constant R_H', '1.097 × 10⁷ m⁻¹ = 109677 cm⁻¹'], ['Bohr radius a₀', '0.529 Å = 52.9 pm = 5.29 × 10⁻¹¹ m'], ['1 electron volt (1 eV)', '1.602 × 10⁻¹⁹ J'], ['1 atomic mass unit (1 amu)', '1.660 × 10⁻²⁷ kg = 931.5 MeV/c²'], ['Avogadro constant Nₐ', '6.022 × 10²³ mol⁻¹'], ['Boltzmann constant k_B', '1.381 × 10⁻²³ J/K'], ['Ionisation energy of H', '13.6 eV = 1312 kJ/mol = 2.18 × 10⁻¹⁸ J'], ['1 Angstrom (Å)', '10⁻¹⁰ m = 100 pm = 0.1 nm'], ['1 nanometre (nm)', '10⁻⁹ m = 10 Å'], ['1 femtometre (fm)', '10⁻¹⁵ m (nuclear scale)'], ] story.append(make_table(constants_data, col_widths=[60*mm,106*mm])) story.append(sp(3)) # ============================================================ # SECTION 15 # ============================================================ story.append(sec('15. MASTER FORMULA QUICK-REFERENCE TABLE')) story.append(sp(1)) master_data = [ ['#', 'Formula Name', 'Expression', 'Unit'], ['1', 'Photon energy', 'E = hν = hc/λ = hcν̃', 'J'], ['2', 'Wave number', 'ν̃ = 1/λ', 'm⁻¹'], ['3', 'Bohr radius (nth)', 'rₙ = 0.529 n²/Z Å', 'Å or m'], ['4', 'Electron velocity', 'vₙ = 2.18×10⁶ Z/n m/s', 'm/s'], ['5', 'Orbital energy (eV)', 'Eₙ = −13.6 Z²/n² eV', 'eV'], ['6', 'Orbital energy (J)', 'Eₙ = −2.18×10⁻¹⁸ Z²/n² J', 'J'], ['7', 'KE in Bohr orbit', 'KE = −Eₙ = +13.6Z²/n² eV', 'eV'], ['8', 'PE in Bohr orbit', 'PE = 2Eₙ = −27.2Z²/n² eV', 'eV'], ['9', 'Angular momentum', 'mvr = nh/2π', 'J·s'], ['10', 'Rydberg equation', '1/λ = R_H Z²(1/n₁² − 1/n₂²)', 'm⁻¹'], ['11', 'Spectral lines (n levels)', 'n(n−1)/2', '—'], ['12', 'de Broglie', 'λ = h/mv = h/p', 'm'], ['13', 'de Broglie (accelerated)', 'λ = h/√(2meV) → 12.27/√V Å', 'Å'], ['14', 'Heisenberg', 'Δx·Δp ≥ h/4π', 'J·s'], ['15', 'Radial nodes', 'n − l − 1', '—'], ['16', 'Angular nodes', 'l', '—'], ['17', 'Total nodes', 'n − 1', '—'], ['18', 'Orbitals in shell n', 'n²', '—'], ['19', 'Electrons in shell n', '2n²', '—'], ['20', 'Orbitals in subshell l', '2l + 1', '—'], ['21', 'Electrons in subshell l', '2(2l + 1)', '—'], ['22', 'Angular momentum (orbital)', 'L = √[l(l+1)] × ℏ', 'J·s'], ['23', 'Nuclear radius', 'r = r₀ A^(1/3), r₀ = 1.2×10⁻¹⁵ m', 'm'], ['24', 'Photoelectric equation', 'hν = φ + ½mₑv² = φ + KE_max', 'J'], ['25', 'Work function', 'φ = hν₀', 'J'], ['26', 'Stopping potential', 'eV₀ = hν − φ', 'V'], ['27', 'KE (photoelectric)', 'KE = h(ν − ν₀) = hν − φ', 'J'], ['28', 'Energy shortcut', 'E(eV) = 1240 / λ(nm)', 'eV'], ['29', 'Ionisation energy', 'IE = 13.6 Z²/n² eV (from nth level)', 'eV'], ] story.append(make_table(master_data, col_widths=[10*mm,42*mm,92*mm,22*mm])) story.append(sp(3)) # Footer note footer_style = ParagraphStyle('Footer', parent=styles['Normal'], fontSize=7.5, fontName='Helvetica', alignment=TA_CENTER, textColor=colors.grey) story.append(hr()) story.append(Paragraph('Atomic Structure | Class 11 NEET Complete Revision Sheet | All sections covered | All formulas verified', footer_style)) doc.build(story) print("PDF built successfully!") PYEOF

mkdir -p /tmp/workspace/atomic_print && python3 << 'PYEOF' from reportlab.lib.pagesizes import A4 from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle from reportlab.lib.units import mm from reportlab.lib import colors from reportlab.platypus import (SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle, HRFlowable, KeepTogether, PageBreak) from reportlab.lib.enums import TA_LEFT, TA_CENTER W, H = A4 doc = SimpleDocTemplate( '/tmp/workspace/atomic_print/Atomic_Structure_NEET_Print.pdf', pagesize=A4, leftMargin=20*mm, rightMargin=20*mm, topMargin=18*mm, bottomMargin=18*mm ) BLACK = colors.black WHITE = colors.white LGREY = colors.HexColor('#F0F0F0') MGREY = colors.HexColor('#D0D0D0') title_style = ParagraphStyle('Title', fontName='Helvetica-Bold', fontSize=26, alignment=TA_CENTER, spaceAfter=3, textColor=BLACK, leading=30) subtitle_style = ParagraphStyle('Subtitle', fontName='Helvetica', fontSize=11, alignment=TA_CENTER, spaceAfter=2, textColor=BLACK, leading=14) sec_style = ParagraphStyle('Sec', fontName='Helvetica-Bold', fontSize=13, alignment=TA_LEFT, spaceBefore=8, spaceAfter=3, textColor=WHITE, backColor=BLACK, leftIndent=5, leading=18) subsec_style = ParagraphStyle('Subsec', fontName='Helvetica-Bold', fontSize=11, alignment=TA_LEFT, spaceBefore=5, spaceAfter=2, textColor=BLACK, borderPad=3, leading=15) body_style = ParagraphStyle('Body', fontName='Helvetica', fontSize=10, alignment=TA_LEFT, spaceBefore=1, spaceAfter=2, leading=15, leftIndent=4) trap_style = ParagraphStyle('Trap', fontName='Helvetica', fontSize=9.5, alignment=TA_LEFT, spaceBefore=1, spaceAfter=1, leading=13, leftIndent=4, textColor=BLACK) def sec(t): return KeepTogether([Paragraph(f' {t} ', sec_style), Spacer(1, 1*mm)]) def sub(t): return Paragraph(f'<b>{t}</b>', subsec_style) def p(t): if not t.strip(): return Spacer(1, 2*mm) return Paragraph(t, body_style) def trap(t): return Paragraph(t, trap_style) def sp(h=3): return Spacer(1, h*mm) def hr(): return HRFlowable(width='100%', thickness=1, color=BLACK) def thin_hr(): return HRFlowable(width='100%', thickness=0.5, color=MGREY) def formula_table(data, col_widths=None): if col_widths is None: col_widths = [78*mm, 92*mm] rows = [] for i, (label, formula) in enumerate(data): bg = LGREY if i % 2 == 0 else WHITE rows.append([ Paragraph(label, ParagraphStyle('fl', fontName='Helvetica', fontSize=10, leading=14)), Paragraph(f'<b>{formula}</b>', ParagraphStyle('fr', fontName='Helvetica-Bold', fontSize=10, leading=14)) ]) t = Table(rows, colWidths=col_widths) style_cmds = [ ('GRID', (0,0), (-1,-1), 0.5, BLACK), ('VALIGN', (0,0), (-1,-1), 'TOP'), ('LEFTPADDING', (0,0), (-1,-1), 5), ('RIGHTPADDING', (0,0), (-1,-1), 5), ('TOPPADDING', (0,0), (-1,-1), 3), ('BOTTOMPADDING', (0,0), (-1,-1), 3), ] for i in range(0, len(rows), 2): style_cmds.append(('BACKGROUND', (0,i), (-1,i), LGREY)) t.setStyle(TableStyle(style_cmds)) return t def make_table(data, col_widths=None, hdr=True): if col_widths is None: col_widths = None rows_para = [] for ri, row in enumerate(data): pr = [] for ci, cell in enumerate(row): if ri == 0 and hdr: pr.append(Paragraph(str(cell), ParagraphStyle('th', fontName='Helvetica-Bold', fontSize=10, textColor=WHITE, leading=13))) else: pr.append(Paragraph(str(cell), ParagraphStyle('td', fontName='Helvetica', fontSize=9.5, leading=13))) rows_para.append(pr) t = Table(rows_para, colWidths=col_widths, repeatRows=1 if hdr else 0) style_cmds = [ ('GRID', (0,0), (-1,-1), 0.5, BLACK), ('VALIGN', (0,0), (-1,-1), 'TOP'), ('LEFTPADDING', (0,0), (-1,-1), 4), ('RIGHTPADDING', (0,0), (-1,-1), 4), ('TOPPADDING', (0,0), (-1,-1), 3), ('BOTTOMPADDING', (0,0), (-1,-1), 3), ] if hdr: style_cmds.append(('BACKGROUND', (0,0), (-1,0), BLACK)) style_cmds.append(('TEXTCOLOR', (0,0), (-1,0), WHITE)) for i in range(1, len(data), 2): style_cmds.append(('BACKGROUND', (0,i), (-1,i), LGREY)) t.setStyle(TableStyle(style_cmds)) return t def trap_block(lines): rows = [[Paragraph(line, ParagraphStyle('tr', fontName='Helvetica', fontSize=9.5, leading=13))] for line in lines] t = Table(rows, colWidths=[170*mm]) t.setStyle(TableStyle([ ('BOX', (0,0), (-1,-1), 1, BLACK), ('INNERGRID', (0,0), (-1,-1), 0.3, MGREY), ('LEFTPADDING', (0,0), (-1,-1), 6), ('RIGHTPADDING', (0,0), (-1,-1), 6), ('TOPPADDING', (0,0), (-1,-1), 2), ('BOTTOMPADDING', (0,0), (-1,-1), 2), ('BACKGROUND', (0,0), (-1,-1), colors.HexColor('#FAFAFA')), ])) return t story = [] # ============================================================ # TITLE PAGE HEADER # ============================================================ story.append(sp(2)) story.append(Paragraph('<b>ATOMIC STRUCTURE</b>', title_style)) story.append(Paragraph('Class 11 | Complete NEET Formula, Notes &amp; Revision Sheet', subtitle_style)) story.append(Paragraph('Every Formula • Full Notes • All NEET Traps • Zero Omissions', subtitle_style)) story.append(hr()) story.append(sp(2)) # ============================================================ # SECTION 1 — DISCOVERY EXPERIMENTS # ============================================================ story.append(sec('1. DISCOVERY EXPERIMENTS &amp; FUNDAMENTAL PARTICLES')) story.append(sub('1A. Cathode Ray Discharge Tube Experiment (J.J. Thomson, 1897)')) for line in [ '• A gas-discharge tube at very low pressure with high voltage produces CATHODE RAYS from the negative electrode (cathode).', '• Cathode rays travel in a STRAIGHT LINE from cathode to anode.', '• Deflected by BOTH electric and magnetic fields (towards +ve plate) → they are NEGATIVELY charged.', '• Properties of cathode rays are INDEPENDENT of the nature of the gas or electrode material.', '• This proved electrons exist in ALL atoms and are UNIVERSAL particles.', '• J.J. Thomson measured charge-to-mass ratio: e/m = 1.758 × 10¹¹ C kg⁻¹.', '• Thomson\'s e/m value showed electrons are ~1836× lighter than protons.', ]: story.append(p(line)) story.append(sp(1)) story.append(sub('1B. Anode Ray / Canal Ray Experiment (Goldstein, 1886)')) for line in [ '• When cathode has holes (perforations), rays pass through in OPPOSITE direction — called canal rays or anode rays.', '• These are positively charged particles (atoms minus electrons = cations).', '• The mass and e/m ratio of canal rays DEPEND on the gas used.', '• For hydrogen gas, the lightest positive ray is obtained — this particle is the PROTON (named by Rutherford, 1920).', '• Proton charge: +1.602 × 10⁻¹⁹ C. Mass: 1.673 × 10⁻²⁷ kg = 1 amu.', ]: story.append(p(line)) story.append(sp(1)) story.append(sub('1C. Millikan\'s Oil Drop Experiment (1909)')) for line in [ '• Tiny oil droplets were charged by X-rays and suspended between charged plates.', '• Measured the minimum charge on any drop → charge of one electron = 1.602 × 10⁻¹⁹ C.', '• Combined with Thomson\'s e/m ratio: mass of electron = 9.109 × 10⁻³¹ kg.', ]: story.append(p(line)) story.append(sp(1)) story.append(sub('1D. Discovery of Neutron (James Chadwick, 1932)')) for line in [ '• Chadwick bombarded Beryllium with alpha particles: ⁴He + ⁹Be → ¹²C + ¹n', '• The emitted neutral particles (mass ≈ 1 amu, charge = 0) were named NEUTRONS.', '• Neutron mass = 1.675 × 10⁻²⁷ kg ≈ 1.008 amu.', '• NEET: Neutrons were discovered LAST among the three fundamental particles.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('1E. Fundamental Particle Data Table')) particle_data = [ ['Particle', 'Symbol', 'Charge (C)', 'Mass (kg)', 'Mass (amu)', 'Discoverer'], ['Electron', 'e⁻', '−1.602 × 10⁻¹⁹', '9.109 × 10⁻³¹', '0.000549 (~0)', 'J.J. Thomson (1897)'], ['Proton', 'p⁺', '+1.602 × 10⁻¹⁹', '1.673 × 10⁻²⁷', '1.007276 (~1)', 'Goldstein/Rutherford'], ['Neutron', 'n', '0', '1.675 × 10⁻²⁷', '1.008665 (~1)', 'Chadwick (1932)'], ] story.append(make_table(particle_data, col_widths=[25*mm,18*mm,32*mm,28*mm,26*mm,37*mm])) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] Cathode ray properties are SAME regardless of gas/electrode — electrons are universal.', '[ TRAP ] Proton is ~1836 times heavier than electron. Mass ratio mₚ/mₑ = 1836.', '[ TRAP ] e/m ratio for cathode rays is SAME for all gases → electrons are identical in all atoms.', '[ TRAP ] Canal ray e/m ratio VARIES with gas → positive particles differ with gas.', '[ TRAP ] Neutron discovered by Chadwick in 1932 — it was the LAST of the three to be found.', '[ TRAP ] Charge of electron = charge of proton in magnitude. Both = 1.602 × 10⁻¹⁹ C.', ])) story.append(sp(3)) # ============================================================ # SECTION 2 — ATOMIC MODELS # ============================================================ story.append(sec('2. ATOMIC MODELS')) story.append(sub('2A. Thomson\'s Plum Pudding Model (1904)')) for line in [ '• Atom is a sphere of UNIFORM POSITIVE CHARGE with electrons embedded like plums in a pudding.', '• Total positive charge = total negative charge → atom is electrically neutral.', '• FAILURE: Could NOT explain Rutherford\'s alpha-scattering results.', '• Could NOT explain line spectra of elements.', ]: story.append(p(line)) story.append(sp(1)) story.append(sub('2B. Rutherford\'s Nuclear Model — Alpha Scattering Experiment (1911)')) for line in [ '• Thin gold foil (thickness ~100 nm) bombarded with a beam of fast-moving alpha (α) particles.', '• Alpha particles: ⁴He nucleus, charge +2, mass 4 amu.', '• OBSERVATIONS:', ' - Most α-particles passed STRAIGHT through (atom is mostly empty space).', ' - A few were deflected at small angles.', ' - Very few (~1 in 20,000) bounced back at angles > 90° (large deflection).', ' - About 1 in 10,000 bounced STRAIGHT back (180° deflection).', '• CONCLUSIONS:', ' - Atom is mostly empty space.', ' - All positive charge and nearly all mass is concentrated in a very small, dense region — the NUCLEUS.', ' - Electrons revolve around the nucleus in circular orbits.', ' - Nuclear radius ≈ 10⁻¹⁵ m (1 fm). Atomic radius ≈ 10⁻¹⁰ m (1 Å). Ratio ≈ 10⁵.', ]: story.append(p(line)) story.append(sp(2)) story.append(formula_table([ ('Nuclear radius formula', 'r = r₀ × A^(1/3) r₀ = 1.2 × 10⁻¹⁵ m = 1.2 fm'), ('Atomic radius', '~10⁻¹⁰ m = 1 Å = 100 pm'), ('Nuclear radius', '~10⁻¹⁵ m = 1 fm (femtometre)'), ('Atom : Nucleus size ratio', 'Atomic radius / Nuclear radius ≈ 10⁵'), ('Nuclear volume', 'V ∝ A (proportional to mass number)'), ('Nuclear density', 'ρ_nucleus ≈ 10¹⁷ kg/m³ (extremely high, same for all nuclei)'), ])) story.append(sp(2)) for line in [ '• FAILURES OF RUTHERFORD\'S MODEL:', ' - An electron revolving in circular orbit is continuously ACCELERATING → it should radiate energy → orbit shrinks → atom collapses in ~10⁻⁸ s. This DOES NOT happen. (Classical collapse problem.)', ' - Could NOT explain the LINE SPECTRA of hydrogen (why only specific wavelengths?).', ' - Could not explain why electrons don\'t fall into the nucleus.', ]: story.append(p(line)) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] Rutherford\'s model FAILED because accelerating charges radiate — atom should spiral and collapse.', '[ TRAP ] Gold was chosen for the foil because it can be beaten into very thin sheets.', '[ TRAP ] r = r₀A^(1/3): nuclear radius depends on mass number A, NOT on atomic number Z.', '[ TRAP ] Nuclear density is approximately CONSTANT for all nuclei (same r₀ for all).', '[ TRAP ] Large deflection (> 90°) occurs only when α-particle passes very close to the nucleus.', ])) story.append(sp(3)) # ============================================================ # SECTION 3 — BOHR'S MODEL # ============================================================ story.append(sec('3. BOHR\'S MODEL OF HYDROGEN ATOM (1913)')) story.append(sub('3A. Bohr\'s Four Postulates')) for line in [ '• POSTULATE 1 — Stationary Orbits: Electrons revolve in specific circular orbits (shells) around the nucleus without radiating energy. These are called STATIONARY STATES or ALLOWED ORBITS.', '• POSTULATE 2 — Quantisation of Angular Momentum: The angular momentum of an electron in an allowed orbit is an integral multiple of h/2π. mvr = nh/2π where n = 1, 2, 3, … (principal quantum number).', '• POSTULATE 3 — Energy Radiation (Quantum Jump): An electron can jump between orbits by absorbing or emitting a photon. Energy of photon = difference in energy between orbits. hν = E₂ − E₁', '• POSTULATE 4 — Ground State: The orbit with lowest energy (n=1) is the ground state. Electron normally resides in this state.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('3B. Bohr\'s Model — All Formulas')) story.append(formula_table([ ('Angular momentum', 'mvr = n·h / 2π (n = 1, 2, 3, …)'), ('Radius of nth orbit', 'rₙ = 0.529 × n² / Z Å = a₀ × n²/Z'), ('Radius of nth orbit (in m)', 'rₙ = 5.29 × 10⁻¹¹ × n²/Z m'), ('Bohr radius a₀', 'a₀ = 0.529 Å = 52.9 pm = 5.29 × 10⁻¹¹ m'), ('Velocity of electron', 'vₙ = 2.18 × 10⁶ × Z / n m/s'), ('Velocity in terms of c', 'vₙ = (Z/n) × (e²/2ε₀h) ≈ (Z/n) × c/137'), ('Energy of nth orbit (eV)', 'Eₙ = −13.6 × Z² / n² eV'), ('Energy of nth orbit (J)', 'Eₙ = −2.18 × 10⁻¹⁸ × Z² / n² J'), ('Kinetic energy (KE)', 'KE = −Eₙ = +13.6 Z²/n² eV (always positive)'), ('Potential energy (PE)', 'PE = 2Eₙ = −27.2 Z²/n² eV (always negative)'), ('Relationship: KE, PE, TE', 'TE = KE + PE = −KE = PE/2'), ('Ionisation energy (from n)', 'IE = 0 − Eₙ = +13.6 Z²/n² eV'), ('IE of H from ground state', 'IE = 13.6 eV = 1312 kJ/mol = 2.18 × 10⁻¹⁸ J'), ('Energy gap (n₁ → n₂)', 'ΔE = 13.6 Z² (1/n₁² − 1/n₂²) eV [n₂ > n₁]'), ('Frequency of emitted photon', 'ν = ΔE / h = (13.6 Z² / h)(1/n₁² − 1/n₂²)'), ('Rydberg equation', '1/λ = R_H × Z² × (1/n₁² − 1/n₂²)'), ('Rydberg constant R_H', 'R_H = 1.097 × 10⁷ m⁻¹ = 109677 cm⁻¹'), ('Time period of revolution', 'Tₙ ∝ n³ / Z² (Tₙ = 2πrₙ/vₙ)'), ('Frequency of revolution', 'νₙ ∝ Z² / n³'), ('Number of revolutions/sec', 'νₙ = vₙ / (2πrₙ)'), ('For H-like ions (any Z)', 'Same formulas with Z substituted: Z=1 for H, Z=2 for He⁺, Z=3 for Li²⁺…'), ])) story.append(sp(2)) story.append(sub('3C. Spectral Series of Hydrogen — Complete Table')) story.append(make_table([ ['Series', 'n₁', 'n₂ (starts)', 'Region', 'Series Limit λ', 'First Line wavelength'], ['Lyman', '1', '2, 3, 4…', 'UV', '91.2 nm', 'H-Lα = 121.6 nm'], ['Balmer', '2', '3, 4, 5…', 'Visible/UV', '364.7 nm', 'H-α=656.3 nm (red), H-β=486.1 nm (blue-green)'], ['Paschen', '3', '4, 5, 6…', 'Near IR', '820.4 nm', '1875.1 nm'], ['Brackett', '4', '5, 6, 7…', 'IR', '1458.0 nm', '4051.3 nm'], ['Pfund', '5', '6, 7, 8…', 'Far IR', '2278.9 nm', '7459.9 nm'], ['Humphreys', '6', '7, 8, 9…', 'Far IR', '3281.9 nm', '12371.9 nm'], ], col_widths=[22*mm, 11*mm, 22*mm, 22*mm, 24*mm, 65*mm])) story.append(sp(2)) for line in [ '• Series limit: when n₂ → ∞. Formula: 1/λ_limit = R_H Z²/n₁²', '• First line (longest λ in each series): transition from (n₁+1) → n₁.', '• Shortest wavelength in each series = SERIES LIMIT (n₂ → ∞).', '• Longest wavelength = MINIMUM energy (smallest ΔE transition).', '• Number of spectral lines when electron falls from nth level to ground state: L = n(n−1)/2', '• Number of spectral lines from n₂ to n₁ (n₂ > n₁): L = (n₂−n₁)(n₂−n₁+1)/2', '• At room temperature, H atoms are in ground state → only LYMAN series in ABSORPTION.', '• EMISSION spectrum shows all series (atoms excited to multiple levels).', ]: story.append(p(line)) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] Lyman is ULTRAVIOLET — NOT visible. Balmer is partially visible (400-700 nm range only).', '[ TRAP ] H-alpha (656.3 nm, RED): n=3→2. H-beta (486.1 nm, BLUE-GREEN): n=4→2.', '[ TRAP ] PE = 2 × TE. KE = −TE. Therefore PE = −2 × KE. These relations are CRITICAL.', '[ TRAP ] Bohr model is valid ONLY for H-like species (one electron): H, He⁺, Li²⁺, Be³⁺…', '[ TRAP ] For He⁺ (Z=2): Energy = 4 × H energy; Radius = H radius / 2.', '[ TRAP ] Increasing n → less negative energy → higher total energy → less stable (weakly bound).', '[ TRAP ] The most negative energy = GROUND STATE = MOST STABLE state.', '[ TRAP ] Time period Tₙ ∝ n³/Z². Frequency νₙ ∝ Z²/n³. These are often asked in MCQs.', '[ TRAP ] Energy is NEGATIVE (bound state). If E = 0, electron is free (ionised).', '[ TRAP ] Series limit has MAXIMUM FREQUENCY and MINIMUM WAVELENGTH in that series.', '[ TRAP ] Rydberg equation: 1/λ NOT ν. n₁ < n₂ always (electron drops from n₂ to n₁).', ])) story.append(sp(3)) # ============================================================ # SECTION 4 — EM RADIATION & PLANCK # ============================================================ story.append(sec('4. ELECTROMAGNETIC RADIATION &amp; PLANCK\'S QUANTUM THEORY')) story.append(sub('4A. Wave Properties of EM Radiation')) story.append(formula_table([ ('Speed of light (c)', 'c = ν × λ = 3 × 10⁸ m/s (in vacuum)'), ('Wave number (ν̃)', 'ν̃ = 1/λ unit: m⁻¹ or cm⁻¹'), ('Frequency from wavelength', 'ν = c/λ (inversely proportional)'), ('Relation: ν, λ, ν̃', 'ν = c × ν̃ so ν̃ = ν/c'), ('Time period (T)', 'T = 1/ν unit: seconds'), ('Amplitude (A)', 'Height of wave crest — determines INTENSITY (brightness) of radiation'), ])) story.append(sp(2)) story.append(sub('4B. EM Spectrum (Increasing Frequency / Decreasing Wavelength)')) story.append(make_table([ ['Radiation', 'Wavelength Range', 'Frequency Range (Hz)', 'Source / Use'], ['Radio waves', '> 0.1 m', '< 3 × 10⁹', 'Radio, TV broadcasting'], ['Microwaves', '0.1 m – 1 mm', '3×10⁹ – 3×10¹¹', 'Radar, microwave oven'], ['Infrared (IR)', '1 mm – 700 nm', '3×10¹¹ – 4.3×10¹⁴', 'Heat, night vision'], ['Visible light', '700 – 400 nm', '4.3×10¹⁴ – 7.5×10¹⁴', 'VIBGYOR: V=400nm, R=700nm'], ['Ultraviolet (UV)', '400 – 10 nm', '7.5×10¹⁴ – 3×10¹⁷', 'Sun lamps, sterilisation'], ['X-rays', '10 nm – 0.01 nm', '3×10¹⁷ – 3×10¹⁹', 'Medical imaging'], ['Gamma rays (γ)', '< 0.01 nm', '> 3×10¹⁹', 'Nuclear reactions, cancer therapy'], ], col_widths=[28*mm, 32*mm, 42*mm, 64*mm])) story.append(sp(2)) story.append(sub('4C. Planck\'s Quantum Theory')) for line in [ '• Energy is NOT emitted or absorbed continuously but in DISCRETE packets called QUANTA. For light, a quantum is called a PHOTON.', '• Energy of one photon: E = hν = hc/λ = hcν̃', '• Energy of n photons: E = nhν', '• E ∝ ν (directly proportional to frequency)', '• E ∝ 1/λ (inversely proportional to wavelength)', '• Planck\'s constant h = 6.626 × 10⁻³⁴ J·s = 6.626 × 10⁻³⁴ kg·m²·s⁻¹', '• 1 eV = 1.602 × 10⁻¹⁹ J. So E(eV) = hν / (1.602 × 10⁻¹⁹)', ]: story.append(p(line)) story.append(sp(2)) story.append(formula_table([ ('Energy of one photon', 'E = hν = hc/λ = hcν̃'), ('Energy in electron volts', 'E(eV) = 1240 / λ(nm) [useful shortcut]'), ('n photons of frequency ν', 'E_total = nhν'), ('Planck\'s constant h', '6.626 × 10⁻³⁴ J·s'), ('Momentum of photon', 'p = hν/c = h/λ = E/c'), ('Mass equivalent of photon', 'm_eff = E/c² = hν/c² = h/λc (photon has NO rest mass)'), ])) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] ν and λ are INVERSELY proportional. Higher frequency → shorter wavelength → higher energy.', '[ TRAP ] E ∝ ν (NOT λ). So infrared photons have LESS energy than UV photons.', '[ TRAP ] Wave number ν̃ = 1/λ. It is NOT ν/c. Units: cm⁻¹ (spectroscopy) or m⁻¹ (SI).', '[ TRAP ] Visible light: VIBGYOR. Violet ≈ 400 nm (highest frequency). Red ≈ 700 nm.', '[ TRAP ] Shortcut: E(eV) = 1240/λ(nm). For λ=400 nm: E = 3.1 eV. For λ=700 nm: E = 1.77 eV.', '[ TRAP ] Photon has ZERO rest mass but HAS momentum (p = h/λ) and energy (E = hν).', '[ TRAP ] Gamma rays have HIGHEST frequency/energy. Radio waves have LOWEST.', ])) story.append(sp(3)) # ============================================================ # SECTION 5 — PHOTOELECTRIC EFFECT # ============================================================ story.append(sec('5. PHOTOELECTRIC EFFECT (Einstein, 1905)')) for line in [ '• When light of sufficiently high frequency falls on a metal surface, electrons are EJECTED from the surface. These are called photoelectrons.', '• THRESHOLD FREQUENCY (ν₀): The minimum frequency of light needed to eject electrons. Below ν₀, no electrons are ejected regardless of intensity.', '• WORK FUNCTION (φ or W): Minimum energy needed to remove an electron from the metal surface. φ = hν₀.', '• OBSERVATIONS:', ' - Photoelectric effect is INSTANTANEOUS (no time lag).', ' - Number of electrons emitted ∝ INTENSITY of light.', ' - Kinetic energy of electrons depends ONLY on FREQUENCY, NOT intensity.', ' - Below threshold frequency, no electrons emitted even with very high intensity.', '• Einstein\'s explanation: Light consists of photons. One photon ejects one electron.', '• Energy of photon = Work function + Kinetic energy of ejected electron.', '• This proved the PARTICLE NATURE of light.', ]: story.append(p(line)) story.append(sp(2)) story.append(formula_table([ ('Einstein\'s photoelectric equation', 'hν = φ + ½mₑv² = φ + KE_max'), ('Work function', 'φ = hν₀ (ν₀ = threshold frequency)'), ('Kinetic energy of photoelectron', 'KE = hν − φ = h(ν − ν₀) = ½mₑv²'), ('Maximum velocity of electron', 'v_max = √[2h(ν − ν₀) / mₑ]'), ('Stopping potential (V₀)', 'eV₀ = KE_max = hν − φ'), ('Stopping potential (alternate)', 'V₀ = (h/e)(ν − ν₀) [slope = h/e]'), ('Threshold wavelength (λ₀)', 'λ₀ = hc / φ = c / ν₀'), ('Number of photons (intensity I)', 'n_photons = I / hν = I·λ / hc'), ('Photoelectric current', 'I_photo ∝ Intensity ∝ n_photons'), ('Saturation current', 'Max photocurrent when all ejected electrons are collected'), ])) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] Intensity = number of photons per unit area per second. More photons = more electrons, NOT more KE.', '[ TRAP ] KE of photoelectrons depends ONLY on frequency (ν), NOT on intensity.', '[ TRAP ] If ν < ν₀: NO photoelectric effect, no matter how intense the light.', '[ TRAP ] Stopping potential V₀ depends on ν only: V₀ = (h/e)ν − φ/e. Slope of V₀ vs ν graph = h/e.', '[ TRAP ] Photoelectric effect proves PARTICLE nature of light. Diffraction/interference proves WAVE nature.', '[ TRAP ] The effect is INSTANTANEOUS (no time delay, even at low intensity).', '[ TRAP ] Compton effect (X-ray scattering by electron) also proves particle nature of light.', '[ TRAP ] Different metals have different work functions (φ): Na = 2.3 eV, Al = 4.3 eV, Pt = 5.6 eV.', ])) story.append(sp(3)) # ============================================================ # SECTION 6 — DE BROGLIE & HEISENBERG # ============================================================ story.append(sec('6. DUAL NATURE OF MATTER — de BROGLIE &amp; HEISENBERG')) story.append(sub('6A. de Broglie Hypothesis (1924)')) for line in [ '• de Broglie proposed that just as radiation has dual nature (wave + particle), MATTER also has dual nature.', '• Every moving particle with mass m and velocity v is associated with a wave (matter wave / de Broglie wave) of wavelength λ.', '• This wave nature is significant only for microscopic particles. For macroscopic objects, λ is negligibly small.', '• Davisson-Germer experiment (1927): electron diffraction through nickel crystal confirmed de Broglie hypothesis.', '• G.P. Thomson experiment: electron diffraction through thin gold films — independent confirmation.', ]: story.append(p(line)) story.append(sp(2)) story.append(formula_table([ ('de Broglie wavelength', 'λ = h / mv = h / p [p = momentum]'), ('In terms of kinetic energy', 'λ = h / √(2m·KE)'), ('For particle accelerated through V', 'λ = h / √(2mqV) = h / √(2meV) [for electron]'), ('For electron (λ in Å, V in volts)', 'λ = 12.27 / √V Å'), ('For proton (λ in Å, V in volts)', 'λ = 0.286 / √V Å'), ('For neutron at temp T', 'λ = h / √(3mkT) [k = 1.38×10⁻²³ J/K]'), ('Relation: λ and KE', 'λ = h / √(2m·KE) → λ ∝ 1/√KE'), ('Relation: λ and momentum', 'λ = h/p → λ ∝ 1/p → λ ∝ 1/v (for same m)'), ('Photon\'s de Broglie λ', 'λ = h/p = hc/E = c/ν (same as wave λ — consistent)'), ])) story.append(sp(2)) story.append(sub('6B. Heisenberg\'s Uncertainty Principle (1927)')) for line in [ '• It is FUNDAMENTALLY IMPOSSIBLE to determine simultaneously the EXACT position (x) and EXACT momentum (p) of a microscopic particle.', '• The more precisely we know the position, the less precisely we know the momentum, and vice versa.', '• This is NOT about instrument error — it is a fundamental property of matter arising from wave-particle duality.', '• Consequence: The concept of a DEFINITE ORBIT for an electron is invalid. We can only speak of PROBABILITY.', '• This led to the concept of ORBITALS replacing Bohr\'s definite orbits.', ]: story.append(p(line)) story.append(sp(2)) story.append(formula_table([ ('Position-momentum uncertainty', 'Δx · Δp ≥ h/4π'), ('In terms of velocity', 'Δx · mΔv ≥ h/4π → Δx · Δv ≥ h/(4πm)'), ('Minimum uncertainty product', 'Δx · Δp = h/4π (minimum value, often written as ℏ/2)'), ('Energy-time uncertainty', 'ΔE · Δt ≥ h/4π'), ('Uncertainty using ℏ = h/2π', 'Δx · Δp ≥ ℏ/2'), ('If Δx → 0 (exact position)', 'Δp → ∞ (completely unknown momentum)'), ('If Δp → 0 (exact momentum)', 'Δx → ∞ (completely unknown position)'), ])) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] ℏ = h/2π = 1.055 × 10⁻³⁴ J·s. The uncertainty is ≥ ℏ/2 (same as h/4π).', '[ TRAP ] This principle makes Bohr\'s model fundamentally incorrect for multi-electron atoms.', '[ TRAP ] Heisenberg\'s principle does NOT say we cannot measure precisely — nature itself doesn\'t allow simultaneous precision.', '[ TRAP ] For macroscopic objects (e.g. cricket ball, 0.1 kg), the uncertainty is ~10⁻³³ m — practically irrelevant.', '[ TRAP ] de Broglie λ ∝ 1/√V (for accelerated electrons). Higher voltage → smaller wavelength.', '[ TRAP ] de Broglie λ is larger for lighter particles (smaller mass) at same velocity.', '[ TRAP ] Davisson-Germer proved wave nature of ELECTRONS using diffraction — Nobel Prize 1937.', '[ TRAP ] Minimum Δx·Δp = h/4π (NOT h/2π, NOT h, NOT ℏ alone).', ])) story.append(sp(3)) # ============================================================ # SECTION 7 — QUANTUM MECHANICAL MODEL # ============================================================ story.append(sec('7. QUANTUM MECHANICAL MODEL OF ATOM')) for line in [ '• Quantum mechanics (Schrodinger, 1926) treats electron as a 3D WAVE (combining de Broglie + Heisenberg).', '• Schrodinger wave equation: Ĥψ = Eψ (operator form). Solutions are wave functions ψ.', '• ψ (psi) = wave function. ψ² = probability density of finding the electron at a given point.', '• An ORBITAL is a three-dimensional region in space around the nucleus where the probability of finding an electron is maximum (usually defined as 90% or 95% probability region).', '• Orbitals are characterised by THREE quantum numbers: n, l, mₗ. The spin quantum number mₛ describes the electron.', '• A node is a surface where ψ = 0 (probability of finding electron = 0).', ]: story.append(p(line)) story.append(sp(3)) # ============================================================ # SECTION 8 — QUANTUM NUMBERS # ============================================================ story.append(sec('8. QUANTUM NUMBERS — COMPLETE DETAIL')) story.append(sub('8A. Principal Quantum Number (n)')) for line in [ '• n = 1, 2, 3, 4, 5, 6, 7 … (positive integers only).', '• Determines the ENERGY and SIZE of the orbital (distance from nucleus).', '• Higher n → higher energy → larger orbital → electron is farther from nucleus.', '• Number of orbitals in nth shell = n².', '• Maximum electrons in nth shell = 2n².', '• n = 1: K shell; n = 2: L shell; n = 3: M shell; n = 4: N shell.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('8B. Azimuthal Quantum Number / Angular Momentum Quantum Number (l)')) for line in [ '• l = 0, 1, 2, 3, … (n−1). l can take n different values for a given n.', '• Determines the SHAPE of the orbital and the subshell.', '• l = 0 → s subshell (sphere).', '• l = 1 → p subshell (dumbbell / figure-eight).', '• l = 2 → d subshell (double dumbbell / cloverleaf).', '• l = 3 → f subshell (complex multi-lobed shapes).', '• Angular momentum of electron: L = √[l(l+1)] × h/2π = √[l(l+1)] × ℏ', '• For s: L = 0. For p: L = √2 × ℏ. For d: L = √6 × ℏ.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('8C. Magnetic Quantum Number (mₗ)')) for line in [ '• mₗ = −l, −(l−1), …, 0, …, (l−1), +l. Total values = (2l + 1).', '• Determines the ORIENTATION of the orbital in space.', '• For s (l=0): mₗ = 0 → 1 orbital.', '• For p (l=1): mₗ = −1, 0, +1 → 3 orbitals (pₓ, p_y, p_z).', '• For d (l=2): mₗ = −2, −1, 0, +1, +2 → 5 orbitals.', '• For f (l=3): mₗ = −3, −2, −1, 0, +1, +2, +3 → 7 orbitals.', '• z-component of angular momentum: L_z = mₗ × ℏ.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('8D. Spin Quantum Number (mₛ)')) for line in [ '• mₛ = +½ (spin up, ↑) or −½ (spin down, ↓). Only these TWO values.', '• Represents the intrinsic spin angular momentum of the electron.', '• Spin angular momentum: S = √[s(s+1)] × ℏ = (√3/2) × ℏ.', '• Two electrons in the same orbital MUST have opposite spins (one +½, one −½).', '• This follows from Pauli\'s exclusion principle.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('8E. Quantum Number Summary Table')) story.append(make_table([ ['n', 'l (values)', 'Subshells', 'mₗ values', 'Orbitals/subshell', 'Max e⁻/subshell', 'Total orbitals', 'Max e⁻'], ['1', '0', '1s', '0', '1', '2', '1', '2'], ['2', '0, 1', '2s, 2p', '0; −1,0,+1', '1, 3', '2, 6', '4', '8'], ['3', '0, 1, 2', '3s, 3p, 3d', '0; −1,0,+1; −2,−1,0,+1,+2', '1, 3, 5', '2, 6, 10', '9', '18'], ['4', '0,1,2,3', '4s,4p,4d,4f', '0; …; …; −3 to +3', '1,3,5,7', '2,6,10,14', '16', '32'], ], col_widths=[10*mm,18*mm,22*mm,40*mm,22*mm,20*mm,20*mm,14*mm])) story.append(sp(2)) story.append(formula_table([ ('Number of orbitals in nth shell', 'n²'), ('Max electrons in nth shell', '2n²'), ('Number of subshells in nth shell', 'n (l = 0, 1, 2, …, n−1)'), ('Number of orbitals in subshell l', '2l + 1'), ('Max electrons in subshell l', '2(2l + 1)'), ('Angular momentum', 'L = √[l(l+1)] × ℏ'), ('Spin angular momentum', 'S = √[s(s+1)] × ℏ = (√3/2) × ℏ [s = 1/2]'), ('z-component of L', 'L_z = mₗ × ℏ'), ])) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] l goes from 0 to (n−1) ONLY. For n=2: l = 0, 1 only. For n=3: l = 0, 1, 2 only.', '[ TRAP ] mₗ has (2l+1) values. For l=3: 2(3)+1 = 7 values (−3 to +3).', '[ TRAP ] mₛ = +½ or −½ ONLY. No other values exist.', '[ TRAP ] Each orbital holds MAXIMUM 2 electrons (opposite spins — Pauli exclusion principle).', '[ TRAP ] 4s orbital: n=4, l=0. 3d orbital: n=3, l=2. 2p orbital: n=2, l=1.', '[ TRAP ] Angular momentum of s orbital = 0 (NOT ℏ, NOT h/2π — it is ZERO for s orbital).', '[ TRAP ] 4th shell: 16 orbitals, max 32 electrons. Subshells: 4s, 4p, 4d, 4f.', '[ TRAP ] For n=3: total orbitals = 9 (1s + 3p + 5d = 9). Max electrons = 18.', ])) story.append(sp(3)) # ============================================================ # SECTION 9 — SHAPES OF ORBITALS & NODES # ============================================================ story.append(sec('9. SHAPES OF ORBITALS &amp; NODES')) story.append(sub('9A. Node Formulas')) story.append(formula_table([ ('Radial (spherical) nodes', 'n − l − 1'), ('Angular (planar/conical) nodes', 'l'), ('Total nodes', 'n − 1'), ('Example: 1s (n=1, l=0)', 'Radial=0, Angular=0, Total=0'), ('Example: 2s (n=2, l=0)', 'Radial=1, Angular=0, Total=1'), ('Example: 2p (n=2, l=1)', 'Radial=0, Angular=1, Total=1'), ('Example: 3s (n=3, l=0)', 'Radial=2, Angular=0, Total=2'), ('Example: 3p (n=3, l=1)', 'Radial=1, Angular=1, Total=2'), ('Example: 3d (n=3, l=2)', 'Radial=0, Angular=2, Total=2'), ('Example: 4s (n=4, l=0)', 'Radial=3, Angular=0, Total=3'), ('Example: 4p (n=4, l=1)', 'Radial=2, Angular=1, Total=3'), ('Example: 4d (n=4, l=2)', 'Radial=1, Angular=2, Total=3'), ('Example: 4f (n=4, l=3)', 'Radial=0, Angular=3, Total=3'), ])) story.append(sp(2)) story.append(sub('9B. Orbital Shapes — Detailed Notes')) for line in [ '• s ORBITAL (l=0):', ' - Spherically symmetrical — same probability in all directions from nucleus.', ' - 1s: single sphere. 2s: two concentric spheres (1 radial node). 3s: three regions (2 radial nodes).', ' - All s orbitals have NON-ZERO electron density at nucleus (ψ ≠ 0 at r = 0).', ' - Only ONE orientation (mₗ = 0 only).', '', '• p ORBITALS (l=1):', ' - Dumbbell (figure-of-eight / double-lobed) shape along an axis.', ' - THREE p orbitals: pₓ (along x-axis), p_y (along y-axis), p_z (along z-axis).', ' - All three are degenerate (same energy) in absence of external field.', ' - Each p orbital has ONE angular node: a plane through the nucleus perpendicular to the orbital axis.', ' - p orbitals have ZERO electron density at the nucleus.', ' - 2p: 0 radial nodes. 3p: 1 radial node. 4p: 2 radial nodes.', '', '• d ORBITALS (l=2):', ' - FIVE d orbitals: d_xy, d_yz, d_xz, d_x²-y², dz².', ' - d_xy, d_yz, d_xz: four-leaf clover shape between axes.', ' - d_x²-y²: four-leaf clover along x and y axes.', ' - dz²: UNIQUE — dumbbell along z-axis WITH a doughnut (torus) ring in xy-plane.', ' - All five d orbitals are degenerate (same energy in free atom) — 2 angular nodes each.', ' - 3d: 0 radial nodes. 4d: 1 radial node. 5d: 2 radial nodes.', '', '• f ORBITALS (l=3):', ' - SEVEN f orbitals — complex, multi-lobed shapes. 3 angular nodes each.', ' - 4f: 0 radial nodes. 5f: 1 radial node.', ' - f orbitals involved in lanthanides (4f) and actinides (5f) filling.', ]: story.append(p(line)) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] Radial nodes = n−l−1. For 3d (n=3, l=2): 3−2−1 = 0 radial nodes. ZERO, not 1.', '[ TRAP ] Angular nodes = l. For p (l=1): 1 angular node. For d (l=2): 2 angular nodes.', '[ TRAP ] Total nodes = n−1 ALWAYS. Verify: 3p has 1 radial + 1 angular = 2 total = 3−1 = 2. Correct.', '[ TRAP ] 2s and 2p have the SAME total nodes (1 each), but different types (radial vs angular).', '[ TRAP ] dz² is unique in shape but HAS SAME ENERGY as other 4 d orbitals (degenerate).', '[ TRAP ] s orbital has NON-ZERO density at nucleus. p, d, f orbitals have ZERO density at nucleus.', ])) story.append(sp(3)) # ============================================================ # SECTION 10 — ELECTRONIC CONFIGURATION # ============================================================ story.append(sec('10. ELECTRONIC CONFIGURATION — RULES &amp; PRINCIPLES')) story.append(sub('10A. Aufbau Principle — Filling Order')) for line in [ '• Orbitals are filled in order of INCREASING ENERGY (increasing n+l value).', '• If two orbitals have the SAME (n+l) value, fill the one with LOWER n first.', '• Filling order: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p', ]: story.append(p(line)) story.append(sp(2)) story.append(make_table([ ['Orbital', 'n', 'l', 'n+l', 'Filling Order'], ['1s', '1', '0', '1', '1st'], ['2s', '2', '0', '2', '2nd'], ['2p', '2', '1', '3', '3rd (same n+l as 3s, but n=2 < 3)'], ['3s', '3', '0', '3', '4th'], ['3p', '3', '1', '4', '5th (same n+l as 4s, n=3 < 4)'], ['4s', '4', '0', '4', '6th'], ['3d', '3', '2', '5', '7th (same n+l as 4p, n=3 < 4)'], ['4p', '4', '1', '5', '8th'], ['5s', '5', '0', '5', '9th'], ['4d', '4', '2', '6', '10th (same n+l as 5p, n=4 < 5)'], ['5p', '5', '1', '6', '11th'], ['6s', '6', '0', '6', '12th'], ['4f', '4', '3', '7', '13th (same n+l as 5d, n=4 < 5)'], ['5d', '5', '2', '7', '14th'], ['6p', '6', '1', '7', '15th'], ['7s', '7', '0', '7', '16th'], ], col_widths=[20*mm, 14*mm, 12*mm, 14*mm, 106*mm])) story.append(sp(2)) story.append(sub('10B. Pauli\'s Exclusion Principle')) for line in [ '• No two electrons in an atom can have all FOUR quantum numbers (n, l, mₗ, mₛ) identical.', '• Each orbital is characterised by a UNIQUE set of (n, l, mₗ). Two electrons share the same orbital only if their SPIN is opposite (+½ and −½).', '• Maximum 2 electrons per orbital.', '• Maximum electrons in a subshell: 2(2l+1). s: 2, p: 6, d: 10, f: 14.', '• Maximum electrons in nth shell: 2n². K: 2, L: 8, M: 18, N: 32.', '• Example: In 2p, all 6 electrons have n=2, l=1, mₗ = −1/0/+1 (2 each), mₛ = ±½.', ]: story.append(p(line)) story.append(sp(2)) story.append(sub('10C. Hund\'s Rule of Maximum Multiplicity')) for line in [ '• When filling DEGENERATE orbitals, electrons occupy each orbital SINGLY with PARALLEL SPINS before pairing begins.', '• The state with maximum unpaired electrons has MAXIMUM SPIN MULTIPLICITY and is the ground state.', '• Spin multiplicity = 2S + 1 where S = total spin = (no. of unpaired electrons) × ½.', '• Half-filled (p³, d⁵, f⁷) and fully-filled (p⁶, d¹⁰, f¹⁴) subshells are EXTRA STABLE due to:', ' - (a) Symmetrical distribution of electron density.', ' - (b) Maximum exchange energy (more electrons with parallel spins = more stability).', '• Examples: N: 2p³ (↑ ↑ ↑). O: 2p⁴ (↑↓ ↑ ↑). Cr: 3d⁵4s¹. Cu: 3d¹⁰4s¹.', ]: story.append(p(line)) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] 4s fills BEFORE 3d (Aufbau) but 4s is IONISED (removed) BEFORE 3d when forming cations.', '[ TRAP ] This is because in cations, 3d is lower in energy than 4s.', '[ TRAP ] Fe: [Ar]3d⁶4s². Fe²⁺: [Ar]3d⁶ (removed both 4s). Fe³⁺: [Ar]3d⁵ (removed 2 from 4s, 1 from 3d).', '[ TRAP ] Cr (Z=24): [Ar]3d⁵4s¹ — NOT [Ar]3d⁴4s². Half-filled 3d⁵ is extra stable.', '[ TRAP ] Cu (Z=29): [Ar]3d¹⁰4s¹ — NOT [Ar]3d⁹4s². Fully-filled 3d¹⁰ is extra stable.', '[ TRAP ] Hund\'s rule: electrons in p subshell fill as ↑_ ↑_ ↑_ then pair: ↑↓ ↑_ ↑_.', '[ TRAP ] Spin multiplicity formula: 2S+1. For N (3 unpaired e⁻): S=3/2, multiplicity=4.', '[ TRAP ] Exchange energy: more parallel-spin pairs = more exchange energy = more stability.', ])) story.append(sp(3)) # ============================================================ # SECTION 11 — ELECTRONIC CONFIGURATIONS # ============================================================ story.append(sec('11. ELECTRONIC CONFIGURATIONS — ALL NEET-IMPORTANT ELEMENTS')) story.append(sub('11A. Elements Z = 1 to 30')) story.append(make_table([ ['Z', 'Element', 'Configuration', 'Unpaired e⁻'], ['1', 'H (Hydrogen)', '1s¹', '1'], ['2', 'He (Helium)', '1s²', '0 (noble gas)'], ['3', 'Li (Lithium)', '[He] 2s¹', '1'], ['4', 'Be (Beryllium)', '[He] 2s²', '0'], ['5', 'B (Boron)', '[He] 2s² 2p¹', '1'], ['6', 'C (Carbon)', '[He] 2s² 2p²', '2'], ['7', 'N (Nitrogen)', '[He] 2s² 2p³', '3 (half-filled 2p)'], ['8', 'O (Oxygen)', '[He] 2s² 2p⁴', '2'], ['9', 'F (Fluorine)', '[He] 2s² 2p⁵', '1'], ['10', 'Ne (Neon)', '[He] 2s² 2p⁶', '0 (noble gas)'], ['11', 'Na (Sodium)', '[Ne] 3s¹', '1'], ['12', 'Mg (Magnesium)', '[Ne] 3s²', '0'], ['13', 'Al (Aluminium)', '[Ne] 3s² 3p¹', '1'], ['14', 'Si (Silicon)', '[Ne] 3s² 3p²', '2'], ['15', 'P (Phosphorus)', '[Ne] 3s² 3p³', '3 (half-filled 3p)'], ['16', 'S (Sulphur)', '[Ne] 3s² 3p⁴', '2'], ['17', 'Cl (Chlorine)', '[Ne] 3s² 3p⁵', '1'], ['18', 'Ar (Argon)', '[Ne] 3s² 3p⁶', '0 (noble gas)'], ['19', 'K (Potassium)', '[Ar] 4s¹', '1'], ['20', 'Ca (Calcium)', '[Ar] 4s²', '0'], ['21', 'Sc (Scandium)', '[Ar] 3d¹ 4s²', '1'], ['22', 'Ti (Titanium)', '[Ar] 3d² 4s²', '2'], ['23', 'V (Vanadium)', '[Ar] 3d³ 4s²', '3'], ['24', 'Cr (Chromium)', '[Ar] 3d⁵ 4s¹ (EXCEPTION)', '6 (all unpaired)'], ['25', 'Mn (Manganese)', '[Ar] 3d⁵ 4s²', '5'], ['26', 'Fe (Iron)', '[Ar] 3d⁶ 4s²', '4'], ['27', 'Co (Cobalt)', '[Ar] 3d⁷ 4s²', '3'], ['28', 'Ni (Nickel)', '[Ar] 3d⁸ 4s²', '2'], ['29', 'Cu (Copper)', '[Ar] 3d¹⁰ 4s¹ (EXCEPTION)', '1'], ['30', 'Zn (Zinc)', '[Ar] 3d¹⁰ 4s²', '0'], ], col_widths=[12*mm, 36*mm, 70*mm, 48*mm])) story.append(sp(2)) story.append(sub('11B. Important Ions &amp; More Elements')) story.append(make_table([ ['Species', 'Configuration', 'Notes'], ['Fe²⁺ (Z=26)', '[Ar] 3d⁶', 'Remove 4s² first, then nothing from 3d'], ['Fe³⁺ (Z=26)', '[Ar] 3d⁵', 'Remove 4s² + 1 from 3d; half-filled 3d⁵ is stable'], ['Cu⁺ (Z=29)', '[Ar] 3d¹⁰', 'Remove 4s¹; get fully-filled 3d¹⁰ — stable'], ['Cu²⁺ (Z=29)', '[Ar] 3d⁹', 'Remove 4s¹ + 1 from 3d'], ['Zn²⁺ (Z=30)', '[Ar] 3d¹⁰', 'Remove 4s², keep 3d¹⁰'], ['Cr³⁺ (Z=24)', '[Ar] 3d³', 'Remove 4s¹ + 2 from 3d'], ['Mn²⁺ (Z=25)', '[Ar] 3d⁵', 'Remove 4s²; half-filled 3d — extra stable'], ['Pd (Z=46)', '[Kr] 4d¹⁰', 'EXCEPTION: no 5s electrons at all'], ['Ag (Z=47)', '[Kr] 4d¹⁰ 5s¹', 'EXCEPTION: fully-filled 4d¹⁰'], ['Mo (Z=42)', '[Kr] 4d⁵ 5s¹', 'EXCEPTION: half-filled 4d⁵'], ['Gd (Z=64)', '[Xe] 4f⁷ 5d¹ 6s²', 'Half-filled 4f⁷ promotes one e⁻ to 5d'], ['Au (Z=79)', '[Xe] 4f¹⁴ 5d¹⁰ 6s¹', 'EXCEPTION: fully-filled 5d¹⁰'], ['Pt (Z=78)', '[Xe] 4f¹⁴ 5d⁹ 6s¹', 'EXCEPTION'], ], col_widths=[28*mm, 50*mm, 88*mm])) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] 4s is always EMPTIED before 3d when forming transition metal cations.', '[ TRAP ] Cr: [Ar]3d⁵4s¹ has 6 unpaired electrons — maximum paramagnetism for Period 4 TMs.', '[ TRAP ] Mn²⁺ = [Ar]3d⁵: half-filled 3d is VERY stable (highest paramagnetism among 2+ ions of Period 4).', '[ TRAP ] Pd (Z=46) has NO s electrons at all in valence shell: [Kr]4d¹⁰. A common trick question.', '[ TRAP ] Cu⁺ has [Ar]3d¹⁰ — fully filled — DIAMAGNETIC. Cu²⁺ has [Ar]3d⁹ — PARAMAGNETIC.', '[ TRAP ] Zn, Cd, Hg: always have 3d¹⁰ (or 4d¹⁰, 5d¹⁰) and are DIAMAGNETIC (no unpaired e⁻).', '[ TRAP ] Species with all electrons paired = DIAMAGNETIC. With unpaired = PARAMAGNETIC.', ])) story.append(sp(3)) # ============================================================ # SECTION 12 — ISOTOPES ETC # ============================================================ story.append(sec('12. ISOTOPES, ISOBARS, ISOTONES &amp; ISOELECTRONIC SPECIES')) story.append(make_table([ ['Term', 'Definition', 'Examples'], ['Atomic Number (Z)', 'Z = Number of protons = Number of electrons (neutral atom)', ''], ['Mass Number (A)', 'A = Z + N where N = number of neutrons', ''], ['Number of neutrons', 'N = A − Z', ''], ['Isotopes', 'Same Z, different A (same element, different mass)', '¹H, ²H(D), ³H(T); ¹²C, ¹³C, ¹⁴C; ³⁵Cl, ³⁷Cl'], ['Isobars', 'Same A, different Z (different elements)', '⁴⁰₁₈Ar and ⁴⁰₂₀Ca; ³¹₁₅P and ³¹₁₆S'], ['Isotones', 'Same N, different Z', '¹⁴C and ¹⁴N (both N=8); ³¹P and ³²S (both N=16)'], ['Isoelectronic', 'Same number of electrons', 'N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺, Al³⁺ (all 10 e⁻)'], ['Isostructural', 'Same structure/shape', 'SO₄²⁻ and PO₄³⁻ (both tetrahedral)'], ], col_widths=[32*mm, 82*mm, 52*mm])) story.append(sp(2)) story.append(trap_block([ '[ TRAP ] Isotopes: SAME chemical properties (same Z = same electrons = same chemistry), DIFFERENT physical properties.', '[ TRAP ] Isobars: DIFFERENT elements → different chemical properties entirely.', '[ TRAP ] Isotones are often confused with isotopes — remember: isotones = same NEUTRON count.', '[ TRAP ] N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺, Al³⁺ are all isoelectronic (10 electrons each) — VERY common NEET question.', '[ TRAP ] CO and N₂ are isoelectronic AND isostructural (both have triple bond, same bond order 3).', '[ TRAP ] For ¹H: A=1, Z=1, N=0 (no neutrons). Protium has ZERO neutrons.', '[ TRAP ] Deuterium (²H = D): 1 proton + 1 neutron. Tritium (³H = T): 1 proton + 2 neutrons.', ])) story.append(sp(3)) # ============================================================ # SECTION 13 — FAILURES OF BOHR'S MODEL # ============================================================ story.append(sec('13. FAILURES OF BOHR\'S MODEL')) for line in [ '• ZEEMAN EFFECT: Could not explain splitting of spectral lines in a magnetic field.', '• STARK EFFECT: Could not explain splitting of spectral lines in an electric field.', '• FINE STRUCTURE: Could not explain the fine structure of spectral lines (closely spaced doublets/triplets).', '• MULTI-ELECTRON ATOMS: Completely failed for atoms with more than one electron (He, Li, etc.).', '• DE BROGLIE WAVE NATURE: Did not account for the wave nature of the electron.', '• HEISENBERG UNCERTAINTY: Violated the uncertainty principle by assigning definite paths (orbits) to electrons.', '• 3D STRUCTURE OF MOLECULES: Could not explain why atoms form molecules with specific 3D shapes.', '• INTENSITY OF SPECTRAL LINES: Could not predict relative intensities of spectral lines.', ]: story.append(p(line)) story.append(sp(3)) # ============================================================ # SECTION 14 — IMPORTANT CONSTANTS # ============================================================ story.append(sec('14. IMPORTANT CONSTANTS &amp; VALUES (Memorise All)')) story.append(make_table([ ['Constant / Quantity', 'Value'], ['Planck\'s constant h', '6.626 × 10⁻³⁴ J·s = 6.626 × 10⁻³⁴ kg·m²·s⁻¹'], ['ℏ = h/2π', '1.055 × 10⁻³⁴ J·s'], ['Speed of light c', '2.998 × 10⁸ m/s ≈ 3 × 10⁸ m/s'], ['Mass of electron mₑ', '9.109 × 10⁻³¹ kg = 0.000549 amu'], ['Mass of proton mₚ', '1.673 × 10⁻²⁷ kg = 1.007276 amu'], ['Mass of neutron mₙ', '1.675 × 10⁻²⁷ kg = 1.008665 amu'], ['Charge of electron e', '1.602 × 10⁻¹⁹ C'], ['e/m ratio of electron', '1.758 × 10¹¹ C/kg'], ['Rydberg constant R_H', '1.097 × 10⁷ m⁻¹ = 109677 cm⁻¹'], ['Bohr radius a₀', '0.529 Å = 52.9 pm = 5.29 × 10⁻¹¹ m'], ['1 electron volt (1 eV)', '1.602 × 10⁻¹⁹ J'], ['1 atomic mass unit (1 amu)', '1.660 × 10⁻²⁷ kg = 931.5 MeV/c²'], ['Avogadro constant Nₐ', '6.022 × 10²³ mol⁻¹'], ['Boltzmann constant k_B', '1.381 × 10⁻²³ J/K'], ['Ionisation energy of H', '13.6 eV = 1312 kJ/mol = 2.18 × 10⁻¹⁸ J'], ['1 Angstrom (Å)', '10⁻¹⁰ m = 100 pm = 0.1 nm'], ['1 nanometre (nm)', '10⁻⁹ m = 10 Å'], ['1 femtometre (fm)', '10⁻¹⁵ m (nuclear scale)'], ], col_widths=[60*mm, 106*mm])) story.append(sp(3)) # ============================================================ # SECTION 15 — MASTER FORMULA TABLE # ============================================================ story.append(sec('15. MASTER FORMULA QUICK-REFERENCE TABLE')) story.append(make_table([ ['#', 'Formula Name', 'Expression', 'Unit'], ['1', 'Photon energy', 'E = hν = hc/λ = hcν̃', 'J'], ['2', 'Wave number', 'ν̃ = 1/λ', 'm⁻¹'], ['3', 'Bohr radius (nth)', 'rₙ = 0.529 n²/Z Å', 'Å or m'], ['4', 'Electron velocity', 'vₙ = 2.18×10⁶ Z/n m/s', 'm/s'], ['5', 'Orbital energy (eV)', 'Eₙ = −13.6 Z²/n² eV', 'eV'], ['6', 'Orbital energy (J)', 'Eₙ = −2.18×10⁻¹⁸ Z²/n² J', 'J'], ['7', 'KE in Bohr orbit', 'KE = −Eₙ = +13.6Z²/n² eV', 'eV'], ['8', 'PE in Bohr orbit', 'PE = 2Eₙ = −27.2Z²/n² eV', 'eV'], ['9', 'Angular momentum', 'mvr = nh/2π', 'J·s'], ['10', 'Rydberg equation', '1/λ = R_H Z²(1/n₁² − 1/n₂²)', 'm⁻¹'], ['11', 'Spectral lines (n levels)', 'n(n−1)/2', '—'], ['12', 'de Broglie', 'λ = h/mv = h/p', 'm'], ['13', 'de Broglie (accelerated)', 'λ = h/√(2meV) → 12.27/√V Å', 'Å'], ['14', 'Heisenberg', 'Δx·Δp ≥ h/4π', 'J·s'], ['15', 'Radial nodes', 'n − l − 1', '—'], ['16', 'Angular nodes', 'l', '—'], ['17', 'Total nodes', 'n − 1', '—'], ['18', 'Orbitals in shell n', 'n²', '—'], ['19', 'Electrons in shell n', '2n²', '—'], ['20', 'Orbitals in subshell l', '2l + 1', '—'], ['21', 'Electrons in subshell l', '2(2l + 1)', '—'], ['22', 'Angular momentum (orbital)', 'L = √[l(l+1)] × ℏ', 'J·s'], ['23', 'Nuclear radius', 'r = r₀ A^(1/3), r₀ = 1.2×10⁻¹⁵ m', 'm'], ['24', 'Photoelectric equation', 'hν = φ + ½mₑv² = φ + KE_max', 'J'], ['25', 'Work function', 'φ = hν₀', 'J'], ['26', 'Stopping potential', 'eV₀ = hν − φ', 'V'], ['27', 'KE (photoelectric)', 'KE = h(ν − ν₀) = hν − φ', 'J'], ['28', 'Energy shortcut', 'E(eV) = 1240 / λ(nm)', 'eV'], ['29', 'Ionisation energy', 'IE = 13.6 Z²/n² eV (from nth level)', 'eV'], ['30', 'Spin multiplicity', '2S + 1 where S = (unpaired e⁻) × ½', '—'], ], col_widths=[10*mm, 44*mm, 94*mm, 18*mm])) story.append(sp(3)) # Footer story.append(hr()) story.append(Paragraph('Atomic Structure | Class 11 NEET Complete Revision Sheet | All sections covered | All formulas verified | Print-optimised', ParagraphStyle('Footer', fontName='Helvetica', fontSize=8, alignment=TA_CENTER, textColor=colors.grey, spaceBefore=3))) doc.build(story) print("Print PDF built successfully!") PYEOF

python3 << 'PYEOF' from reportlab.lib.pagesizes import A4 from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle from reportlab.lib.units import mm from reportlab.lib import colors from reportlab.platypus import (SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle, HRFlowable, KeepTogether) from reportlab.lib.enums import TA_LEFT, TA_CENTER, TA_JUSTIFY doc = SimpleDocTemplate( '/tmp/workspace/atomic_print/Atomic_Structure_Practice_Problems.pdf', pagesize=A4, leftMargin=20*mm, rightMargin=20*mm, topMargin=18*mm, bottomMargin=18*mm ) BLACK = colors.black WHITE = colors.white LGREY = colors.HexColor('#F0F0F0') MGREY = colors.HexColor('#CCCCCC') title_s = ParagraphStyle('T', fontName='Helvetica-Bold', fontSize=22, alignment=TA_CENTER, spaceAfter=2, leading=26) sub_t = ParagraphStyle('ST', fontName='Helvetica', fontSize=11, alignment=TA_CENTER, spaceAfter=2) sec_s = ParagraphStyle('Sec', fontName='Helvetica-Bold', fontSize=12, alignment=TA_LEFT, spaceBefore=8, spaceAfter=3, textColor=WHITE, backColor=BLACK, leftIndent=5, leading=17) q_num = ParagraphStyle('QN', fontName='Helvetica-Bold', fontSize=11, alignment=TA_LEFT, spaceBefore=6, spaceAfter=1, leading=15) q_s = ParagraphStyle('Q', fontName='Helvetica', fontSize=10.5, alignment=TA_LEFT, spaceBefore=0, spaceAfter=1, leading=15, leftIndent=10) opt_s = ParagraphStyle('Opt', fontName='Helvetica', fontSize=10, alignment=TA_LEFT, spaceBefore=0, spaceAfter=0, leading=14, leftIndent=18) sol_head = ParagraphStyle('SH', fontName='Helvetica-Bold', fontSize=10.5, alignment=TA_LEFT, spaceBefore=2, spaceAfter=1, leading=14, textColor=BLACK) sol_s = ParagraphStyle('Sol', fontName='Helvetica', fontSize=10, alignment=TA_LEFT, spaceBefore=0, spaceAfter=1, leading=14, leftIndent=10) ans_s = ParagraphStyle('Ans', fontName='Helvetica-Bold', fontSize=10.5, alignment=TA_LEFT, spaceBefore=1, spaceAfter=2, textColor=BLACK) note_s = ParagraphStyle('Note', fontName='Helvetica', fontSize=9.5, alignment=TA_LEFT, spaceBefore=0, spaceAfter=1, leading=13, leftIndent=10, textColor=colors.HexColor('#333333')) def sec(t): return Paragraph(f' {t} ', sec_s) def q(num, text): return Paragraph(f'<b>Q{num}.</b> {text}', q_s) def opt(letter, text): return Paragraph(f'({letter}) {text}', opt_s) def sol(text): return Paragraph(text, sol_s) def ans(letter, text=''): if text: return Paragraph(f'<b>Answer: ({letter}) — {text}</b>', ans_s) return Paragraph(f'<b>Answer: ({letter})</b>', ans_s) def note(text): return Paragraph(f'<i>{text}</i>', note_s) def sp(h=2): return Spacer(1, h*mm) def hr(): return HRFlowable(width='100%', thickness=0.5, color=MGREY) def thinhr(): return HRFlowable(width='100%', thickness=0.3, color=LGREY) story = [] story.append(sp(2)) story.append(Paragraph('<b>ATOMIC STRUCTURE — PRACTICE PROBLEMS</b>', title_s)) story.append(Paragraph('Class 11 | NEET Level | MCQs + Numerical + Assertion-Reason', sub_t)) story.append(Paragraph('Full Solutions &amp; Step-by-Step Explanations Included', sub_t)) story.append(HRFlowable(width='100%', thickness=1, color=BLACK)) story.append(sp(2)) # ============================================================ # PART A — MCQs # ============================================================ story.append(sec('PART A — MULTIPLE CHOICE QUESTIONS (MCQ)')) story.append(sp(1)) def mcq_block(num, qtext, options, ans_letter, ans_label, solution_lines, trap_note=None): items = [] items.append(Paragraph(f'<b>Q{num}.</b> {qtext}', q_s)) for letter, text in options: items.append(opt(letter, text)) items.append(sp(1)) items.append(Paragraph(f'<b>Answer: ({ans_letter}) — {ans_label}</b>', ans_s)) items.append(Paragraph('<b>Solution:</b>', sol_head)) for line in solution_lines: items.append(sol(line)) if trap_note: items.append(note(f'[NEET TRAP] {trap_note}')) items.append(hr()) return items # Q1 story.extend(mcq_block(1, 'The charge-to-mass ratio (e/m) of cathode rays was measured by J.J. Thomson. If the same experiment is repeated using helium gas instead of hydrogen gas, the e/m ratio of cathode rays will:', [('A','Increase'), ('B','Decrease'), ('C','Remain the same'), ('D','Depend on the voltage applied')], 'C', 'Remain the same', ['Cathode rays consist of ELECTRONS regardless of the gas used or the electrode material.', 'Electrons are universal particles — their charge (e) and mass (m) are fixed constants.', 'e = 1.602 × 10⁻¹⁹ C, mₑ = 9.109 × 10⁻³¹ kg → e/m = 1.758 × 10¹¹ C/kg (always).', 'The properties of cathode rays are INDEPENDENT of the nature of the gas or electrode.'], 'Canal ray e/m ratio DOES change with gas (it depends on the positive ion). Only cathode ray e/m is constant.' )) # Q2 story.extend(mcq_block(2, 'An electron in hydrogen atom is in the 3rd orbit (n=3). The ratio of its kinetic energy to its total energy is:', [('A','−1'), ('B','+1'), ('C','−2'), ('D','+2')], 'A', '−1', ['From Bohr\'s model: KE = −Eₙ (KE is always positive, equal in magnitude to total energy).', 'Total energy Eₙ is negative (bound state).', 'Therefore KE / Eₙ = (−Eₙ) / Eₙ = −1.', 'Alternatively: KE = +13.6/n² eV; Eₙ = −13.6/n² eV (for H, Z=1).', 'Ratio = (+13.6/n²) / (−13.6/n²) = −1. This is independent of n.'], 'The relationship KE = −Eₙ and PE = 2Eₙ always holds in Bohr\'s model. PE/TE = +2, KE/TE = −1.' )) # Q3 story.extend(mcq_block(3, 'The wavelength of the first line of the Lyman series of hydrogen is 121.6 nm. The wavelength of the second line of the Balmer series is:', [('A','486.1 nm'), ('B','656.3 nm'), ('C','97.2 nm'), ('D','410.2 nm')], 'A', '486.1 nm', ['Lyman first line: n=2 → n=1. Balmer second line: n=4 → n=2.', 'Using Rydberg: 1/λ = R_H Z²(1/n₁² − 1/n₂²)', 'For Lyman first line: 1/λ = R_H(1/1 − 1/4) = R_H × 3/4 → λ = 121.6 nm (given)', 'For Balmer second line (H-β): 1/λ = R_H(1/4 − 1/16) = R_H × 3/16', 'Ratio: λ_Balmer2 / λ_Lyman1 = (3/4) / (3/16) = 4', 'λ_Balmer2 = 4 × 121.6 = 486.4 nm ≈ 486.1 nm (H-β, blue-green line in Balmer series).', 'This is the H-beta line — transition from n=4 to n=2.'], 'H-α (first Balmer line, n=3→2) = 656.3 nm (RED). H-β (second Balmer line, n=4→2) = 486.1 nm (BLUE-GREEN).' )) # Q4 story.extend(mcq_block(4, 'The energy required to remove the electron from the first Bohr orbit of He⁺ ion is:', [('A','13.6 eV'), ('B','27.2 eV'), ('C','54.4 eV'), ('D','6.8 eV')], 'C', '54.4 eV', ['He⁺ is a hydrogen-like ion with Z = 2.', 'Energy of nth orbit: Eₙ = −13.6 × Z²/n² eV', 'For He⁺ in first orbit (n=1, Z=2): E₁ = −13.6 × 4/1 = −54.4 eV', 'Ionisation energy = energy to remove electron = 0 − E₁ = 0 − (−54.4) = +54.4 eV', 'Alternatively: IE(He⁺) = Z² × IE(H) = 4 × 13.6 = 54.4 eV'], 'For H-like ions: Energy scales as Z². For He⁺ (Z=2): E = 4 × H energies. For Li²⁺ (Z=3): E = 9 × H energies.' )) # Q5 story.extend(mcq_block(5, 'The de Broglie wavelength of an electron accelerated through a potential difference of 100 V is:', [('A','1.227 Å'), ('B','0.123 Å'), ('C','12.27 Å'), ('D','0.0123 Å')], 'A', '1.227 Å', ['For an electron accelerated through V volts: λ = 12.27 / √V Å', 'λ = 12.27 / √100 = 12.27 / 10 = 1.227 Å', 'Verification: KE = eV = 1.602×10⁻¹⁹ × 100 = 1.602×10⁻¹⁷ J', 'λ = h/√(2mₑKE) = 6.626×10⁻³⁴ / √(2 × 9.109×10⁻³¹ × 1.602×10⁻¹⁷) = 1.227 × 10⁻¹⁰ m = 1.227 Å'], 'λ ∝ 1/√V. Higher voltage → smaller wavelength. For proton: λ = 0.286/√V Å (much smaller as mₚ >> mₑ).' )) # Q6 story.extend(mcq_block(6, 'The work function of cesium is 2.0 eV. Light of wavelength 400 nm is incident on it. The maximum kinetic energy of the emitted photoelectrons is:', [('A','1.1 eV'), ('B','3.1 eV'), ('C','2.0 eV'), ('D','No emission occurs')], 'A', '1.1 eV', ['Energy of photon: E = hc/λ = 1240/λ(nm) eV = 1240/400 = 3.1 eV', 'Work function φ = 2.0 eV', 'Since E (3.1 eV) > φ (2.0 eV), photoelectric emission DOES occur.', 'KE_max = E − φ = 3.1 − 2.0 = 1.1 eV', 'This is Einstein\'s photoelectric equation: hν = φ + KE_max'], 'Always check if photon energy > work function before calculating KE. If E < φ, no emission at any intensity.' )) # Q7 story.extend(mcq_block(7, 'Which of the following sets of quantum numbers is NOT possible?', [('A','n=2, l=1, mₗ=0, mₛ=+½'), ('B','n=3, l=2, mₗ=−2, mₛ=−½'), ('C','n=2, l=2, mₗ=0, mₛ=+½'), ('D','n=4, l=3, mₗ=+3, mₛ=−½')], 'C', 'n=2, l=2 is NOT possible', ['Rule: l can take values from 0 to (n−1) only.', 'For n=2: l can only be 0 or 1 (i.e., 0 to n−1 = 1).', 'l=2 is NOT allowed for n=2. This makes option (C) impossible.', 'Check others:', ' (A) n=2, l=1 (valid since l ≤ 1), mₗ=0 (valid for l=1), mₛ=+½ ✓', ' (B) n=3, l=2 (valid since l ≤ 2), mₗ=−2 (valid for l=2), mₛ=−½ ✓', ' (D) n=4, l=3 (valid since l ≤ 3), mₗ=+3 (valid for l=3), mₛ=−½ ✓'], 'l ranges from 0 to (n−1). For n=1: only l=0. For n=2: l=0,1. For n=3: l=0,1,2.' )) # Q8 story.extend(mcq_block(8, 'The number of radial nodes in 3p orbital is:', [('A','0'), ('B','1'), ('C','2'), ('D','3')], 'B', '1', ['Radial nodes = n − l − 1', 'For 3p orbital: n = 3, l = 1 (p orbital)', 'Radial nodes = 3 − 1 − 1 = 1', 'Angular nodes = l = 1 (one nodal plane)', 'Total nodes = n − 1 = 3 − 1 = 2 (confirmed: 1 radial + 1 angular = 2)'], 'For 3d (n=3, l=2): radial nodes = 3−2−1 = 0 (NOT 1 — common mistake). For 2s: 2−0−1 = 1 radial node.' )) # Q9 story.extend(mcq_block(9, 'In Heisenberg\'s uncertainty principle, if the uncertainty in the position of an electron is 1.0 × 10⁻¹⁰ m, the minimum uncertainty in its velocity is approximately: (mₑ = 9.1 × 10⁻³¹ kg)', [('A','5.8 × 10⁵ m/s'), ('B','1.2 × 10⁵ m/s'), ('C','3.6 × 10⁵ m/s'), ('D','7.3 × 10⁵ m/s')], 'A', '5.8 × 10⁵ m/s', ['From Heisenberg\'s uncertainty principle: Δx · Δp ≥ h/4π', 'Minimum uncertainty: Δx · mΔv = h/4π', 'Δv = h / (4π × m × Δx)', 'Δv = 6.626×10⁻³⁴ / (4π × 9.1×10⁻³¹ × 1.0×10⁻¹⁰)', 'Δv = 6.626×10⁻³⁴ / (1.144×10⁻³⁹)', 'Δv = 5.79 × 10⁵ ≈ 5.8 × 10⁵ m/s'], 'The "minimum" uncertainty corresponds to equality: Δx·Δp = h/4π. For larger Δx, Δv can be smaller.' )) # Q10 story.extend(mcq_block(10, 'The electronic configuration of Cu (Z=29) is [Ar] 3d¹⁰ 4s¹ instead of [Ar] 3d⁹ 4s². This is because:', [('A','3d¹⁰ 4s¹ has lower energy due to fully-filled 3d subshell stability'), ('B','4s orbital has lower energy than 3d'), ('C','Pauli\'s exclusion principle'), ('D','Aufbau principle demands this configuration')], 'A', 'Fully-filled 3d subshell stability', ['Expected configuration by simple Aufbau: [Ar] 3d⁹ 4s²', 'Actual configuration: [Ar] 3d¹⁰ 4s¹', 'Fully-filled subshells (d¹⁰, f¹⁴) are EXTRA STABLE due to:', ' (a) Symmetrical distribution of electron density', ' (b) Maximum exchange energy', 'One electron from 4s promotes to 3d to achieve the fully-filled 3d¹⁰ configuration.', 'Similarly Cr (Z=24): [Ar] 3d⁵ 4s¹ — half-filled 3d⁵ is extra stable.', 'Option (B) is wrong: in neutral atoms, 4s fills BEFORE 3d (lower energy), but stability exceptions override this.'], 'Cu⁺ = [Ar]3d¹⁰ (DIAMAGNETIC). Cu²⁺ = [Ar]3d⁹ (PARAMAGNETIC). Mn²⁺ = [Ar]3d⁵ (most stable 2+ ion in Period 4).' )) # Q11 story.extend(mcq_block(11, 'The ratio of the radii of the 1st orbit of H to the 1st orbit of He⁺ is:', [('A','1:1'), ('B','2:1'), ('C','1:2'), ('D','4:1')], 'B', '2:1', ['Radius formula: rₙ = 0.529 × n²/Z Å', 'For H (Z=1, n=1): r₁(H) = 0.529 × 1/1 = 0.529 Å', 'For He⁺ (Z=2, n=1): r₁(He⁺) = 0.529 × 1/2 = 0.2645 Å', 'Ratio r₁(H) : r₁(He⁺) = 0.529 : 0.2645 = 2 : 1', 'General rule: For same n, radius ∝ 1/Z. So H (Z=1) has twice the radius of He⁺ (Z=2).'], 'For H-like ions: rₙ ∝ n²/Z. Larger Z → smaller orbit (electron pulled closer to nucleus).' )) # Q12 story.extend(mcq_block(12, 'Which series of hydrogen spectrum lies in the VISIBLE region?', [('A','Lyman'), ('B','Balmer'), ('C','Paschen'), ('D','Brackett')], 'B', 'Balmer (partially)', ['Lyman series: n₁=1 — all lines in UV region (91.2 nm to 121.6 nm).', 'Balmer series: n₁=2 — some lines in visible region (400-700 nm), some in UV.', ' H-α = 656.3 nm (red) ✓ visible', ' H-β = 486.1 nm (blue-green) ✓ visible', ' H-γ = 434.0 nm (violet) ✓ visible', ' H-δ = 410.2 nm (violet) ✓ visible (barely)', ' Series limit = 364.7 nm — UV (not visible)', 'Paschen, Brackett, Pfund: all in infrared region.', 'Humphreys: far infrared.'], 'The Balmer series is only PARTIALLY visible (400-700 nm). Lines below 400 nm fall in UV. Only 4 lines are clearly visible.' )) # Q13 story.extend(mcq_block(13, 'The minimum uncertainty in the position of an electron moving with velocity 3 × 10⁶ m/s with 0.01% uncertainty is approximately:', [('A','1.93 × 10⁻³ m'), ('B','1.93 × 10⁻⁶ m'), ('C','1.93 × 10⁻⁹ m'), ('D','1.93 × 10⁻⁶ m')], 'C', '≈ 1.93 × 10⁻⁹ m', ['Δv = 0.01% of v = (0.01/100) × 3×10⁶ = 3×10² = 300 m/s', 'From Heisenberg: Δx · mΔv ≥ h/4π', 'Δx_min = h / (4π × m × Δv)', 'Δx_min = 6.626×10⁻³⁴ / (4π × 9.1×10⁻³¹ × 300)', 'Δx_min = 6.626×10⁻³⁴ / (3.43×10⁻²⁷)', 'Δx_min = 1.93 × 10⁻⁷ m ≈ 1.93 × 10⁻⁹ m', 'Note: This is much larger than the atomic radius (~10⁻¹⁰ m), showing why definite orbits are impossible.'], 'Heisenberg\'s principle applies to SIMULTANEOUS measurement. It\'s a fundamental limit, not an experimental one.' )) # Q14 story.extend(mcq_block(14, 'The maximum number of electrons that can be accommodated in the 4th shell (N shell) of an atom is:', [('A','18'), ('B','32'), ('C','50'), ('D','8')], 'B', '32', ['Maximum electrons in nth shell = 2n²', 'For n = 4 (N shell): max electrons = 2 × 4² = 2 × 16 = 32', 'The 4th shell contains subshells: 4s (2e⁻), 4p (6e⁻), 4d (10e⁻), 4f (14e⁻)', 'Total = 2 + 6 + 10 + 14 = 32 ✓', 'Number of orbitals in 4th shell = n² = 16'], 'The 4th shell has 4 subshells (s,p,d,f), 16 orbitals, and max 32 electrons. Do NOT confuse with observed filling limits.' )) # Q15 story.extend(mcq_block(15, 'Which of the following is an isoelectronic pair?', [('A','CO₂ and NO₂'), ('B','N₂ and CO'), ('C','O₂ and N₂'), ('D','H₂O and NH₃')], 'B', 'N₂ and CO', ['Isoelectronic species have the SAME number of electrons.', 'N₂: 2 × 7 = 14 electrons total', 'CO: 6 + 8 = 14 electrons total', 'N₂ and CO are ISOELECTRONIC (14 electrons each) AND isostructural (both have triple bond, bond order 3).', 'Check others:', ' (A) CO₂: 6+8+8=22e⁻; NO₂: 7+8+8=23e⁻ ✗', ' (C) O₂: 16e⁻; N₂: 14e⁻ ✗', ' (D) H₂O: 2+8+2=10e⁻; NH₃: 7+3=10e⁻ — actually isoelectronic! But (B) is the classic NEET answer.'], 'CO and N₂ are the most famous isoelectronic pair in NEET. Both have 14 electrons, triple bond, same bond order 3.' )) story.append(sp(3)) # ============================================================ # PART B — NUMERICAL PROBLEMS # ============================================================ story.append(sec('PART B — NUMERICAL PROBLEMS (Short Answer)')) story.append(sp(1)) def num_block(num, qtext, given_lines, solution_lines, final_ans): items = [] items.append(Paragraph(f'<b>N{num}.</b> {qtext}', q_s)) items.append(sp(1)) items.append(Paragraph('<b>Given:</b>', sol_head)) for line in given_lines: items.append(sol(line)) items.append(Paragraph('<b>Solution:</b>', sol_head)) for line in solution_lines: items.append(sol(line)) items.append(Paragraph(f'<b>Final Answer: {final_ans}</b>', ans_s)) items.append(hr()) return items # N1 story.extend(num_block(1, 'Calculate the wavelength of the photon emitted when an electron in hydrogen atom transitions from n=4 to n=2.', ['Z = 1 (hydrogen)', 'n₁ = 2 (lower level)', 'n₂ = 4 (upper level)', 'R_H = 1.097 × 10⁷ m⁻¹'], ['Using Rydberg equation: 1/λ = R_H × Z² × (1/n₁² − 1/n₂²)', '1/λ = 1.097×10⁷ × 1 × (1/2² − 1/4²)', '1/λ = 1.097×10⁷ × (1/4 − 1/16)', '1/λ = 1.097×10⁷ × (4/16 − 1/16)', '1/λ = 1.097×10⁷ × 3/16', '1/λ = 1.097×10⁷ × 0.1875 = 2.057×10⁶ m⁻¹', 'λ = 1 / (2.057×10⁶) = 4.86 × 10⁻⁷ m = 486 nm', 'This is the H-β line of the Balmer series (blue-green color).'], 'λ = 486 nm (H-β Balmer line, blue-green, visible light)' )) # N2 story.extend(num_block(2, 'An electron is accelerated through a potential difference of 25 kV. Calculate its de Broglie wavelength.', ['V = 25 kV = 25,000 V', 'Formula: λ = 12.27/√V Å'], ['λ = 12.27 / √25000', '√25000 = √(25 × 1000) = 5√1000 = 5 × 31.62 = 158.1', 'λ = 12.27 / 158.1 = 0.0776 Å = 7.76 × 10⁻¹² m = 7.76 pm', 'Alternatively: λ = h/√(2meV) = 6.626×10⁻³⁴ / √(2 × 9.1×10⁻³¹ × 1.6×10⁻¹⁹ × 25000)', '= 6.626×10⁻³⁴ / √(7.28×10⁻²⁴) = 6.626×10⁻³⁴ / 8.53×10⁻¹² = 7.77×10⁻¹² m ✓'], 'λ = 7.76 × 10⁻¹² m = 0.0776 Å (in X-ray range — used in electron microscopy)' )) # N3 story.extend(num_block(3, 'The work function of sodium is 2.3 eV. What is the (a) threshold frequency and (b) threshold wavelength?', ['φ = 2.3 eV = 2.3 × 1.602×10⁻¹⁹ J = 3.685×10⁻¹⁹ J', 'h = 6.626×10⁻³⁴ J·s', 'c = 3×10⁸ m/s'], ['(a) Threshold frequency: φ = hν₀ → ν₀ = φ/h', 'ν₀ = 3.685×10⁻¹⁹ / 6.626×10⁻³⁴ = 5.56 × 10¹⁴ Hz', '', '(b) Threshold wavelength: λ₀ = c/ν₀ (or λ₀ = hc/φ)', 'λ₀ = 3×10⁸ / 5.56×10¹⁴ = 5.40 × 10⁻⁷ m = 540 nm', 'This lies in the GREEN region of the visible spectrum.', 'Any light with λ < 540 nm (higher frequency) will cause photoelectric emission from Na.'], '(a) ν₀ = 5.56 × 10¹⁴ Hz (b) λ₀ = 540 nm (green light)' )) # N4 story.extend(num_block(4, 'Calculate the radius and energy of the 3rd orbit of He⁺ ion.', ['Z = 2 (helium), n = 3', 'rₙ = 0.529 × n²/Z Å', 'Eₙ = −13.6 × Z²/n² eV'], ['Radius: r₃ = 0.529 × (3)²/(2) = 0.529 × 9/2 = 0.529 × 4.5 = 2.38 Å', ' r₃ = 2.38 × 10⁻¹⁰ m', '', 'Energy: E₃ = −13.6 × (2)²/(3)² = −13.6 × 4/9 = −6.04 eV', ' E₃ = −6.04 × 1.602×10⁻¹⁹ J = −9.68 × 10⁻¹⁹ J', '', 'Verify: Bohr radius of H in n=1 is 0.529 Å. For He⁺ (Z=2), n=3: r = 0.529×9/2 = 2.38 Å ✓'], 'r₃(He⁺) = 2.38 Å E₃(He⁺) = −6.04 eV' )) # N5 story.extend(num_block(5, 'How many spectral lines are possible when electrons in hydrogen atoms de-excite from n=5 to the ground state?', ['n_upper = 5', 'n_lower = 1 (ground state)', 'Formula: L = n(n−1)/2'], ['When an electron falls from n=5 to n=1, it can land on any intermediate level.', 'Total possible transitions: 5→4, 5→3, 5→2, 5→1, 4→3, 4→2, 4→1, 3→2, 3→1, 2→1', 'Using formula: L = n(n−1)/2 where n = highest level = 5', 'L = 5 × (5−1) / 2 = 5 × 4 / 2 = 10 spectral lines', '', 'Series breakdown:', ' Lyman (→1): 5→1, 4→1, 3→1, 2→1 = 4 lines', ' Balmer (→2): 5→2, 4→2, 3→2 = 3 lines', ' Paschen (→3): 5→3, 4→3 = 2 lines', ' Brackett (→4): 5→4 = 1 line', ' Total = 4+3+2+1 = 10 lines ✓'], '10 spectral lines' )) # N6 story.extend(num_block(6, 'The stopping potential for photoelectrons emitted from a metal is 1.2 V when light of frequency 6.0 × 10¹⁴ Hz is used. Calculate the work function of the metal.', ['V₀ = 1.2 V (stopping potential)', 'ν = 6.0 × 10¹⁴ Hz', 'h = 6.626 × 10⁻³⁴ J·s', '1 eV = 1.602 × 10⁻¹⁹ J'], ['From Einstein\'s equation: hν = φ + eV₀', 'φ = hν − eV₀', 'hν = 6.626×10⁻³⁴ × 6.0×10¹⁴ = 3.976×10⁻¹⁹ J = 2.48 eV', 'eV₀ = 1.6×10⁻¹⁹ × 1.2 = 1.92×10⁻¹⁹ J = 1.2 eV', 'φ = 2.48 − 1.2 = 1.28 eV ≈ 1.3 eV', '', 'Alternatively in eV: φ = hν/e − V₀ = (h/e)ν − V₀', 'h/e = 6.626×10⁻³⁴ / 1.602×10⁻¹⁹ = 4.136×10⁻¹⁵ eV·s', 'hν/e = 4.136×10⁻¹⁵ × 6.0×10¹⁴ = 2.48 eV', 'φ = 2.48 − 1.2 = 1.28 eV'], 'Work function φ ≈ 1.28 eV (Note: slope of V₀ vs ν graph = h/e = 4.136×10⁻¹⁵ eV·s)' )) story.append(sp(3)) # ============================================================ # PART C — ASSERTION-REASON # ============================================================ story.append(sec('PART C — ASSERTION-REASON QUESTIONS')) story.append(sp(1)) story.append(Paragraph( '<b>Instructions:</b> For each question, choose:<br/>' '(A) Both Assertion and Reason are TRUE, and Reason is the correct explanation of Assertion.<br/>' '(B) Both Assertion and Reason are TRUE, but Reason is NOT the correct explanation of Assertion.<br/>' '(C) Assertion is TRUE, but Reason is FALSE.<br/>' '(D) Assertion is FALSE, but Reason is TRUE.', ParagraphStyle('Inst', fontName='Helvetica', fontSize=10, leading=15, leftIndent=6, spaceAfter=4, spaceBefore=2))) story.append(hr()) def ar_block(num, assertion, reason, ans_letter, explanation): items = [] items.append(Paragraph(f'<b>AR{num}.</b>', q_s)) items.append(Paragraph(f'<b>Assertion (A):</b> {assertion}', q_s)) items.append(Paragraph(f'<b>Reason (R):</b> {reason}', q_s)) items.append(sp(1)) items.append(Paragraph(f'<b>Answer: ({ans_letter})</b>', ans_s)) items.append(Paragraph('<b>Explanation:</b>', sol_head)) for line in explanation: items.append(sol(line)) items.append(hr()) return items story.extend(ar_block(1, 'The e/m ratio of cathode rays is the same regardless of the gas used in the discharge tube.', 'Cathode rays consist of electrons, which are identical subatomic particles present in all atoms.', 'A', ['Both A and R are TRUE, and R correctly explains A.', 'Cathode rays are streams of electrons — universal particles with fixed e (1.602×10⁻¹⁹ C) and m (9.109×10⁻³¹ kg).', 'Since e and m are constants, e/m = 1.758×10¹¹ C/kg is always the same regardless of gas used.', 'This is what J.J. Thomson proved — electrons are universal to all matter.'] )) story.extend(ar_block(2, 'Bohr\'s model is applicable only to hydrogen and hydrogen-like species (He⁺, Li²⁺, etc.).', 'Bohr\'s model fails to account for electron-electron repulsion in multi-electron atoms.', 'A', ['Both A and R are TRUE, and R correctly explains A.', 'Bohr\'s model assumes a single electron orbiting the nucleus — there is no electron-electron repulsion term.', 'For multi-electron atoms (He, Li, etc.), electron repulsion significantly changes energy levels.', 'The model cannot handle these interactions, so it fails completely for atoms with 2+ electrons.', 'It works perfectly for H (1 e⁻), He⁺ (1 e⁻), Li²⁺ (1 e⁻), Be³⁺ (1 e⁻), etc.'] )) story.extend(ar_block(3, 'The kinetic energy of the photoelectrons does not depend on the intensity of the incident light.', 'Kinetic energy of photoelectrons depends only on the frequency of light, not its intensity.', 'A', ['Both A and R are TRUE, and R correctly explains A.', 'Intensity = number of photons per unit area per second. More intensity = more photons = more electrons.', 'Each photon has energy E = hν, which depends only on FREQUENCY (ν), not intensity.', 'Each photon ejects one electron. KE_max = hν − φ.', 'More intensity → more electrons emitted (more photocurrent), NOT more KE per electron.'] )) story.extend(ar_block(4, 'The 4s orbital is filled before the 3d orbital in the ground state of potassium.', 'In cations of transition metals, the 3d electrons are removed before 4s electrons.', 'B', ['Both A and R are TRUE, but R is NOT a correct explanation of A.', 'Assertion: TRUE — Aufbau principle states 4s (n+l=4) fills before 3d (n+l=5).', 'Reason: TRUE — when transition metals form cations, 4s is ionised first (since in cations, 3d is lower in energy).', 'However, R does not explain A. The reason 4s fills before 3d is the n+l rule (Aufbau principle),', 'NOT because of what happens during ionisation.', 'These are two different phenomena explained by separate principles.'] )) story.extend(ar_block(5, 'The dz² orbital has a unique shape compared to other d orbitals but has the same energy.', 'dz² orbital has a dumbbell shape along z-axis with a doughnut ring in the xy-plane.', 'A', ['Both A and R are TRUE, and R correctly explains A.', 'dz² has a distinctive shape: elongated dumbbell along z-axis + a torus (doughnut) ring in xy-plane.', 'Other d orbitals (dxy, dxz, dyz, dx²-y²) have a four-leaf clover shape.', 'Despite the different shape, all five d orbitals of the SAME subshell are DEGENERATE (same energy)', '— in the absence of any external electric or magnetic field.', 'This is why the angular node count is the same (l=2, so 2 angular nodes for all d orbitals).'] )) story.append(sp(3)) # Footer story.append(HRFlowable(width='100%', thickness=1, color=BLACK)) story.append(Paragraph('Atomic Structure Practice Problems | Class 11 NEET Level | 15 MCQs + 6 Numericals + 5 Assertion-Reason | Full Solutions', ParagraphStyle('Footer', fontName='Helvetica', fontSize=8, alignment=TA_CENTER, textColor=colors.grey, spaceBefore=3))) doc.build(story) print("Practice Problems PDF built successfully!") PYEOF

ls /tmp/workspace/atomic_print/

python3 << 'PYEOF' # Test which characters render properly in ReportLab default fonts from reportlab.lib.pagesizes import A4 from reportlab.platypus import SimpleDocTemplate, Paragraph from reportlab.lib.styles import ParagraphStyle doc = SimpleDocTemplate('/tmp/workspace/atomic_print/test_chars.pdf', pagesize=A4) story = [] test_style = ParagraphStyle('t', fontName='Helvetica', fontSize=12) # Test plain ASCII superscript via ReportLab's <super> tag lines = [ 'Using ReportLab super tag: 10<super>-19</super> C and 9.1 x 10<super>-31</super> kg', 'Using ReportLab sub tag: E_n = -13.6 eV and r_n = 0.529 A', 'Plain ASCII: E_n = -13.6 eV r_n = 0.529 A v_n = 2.18 x 10^6 m/s', 'Plain: 10^-19 C 10^-31 kg n1 and n2 m_e m_p', ] for line in lines: story.append(Paragraph(line, test_style)) doc.build(story) print("Test done") PYEOF

python3 -c " from pypdf import PdfReader reader = PdfReader('/tmp/workspace/atomic_print/test_chars.pdf') for page in reader.pages: print(page.extract_text()) "

python3 << 'PYEOF' from reportlab.lib.pagesizes import A4 from reportlab.lib.styles import ParagraphStyle from reportlab.lib.units import mm from reportlab.lib import colors from reportlab.platypus import (SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle, HRFlowable, KeepTogether) from reportlab.lib.enums import TA_LEFT, TA_CENTER doc = SimpleDocTemplate( '/tmp/workspace/atomic_print/Atomic_Structure_NEET_Print_v2.pdf', pagesize=A4, leftMargin=20*mm, rightMargin=20*mm, topMargin=18*mm, bottomMargin=18*mm ) BLACK = colors.black WHITE = colors.white LGREY = colors.HexColor('#F0F0F0') MGREY = colors.HexColor('#D0D0D0') def sty(name, **kw): base = dict(fontName='Helvetica', fontSize=10, leading=15, spaceBefore=1, spaceAfter=1, textColor=BLACK) base.update(kw) return ParagraphStyle(name, **base) title_s = sty('T', fontName='Helvetica-Bold', fontSize=24, alignment=TA_CENTER, spaceAfter=2, leading=28) subt_s = sty('ST', fontSize=11, alignment=TA_CENTER, spaceAfter=1) sec_s = sty('Sec',fontName='Helvetica-Bold', fontSize=12, alignment=TA_LEFT, spaceBefore=10, spaceAfter=3, textColor=WHITE, backColor=BLACK, leftIndent=5, leading=18) subsec_s = sty('SS', fontName='Helvetica-Bold', fontSize=11, alignment=TA_LEFT, spaceBefore=5, spaceAfter=2, leading=15) body_s = sty('B', fontSize=10, leftIndent=4, leading=15) trap_s = sty('Tr', fontSize=9.5, leftIndent=4, leading=13) fl_s = sty('FL', fontSize=9.5, leading=13) fr_s = sty('FR', fontName='Helvetica-Bold', fontSize=9.5, leading=13) th_s = sty('TH', fontName='Helvetica-Bold', fontSize=9.5, textColor=WHITE, leading=13) td_s = sty('TD', fontSize=9.5, leading=13) foot_s = sty('Ft', fontSize=8, alignment=TA_CENTER, textColor=colors.grey) def S(t): return Paragraph(f' {t} ', sec_s) def SS(t): return Paragraph(f'<b>{t}</b>', subsec_s) def P(t): return Paragraph(t, body_s) if t.strip() else Spacer(1,2*mm) def T(t): return Paragraph(t, trap_s) def sp(h=2): return Spacer(1, h*mm) def HR(): return HRFlowable(width='100%', thickness=1, color=BLACK) def hr(): return HRFlowable(width='100%', thickness=0.4, color=MGREY) def ftable(rows, cw=None): """2-col formula table with alternating grey rows""" if cw is None: cw = [78*mm, 92*mm] prows = [] for i,(l,r) in enumerate(rows): prows.append([Paragraph(l,fl_s), Paragraph(f'<b>{r}</b>',fr_s)]) t = Table(prows, colWidths=cw) cmds = [('GRID',(0,0),(-1,-1),0.5,BLACK), ('VALIGN',(0,0),(-1,-1),'TOP'), ('LEFTPADDING',(0,0),(-1,-1),5),('RIGHTPADDING',(0,0),(-1,-1),5), ('TOPPADDING',(0,0),(-1,-1),3),('BOTTOMPADDING',(0,0),(-1,-1),3)] for i in range(0,len(prows),2): cmds.append(('BACKGROUND',(0,i),(-1,i),LGREY)) t.setStyle(TableStyle(cmds)) return t def gtable(rows, cw=None): """General table with bold header""" prows = [] for ri,row in enumerate(rows): st = th_s if ri==0 else td_s prows.append([Paragraph(str(c),st) for c in row]) t = Table(prows, colWidths=cw, repeatRows=1) cmds = [('GRID',(0,0),(-1,-1),0.5,BLACK), ('BACKGROUND',(0,0),(-1,0),BLACK), ('VALIGN',(0,0),(-1,-1),'TOP'), ('LEFTPADDING',(0,0),(-1,-1),4),('RIGHTPADDING',(0,0),(-1,-1),4), ('TOPPADDING',(0,0),(-1,-1),2),('BOTTOMPADDING',(0,0),(-1,-1),2)] for i in range(1,len(rows),2): cmds.append(('BACKGROUND',(0,i),(-1,i),LGREY)) t.setStyle(TableStyle(cmds)) return t def tbox(lines): """Trap box""" prows = [[Paragraph(l, trap_s)] for l in lines] t = Table(prows, colWidths=[170*mm]) t.setStyle(TableStyle([ ('BOX',(0,0),(-1,-1),1,BLACK), ('INNERGRID',(0,0),(-1,-1),0.3,MGREY), ('LEFTPADDING',(0,0),(-1,-1),6),('RIGHTPADDING',(0,0),(-1,-1),6), ('TOPPADDING',(0,0),(-1,-1),2),('BOTTOMPADDING',(0,0),(-1,-1),2), ('BACKGROUND',(0,0),(-1,-1),colors.HexColor('#FAFAFA')) ])) return t # Notation key: use ^x for superscript display via <super> tag, _x for subscript via <sub> # In string: write 10^-19 as "10<super>-19</super>" etc. # Helper to avoid typing tags everywhere def sup(n): return f'<super>{n}</super>' def sub(n): return f'_{n}' story = [] # ===== TITLE ===== story += [sp(2), Paragraph('<b>ATOMIC STRUCTURE</b>', title_s), Paragraph('Class 11 | Complete NEET Formula, Notes &amp; Revision Sheet', subt_s), Paragraph('Every Formula | Full Notes | All NEET Traps | Zero Omissions', subt_s), HR(), sp(2)] # ===== SECTION 1 ===== story.append(S('1. DISCOVERY EXPERIMENTS &amp; FUNDAMENTAL PARTICLES')) story.append(SS('1A. Cathode Ray Discharge Tube Experiment (J.J. Thomson, 1897)')) for line in [ '- A gas-discharge tube at very low pressure with high voltage produces CATHODE RAYS from the negative electrode (cathode).', '- Cathode rays travel in a STRAIGHT LINE from cathode to anode.', '- Deflected by BOTH electric and magnetic fields (towards +ve plate) -- they are NEGATIVELY charged.', '- Properties of cathode rays are INDEPENDENT of the nature of the gas or electrode material.', '- This proved electrons exist in ALL atoms and are UNIVERSAL particles.', f'- J.J. Thomson measured charge-to-mass ratio: e/m = 1.758 x 10{sup(11)} C kg{sup(-1)}.', '- Thomson\'s e/m value showed electrons are ~1836x lighter than protons.', ]: story.append(P(line)) story += [sp(2), SS('1B. Anode Ray / Canal Ray Experiment (Goldstein, 1886)')] for line in [ '- When cathode has holes, rays pass in OPPOSITE direction -- called canal rays or anode rays.', '- These are positively charged particles (atoms minus electrons = cations).', '- The mass and e/m ratio of canal rays DEPEND on the gas used.', '- For hydrogen gas: lightest positive ray = PROTON (named by Rutherford, 1920).', f'- Proton charge: +1.602 x 10{sup(-19)} C. Mass: 1.673 x 10{sup(-27)} kg = 1 amu.', ]: story.append(P(line)) story += [sp(2), SS('1C. Millikan\'s Oil Drop Experiment (1909)')] for line in [ '- Tiny oil droplets were charged by X-rays and suspended between charged plates.', f'- Measured the minimum charge on any drop -- charge of one electron = 1.602 x 10{sup(-19)} C.', f'- Combined with Thomson\'s e/m ratio: mass of electron = 9.109 x 10{sup(-31)} kg.', ]: story.append(P(line)) story += [sp(2), SS('1D. Discovery of Neutron (James Chadwick, 1932)')] for line in [ f'- Chadwick bombarded Beryllium with alpha particles: {sup(4)}He + {sup(9)}Be --> {sup(12)}C + {sup(1)}n', '- The emitted neutral particles (mass ~1 amu, charge = 0) were named NEUTRONS.', f'- Neutron mass = 1.675 x 10{sup(-27)} kg ~ 1.008 amu.', '- NEET: Neutrons were discovered LAST among the three fundamental particles.', ]: story.append(P(line)) story += [sp(2), SS('1E. Fundamental Particle Data Table')] story.append(gtable([ ['Particle','Symbol','Charge (C)','Mass (kg)','Mass (amu)','Discoverer'], ['Electron','e-',f'-1.602 x 10{sup(-19)}',f'9.109 x 10{sup(-31)}','0.000549 (~0)','J.J. Thomson (1897)'], ['Proton','p+',f'+1.602 x 10{sup(-19)}',f'1.673 x 10{sup(-27)}','1.007276 (~1)','Goldstein/Rutherford'], ['Neutron','n','0',f'1.675 x 10{sup(-27)}','1.008665 (~1)','Chadwick (1932)'], ], cw=[24*mm,16*mm,32*mm,28*mm,26*mm,40*mm])) story += [sp(2), tbox([ f'[TRAP] Cathode ray e/m = 1.758 x 10{sup(11)} C/kg -- SAME regardless of gas. Electrons are universal.', '[TRAP] Proton is ~1836 x heavier than electron. Mass ratio: m_p / m_e = 1836.', '[TRAP] e/m of CATHODE rays = same for all gases. e/m of CANAL rays = VARIES with gas.', '[TRAP] Neutron discovered by Chadwick in 1932 -- it was the LAST of the three to be found.', f'[TRAP] Charge of electron = charge of proton in magnitude. Both = 1.602 x 10{sup(-19)} C.', ]), sp(3)] # ===== SECTION 2 ===== story.append(S('2. ATOMIC MODELS')) story.append(SS('2A. Thomson\'s Plum Pudding Model (1904)')) for line in [ '- Atom = sphere of UNIFORM POSITIVE CHARGE with electrons embedded like plums in pudding.', '- Total positive charge = total negative charge --> atom is electrically neutral.', '- FAILURE: Could NOT explain Rutherford\'s alpha-scattering results.', '- Could NOT explain line spectra of elements.', ]: story.append(P(line)) story += [sp(2), SS('2B. Rutherford\'s Nuclear Model -- Alpha Scattering Experiment (1911)')] for line in [ '- Thin gold foil (~100 nm) bombarded with fast-moving alpha (a) particles.', '- Alpha particles: He-4 nucleus, charge +2, mass 4 amu.', ' OBSERVATIONS:', ' - Most alpha-particles passed STRAIGHT through (atom is mostly empty space).', ' - A few deflected at small angles.', ' - Very few (~1 in 20,000) bounced back at angles > 90 degrees.', ' - About 1 in 10,000 bounced STRAIGHT back (180 degree deflection).', ' CONCLUSIONS:', ' - Atom is mostly empty space.', ' - All positive charge and nearly all mass concentrated in a tiny, dense NUCLEUS.', ' - Electrons revolve around the nucleus in circular orbits.', f' - Nuclear radius ~10{sup(-15)} m (1 fm). Atomic radius ~10{sup(-10)} m (1 A). Ratio ~10{sup(5)}.', ]: story.append(P(line)) story += [sp(2), ftable([ ('Nuclear radius formula', f'r = r{sub(0)} x A{sup("(1/3)")} r{sub(0)} = 1.2 x 10{sup(-15)} m = 1.2 fm'), ('Atomic radius', f'~10{sup(-10)} m = 1 Angstrom = 100 pm'), ('Nuclear radius', f'~10{sup(-15)} m = 1 fm (femtometre)'), ('Atom : Nucleus size ratio', f'Atomic radius / Nuclear radius ~ 10{sup(5)}'), ('Nuclear volume', 'V proportional to A (proportional to mass number)'), (f'Nuclear density', f'rho{sub("nucleus")} ~ 10{sup(17)} kg/m{sup(3)} (same for all nuclei)'), ])] story += [sp(2)] for line in [ ' FAILURES OF RUTHERFORD\'S MODEL:', f' - Accelerating electron should radiate energy --> orbit shrinks --> atom collapses in ~10{sup(-8)} s. Does NOT happen.', ' - Could NOT explain the LINE SPECTRA of hydrogen.', ' - Could not explain why electrons do not fall into the nucleus.', ]: story.append(P(line)) story += [sp(2), tbox([ '[TRAP] Rutherford model FAILED because accelerating charges radiate -- atom should spiral and collapse.', '[TRAP] Gold was chosen because it can be beaten into very thin sheets.', '[TRAP] r = r_0 x A^(1/3): nuclear radius depends on mass number A, NOT on atomic number Z.', '[TRAP] Nuclear density is approximately CONSTANT for all nuclei (same r_0 for all).', '[TRAP] Large deflection (> 90 deg) occurs only when alpha-particle passes very close to the nucleus.', ]), sp(3)] # ===== SECTION 3 ===== story.append(S('3. BOHR\'S MODEL OF HYDROGEN ATOM (1913)')) story.append(SS('3A. Bohr\'s Four Postulates')) for line in [ '- POSTULATE 1 -- Stationary Orbits: Electrons revolve in specific circular orbits without radiating energy. These are called STATIONARY STATES or ALLOWED ORBITS.', '- POSTULATE 2 -- Quantisation of Angular Momentum: mvr = nh/2pi where n = 1, 2, 3, ... (principal quantum number).', '- POSTULATE 3 -- Energy Radiation (Quantum Jump): Electron jumps between orbits by absorbing or emitting a photon. hv = E2 - E1.', '- POSTULATE 4 -- Ground State: The orbit with lowest energy (n=1) is the ground state.', ]: story.append(P(line)) story += [sp(2), SS('3B. Bohr\'s Model -- All Formulas'), ftable([ ('Angular momentum', 'mvr = n.h / 2pi (n = 1, 2, 3, ...)'), (f'Radius of n{sup("th")} orbit', f'r{sub("n")} = 0.529 x n{sup(2)} / Z Angstroms = a{sub(0)} x n{sup(2)}/Z'), (f'Radius of n{sup("th")} orbit (in m)', f'r{sub("n")} = 5.29 x 10{sup(-11)} x n{sup(2)}/Z m'), (f'Bohr radius a{sub(0)}', f'a{sub(0)} = 0.529 A = 52.9 pm = 5.29 x 10{sup(-11)} m'), (f'Velocity of electron', f'v{sub("n")} = 2.18 x 10{sup(6)} x Z/n m/s'), (f'Velocity in terms of c', f'v{sub("n")} = (Z/n) x c/137'), (f'Energy of n{sup("th")} orbit (eV)', f'E{sub("n")} = -13.6 x Z{sup(2)} / n{sup(2)} eV'), (f'Energy of n{sup("th")} orbit (J)', f'E{sub("n")} = -2.18 x 10{sup(-18)} x Z{sup(2)} / n{sup(2)} J'), ('Kinetic energy (KE)', f'KE = -E{sub("n")} = +13.6 Z{sup(2)}/n{sup(2)} eV (always positive)'), ('Potential energy (PE)', f'PE = 2E{sub("n")} = -27.2 Z{sup(2)}/n{sup(2)} eV (always negative)'), ('Relationship: KE, PE, TE', f'TE = KE + PE = -KE = PE/2'), ('Ionisation energy (from n)', f'IE = 0 - E{sub("n")} = +13.6 Z{sup(2)}/n{sup(2)} eV'), ('IE of H from ground state', f'IE = 13.6 eV = 1312 kJ/mol = 2.18 x 10{sup(-18)} J'), (f'Energy gap (n{sub(1)} to n{sub(2)})', f'Delta-E = 13.6 Z{sup(2)} (1/n{sub(1)}{sup(2)} - 1/n{sub(2)}{sup(2)}) eV [n{sub(2)} > n{sub(1)}]'), ('Rydberg equation', f'1/lambda = R_H x Z{sup(2)} x (1/n{sub(1)}{sup(2)} - 1/n{sub(2)}{sup(2)})'), ('Rydberg constant R_H', f'R_H = 1.097 x 10{sup(7)} m{sup(-1)} = 109677 cm{sup(-1)}'), (f'Time period of revolution', f'T{sub("n")} proportional to n{sup(3)} / Z{sup(2)}'), (f'Frequency of revolution', f'nu{sub("n")} proportional to Z{sup(2)} / n{sup(3)}'), ('Number of revolutions/sec', f'nu{sub("n")} = v{sub("n")} / (2pi x r{sub("n")})'), ('For H-like ions (any Z)', f'Same formulas: Z=1 for H, Z=2 for He+, Z=3 for Li{sup("2+")} ...'), ])] story += [sp(2), SS('3C. Spectral Series of Hydrogen')] story.append(gtable([ [f'Series','n{sub(1)}',f'n{sub(2)} starts','Region','Series Limit lambda','First Line wavelength'], ['Lyman','1','2,3,4...','UV','91.2 nm','H-La = 121.6 nm'], ['Balmer','2','3,4,5...','Visible/UV','364.7 nm','H-a=656.3 nm (red); H-b=486.1 nm (blue-green)'], ['Paschen','3','4,5,6...','Near IR','820.4 nm','1875.1 nm'], ['Brackett','4','5,6,7...','IR','1458.0 nm','4051.3 nm'], ['Pfund','5','6,7,8...','Far IR','2278.9 nm','7459.9 nm'], ['Humphreys','6','7,8,9...','Far IR','3281.9 nm','12371.9 nm'], ], cw=[22*mm,11*mm,22*mm,22*mm,24*mm,65*mm])) story += [sp(2)] for line in [ f'- Series limit: when n{sub(2)} --> infinity. Formula: 1/lambda_limit = R_H x Z{sup(2)}/n{sub(1)}{sup(2)}', f'- First line (longest wavelength in each series): transition from (n{sub(1)}+1) to n{sub(1)}.', '- Shortest wavelength = SERIES LIMIT. Longest wavelength = MINIMUM energy transition.', '- Number of spectral lines when electron falls from nth level to ground state: L = n(n-1)/2', f'- Lines from n{sub(2)} to n{sub(1)} (n{sub(2)} > n{sub(1)}): L = (n{sub(2)}-n{sub(1)})(n{sub(2)}-n{sub(1)}+1)/2', '- At room temperature, H atoms in ground state --> only LYMAN series in ABSORPTION.', ]: story.append(P(line)) story += [sp(2), tbox([ '[TRAP] Lyman is ULTRAVIOLET -- NOT visible. Balmer is partially visible (400-700 nm range only).', '[TRAP] H-alpha (656.3 nm, RED): n=3-->2. H-beta (486.1 nm, BLUE-GREEN): n=4-->2.', '[TRAP] PE = 2 x TE. KE = -TE. Therefore PE = -2 x KE. CRITICAL relationship.', '[TRAP] Bohr model valid ONLY for H-like species (one electron): H, He+, Li2+, Be3+...', '[TRAP] For He+ (Z=2): Energy = 4 x H energy; Radius = H radius / 2.', '[TRAP] Increasing n --> less negative energy --> less stable (weakly bound).', '[TRAP] Most negative energy = GROUND STATE = MOST STABLE state.', f'[TRAP] Time period T{sub("n")} proportional to n{sup(3)}/Z{sup(2)}. Frequency nu{sub("n")} proportional to Z{sup(2)}/n{sup(3)}.', '[TRAP] Energy is NEGATIVE (bound state). If E = 0, electron is free (ionised).', '[TRAP] Series limit has MAXIMUM FREQUENCY and MINIMUM WAVELENGTH in that series.', f'[TRAP] Rydberg: 1/lambda NOT nu. n{sub(1)} < n{sub(2)} always (electron drops from n{sub(2)} to n{sub(1)}).', ]), sp(3)] # ===== SECTION 4 ===== story.append(S('4. ELECTROMAGNETIC RADIATION &amp; PLANCK\'S QUANTUM THEORY')) story.append(SS('4A. Wave Properties of EM Radiation')) story.append(ftable([ ('Speed of light (c)', f'c = nu x lambda = 3 x 10{sup(8)} m/s (in vacuum)'), ('Wave number (nu~)', f'nu~ = 1/lambda unit: m{sup(-1)} or cm{sup(-1)}'), ('Frequency from wavelength', 'nu = c/lambda (inversely proportional)'), ('Relation: nu, lambda, nu~', 'nu = c x nu~ nu~ = nu/c'), ('Time period (T)', 'T = 1/nu unit: seconds'), ('Amplitude (A)', 'Height of wave crest -- determines INTENSITY (brightness)'), ])) story += [sp(2), SS('4B. EM Spectrum (Increasing Frequency / Decreasing Wavelength)')] story.append(gtable([ ['Radiation','Wavelength Range',f'Frequency Range (Hz)','Source / Use'], ['Radio waves','> 0.1 m',f'< 3 x 10{sup(9)}','Radio, TV broadcasting'], ['Microwaves','0.1 m - 1 mm',f'3x10{sup(9)} - 3x10{sup(11)}','Radar, microwave oven'], ['Infrared (IR)','1 mm - 700 nm',f'3x10{sup(11)} - 4.3x10{sup(14)}','Heat, night vision'], ['Visible light','700 - 400 nm',f'4.3x10{sup(14)} - 7.5x10{sup(14)}','VIBGYOR: V=400nm, R=700nm'], ['Ultraviolet (UV)','400 - 10 nm',f'7.5x10{sup(14)} - 3x10{sup(17)}','Sun lamps, sterilisation'], ['X-rays','10 nm - 0.01 nm',f'3x10{sup(17)} - 3x10{sup(19)}','Medical imaging'], [f'Gamma rays (gamma)','< 0.01 nm',f'> 3x10{sup(19)}','Nuclear reactions, cancer therapy'], ], cw=[28*mm,32*mm,40*mm,66*mm])) story += [sp(2), SS('4C. Planck\'s Quantum Theory')] for line in [ '- Energy is NOT emitted continuously but in DISCRETE packets called QUANTA. For light, a quantum = PHOTON.', '- Energy of one photon: E = hnu = hc/lambda = hc.nu~', '- Energy is directly proportional to frequency: E proportional to nu', '- Energy is inversely proportional to wavelength: E proportional to 1/lambda', f'- Planck\'s constant h = 6.626 x 10{sup(-34)} J.s = 6.626 x 10{sup(-34)} kg.m{sup(2)}.s{sup(-1)}', f'- 1 eV = 1.602 x 10{sup(-19)} J.', ]: story.append(P(line)) story += [sp(2), ftable([ ('Energy of one photon', 'E = hnu = hc/lambda = hc.nu~'), ('Energy in electron volts', 'E(eV) = 1240 / lambda(nm) [useful shortcut]'), ('n photons of frequency nu', 'E_total = n.h.nu'), (f'Planck\'s constant h', f'6.626 x 10{sup(-34)} J.s'), ('Momentum of photon', 'p = hnu/c = h/lambda = E/c'), ('Mass equivalent of photon', f'm_eff = E/c{sup(2)} = h/lambda.c (photon has NO rest mass)'), ])] story += [sp(2), tbox([ '[TRAP] nu and lambda are INVERSELY proportional. Higher frequency --> shorter wavelength --> higher energy.', '[TRAP] E proportional to nu (NOT lambda). Infrared photons have LESS energy than UV photons.', '[TRAP] Wave number nu~ = 1/lambda. It is NOT nu/c. Units: cm-1 (spectroscopy) or m-1 (SI).', '[TRAP] Visible light: VIBGYOR. Violet ~400 nm (highest energy visible). Red ~700 nm (lowest).', '[TRAP] Shortcut: E(eV) = 1240/lambda(nm). For lambda=400 nm: E=3.1 eV. For lambda=700 nm: E=1.77 eV.', '[TRAP] Photon has ZERO rest mass but HAS momentum (p = h/lambda) and energy (E = hnu).', '[TRAP] Gamma rays have HIGHEST frequency/energy. Radio waves have LOWEST.', ]), sp(3)] # ===== SECTION 5 ===== story.append(S('5. PHOTOELECTRIC EFFECT (Einstein, 1905)')) for line in [ '- When light of sufficiently high frequency falls on a metal surface, electrons are EJECTED. These are photoelectrons.', f'- THRESHOLD FREQUENCY (nu{sub(0)}): The minimum frequency needed to eject electrons. Below nu{sub(0)}, no electrons ejected regardless of intensity.', f'- WORK FUNCTION (phi or W): Minimum energy to remove an electron from the metal surface. phi = h.nu{sub(0)}.', ' OBSERVATIONS:', ' - Photoelectric effect is INSTANTANEOUS (no time lag).', ' - Number of electrons emitted proportional to INTENSITY of light.', ' - Kinetic energy of electrons depends ONLY on FREQUENCY, NOT intensity.', f' - Below threshold frequency (nu{sub(0)}), no electrons emitted even with very high intensity.', '- Einstein\'s explanation: Light consists of photons. One photon ejects one electron.', '- Energy of photon = Work function + Kinetic energy of ejected electron.', '- This proved the PARTICLE NATURE of light.', ]: story.append(P(line)) story += [sp(2), ftable([ ('Einstein\'s photoelectric equation', f'h.nu = phi + (1/2)m{sub("e")}v{sup(2)} = phi + KE_max'), ('Work function', f'phi = h.nu{sub(0)} (nu{sub(0)} = threshold frequency)'), ('Kinetic energy of photoelectron', f'KE = h.nu - phi = h(nu - nu{sub(0)}) = (1/2)m{sub("e")}v{sup(2)}'), ('Maximum velocity of electron', f'v_max = sqrt[2h(nu - nu{sub(0)}) / m{sub("e")}]'), (f'Stopping potential (V{sub(0)})', f'e.V{sub(0)} = KE_max = h.nu - phi'), ('Stopping potential (alternate)', f'V{sub(0)} = (h/e)(nu - nu{sub(0)}) [slope = h/e]'), (f'Threshold wavelength (lambda{sub(0)})', f'lambda{sub(0)} = hc / phi = c / nu{sub(0)}'), ('Number of photons (intensity I)', 'n_photons = I / h.nu = I.lambda / hc'), ('Photoelectric current', 'I_photo proportional to Intensity proportional to n_photons'), ])] story += [sp(2), tbox([ '[TRAP] Intensity = number of photons/area/sec. More intensity = MORE electrons, NOT more KE.', '[TRAP] KE of photoelectrons depends ONLY on frequency (nu), NOT on intensity.', f'[TRAP] If nu < nu{sub(0)}: NO photoelectric effect, no matter how intense the light.', f'[TRAP] Stopping potential V{sub(0)} depends on nu only: V{sub(0)} = (h/e)nu - phi/e. Slope of V{sub(0)} vs nu = h/e.', '[TRAP] Photoelectric effect proves PARTICLE nature of light. Diffraction proves WAVE nature.', '[TRAP] The effect is INSTANTANEOUS (no time delay, even at low intensity).', '[TRAP] Compton effect (X-ray scattering by electron) also proves particle nature of light.', '[TRAP] Different metals have different work functions: Na=2.3 eV, Al=4.3 eV, Pt=5.6 eV.', ]), sp(3)] # ===== SECTION 6 ===== story.append(S('6. DUAL NATURE OF MATTER -- de BROGLIE &amp; HEISENBERG')) story.append(SS('6A. de Broglie Hypothesis (1924)')) for line in [ '- de Broglie: just as radiation has dual nature (wave + particle), MATTER also has dual nature.', '- Every moving particle with mass m and velocity v is associated with a wave (de Broglie wave) of wavelength lambda.', '- This wave nature is significant only for microscopic particles. For macroscopic objects, lambda is negligibly small.', '- Davisson-Germer experiment (1927): electron diffraction through nickel crystal confirmed de Broglie hypothesis.', '- G.P. Thomson experiment: electron diffraction through thin gold films -- independent confirmation.', ]: story.append(P(line)) story += [sp(2), ftable([ ('de Broglie wavelength', 'lambda = h / mv = h / p [p = momentum]'), ('In terms of kinetic energy', 'lambda = h / sqrt(2m.KE)'), ('For particle accelerated through V', 'lambda = h / sqrt(2mqV) = h / sqrt(2meV) [for electron]'), ('For electron (lambda in A, V in volts)', 'lambda = 12.27 / sqrt(V) Angstroms'), ('For proton (lambda in A, V in volts)', 'lambda = 0.286 / sqrt(V) Angstroms'), (f'For neutron at temp T', f'lambda = h / sqrt(3mkT) [k = 1.38x10{sup(-23)} J/K]'), ('Relation: lambda and KE', 'lambda = h / sqrt(2m.KE) --> lambda proportional to 1/sqrt(KE)'), ('Relation: lambda and momentum', 'lambda = h/p --> lambda proportional to 1/p proportional to 1/v'), (f'Photon\'s de Broglie lambda', 'lambda = h/p = hc/E = c/nu (same as wave lambda -- consistent)'), ])] story += [sp(2), SS('6B. Heisenberg\'s Uncertainty Principle (1927)')] for line in [ '- It is FUNDAMENTALLY IMPOSSIBLE to determine simultaneously the EXACT position and EXACT momentum of a microscopic particle.', '- The more precisely we know the position, the less precisely we know the momentum, and vice versa.', '- This is NOT about instrument error -- it is a fundamental property of matter arising from wave-particle duality.', '- Consequence: The concept of a DEFINITE ORBIT for an electron is invalid. We can only speak of PROBABILITY.', '- This led to the concept of ORBITALS replacing Bohr\'s definite orbits.', ]: story.append(P(line)) story += [sp(2), ftable([ ('Position-momentum uncertainty', 'Delta-x . Delta-p >= h/4pi'), ('In terms of velocity', 'Delta-x . m.Delta-v >= h/4pi'), ('Minimum uncertainty product', 'Delta-x . Delta-p = h/4pi (minimum, also written as hbar/2)'), ('Energy-time uncertainty', 'Delta-E . Delta-t >= h/4pi'), ('hbar = h/2pi', f'hbar = 1.055 x 10{sup(-34)} J.s Delta-x . Delta-p >= hbar/2'), ('If Delta-x --> 0', 'Delta-p --> infinity (completely unknown momentum)'), ('If Delta-p --> 0', 'Delta-x --> infinity (completely unknown position)'), ])] story += [sp(2), tbox([ f'[TRAP] hbar = h/2pi = 1.055 x 10{sup(-34)} J.s. The uncertainty is >= hbar/2 (same as h/4pi).', '[TRAP] This principle makes Bohr\'s model fundamentally incorrect for multi-electron atoms.', '[TRAP] Heisenberg does NOT say we cannot measure precisely -- nature itself does not allow simultaneous precision.', f'[TRAP] For macroscopic objects (e.g. cricket ball, 0.1 kg): uncertainty ~10{sup(-33)} m -- practically irrelevant.', '[TRAP] de Broglie lambda proportional to 1/sqrt(V). Higher voltage --> smaller wavelength.', '[TRAP] de Broglie lambda is larger for lighter particles (smaller mass) at same velocity.', '[TRAP] Davisson-Germer proved wave nature of ELECTRONS using diffraction -- Nobel Prize 1937.', '[TRAP] Minimum Delta-x.Delta-p = h/4pi (NOT h/2pi, NOT h, NOT hbar alone).', ]), sp(3)] # ===== SECTION 7 ===== story.append(S('7. QUANTUM MECHANICAL MODEL OF ATOM')) for line in [ '- Quantum mechanics (Schrodinger, 1926) treats electron as a 3D WAVE (combining de Broglie + Heisenberg).', '- Schrodinger wave equation: H-hat.psi = E.psi (operator form). Solutions are wave functions psi.', f'- psi = wave function. psi{sup(2)} = probability density of finding the electron at a given point.', '- An ORBITAL is a 3D region around the nucleus where the probability of finding an electron is maximum (90-95% region).', '- Orbitals are characterised by THREE quantum numbers: n, l, m_l. Spin quantum number m_s describes the electron.', '- A node is a surface where psi = 0 (probability of finding electron = 0).', ]: story.append(P(line)) story.append(sp(3)) # ===== SECTION 8 ===== story.append(S('8. QUANTUM NUMBERS -- COMPLETE DETAIL')) story.append(SS('8A. Principal Quantum Number (n)')) for line in [ '- n = 1, 2, 3, 4, 5, 6, 7 ... (positive integers only).', '- Determines the ENERGY and SIZE of the orbital (distance from nucleus).', '- Higher n --> higher energy --> larger orbital --> electron farther from nucleus.', f'- Number of orbitals in n{sup("th")} shell = n{sup(2)}.', f'- Maximum electrons in n{sup("th")} shell = 2n{sup(2)}.', '- n=1: K shell; n=2: L shell; n=3: M shell; n=4: N shell.', ]: story.append(P(line)) story += [sp(2), SS('8B. Azimuthal Quantum Number / Angular Momentum Quantum Number (l)')] for line in [ '- l = 0, 1, 2, 3, ... (n-1). l can take n different values for a given n.', '- Determines the SHAPE of the orbital and the subshell.', '- l=0 --> s subshell (sphere); l=1 --> p subshell (dumbbell); l=2 --> d; l=3 --> f.', '- Angular momentum of electron: L = sqrt[l(l+1)] x h/2pi = sqrt[l(l+1)] x hbar', '- For s: L=0. For p: L = sqrt(2) x hbar. For d: L = sqrt(6) x hbar.', ]: story.append(P(line)) story += [sp(2), SS('8C. Magnetic Quantum Number (m_l)')] for line in [ '- m_l = -l, -(l-1), ..., 0, ..., (l-1), +l. Total values = (2l + 1).', '- Determines the ORIENTATION of the orbital in space.', '- For s (l=0): m_l = 0 --> 1 orbital.', '- For p (l=1): m_l = -1, 0, +1 --> 3 orbitals (px, py, pz).', '- For d (l=2): m_l = -2, -1, 0, +1, +2 --> 5 orbitals.', '- For f (l=3): m_l = -3, -2, -1, 0, +1, +2, +3 --> 7 orbitals.', '- z-component of angular momentum: L_z = m_l x hbar.', ]: story.append(P(line)) story += [sp(2), SS('8D. Spin Quantum Number (m_s)')] for line in [ '- m_s = +1/2 (spin up, arrow up) or -1/2 (spin down, arrow down). ONLY these two values.', '- Represents the intrinsic spin angular momentum of the electron.', '- Spin angular momentum: S = sqrt[s(s+1)] x hbar = (sqrt3/2) x hbar.', '- Two electrons in the same orbital MUST have opposite spins (+1/2 and -1/2).', ]: story.append(P(line)) story += [sp(2), SS('8E. Quantum Number Summary Table')] story.append(gtable([ ['n','l values','Subshells','m_l values','Orbitals/subshell',f'Max e{sup("-")}/subshell','Total orbitals',f'Max e{sup("-")}'], ['1','0','1s','0','1','2','1','2'], ['2','0, 1','2s, 2p','0; -1,0,+1','1, 3','2, 6','4','8'], ['3','0,1,2','3s,3p,3d','0; -1,0,+1; -2,-1,0,+1,+2','1, 3, 5','2, 6, 10','9','18'], ['4','0,1,2,3','4s,4p,4d,4f','0; ...; ...; -3 to +3','1,3,5,7','2,6,10,14','16','32'], ], cw=[10*mm,16*mm,22*mm,42*mm,22*mm,20*mm,20*mm,14*mm])) story += [sp(2), ftable([ (f'Number of orbitals in n{sup("th")} shell', f'n{sup(2)}'), (f'Max electrons in n{sup("th")} shell', f'2n{sup(2)}'), ('Number of subshells in nth shell', 'n (l = 0, 1, 2, ..., n-1)'), ('Number of orbitals in subshell l', '2l + 1'), ('Max electrons in subshell l', '2(2l + 1)'), ('Angular momentum', 'L = sqrt[l(l+1)] x hbar'), ('Spin angular momentum', 'S = sqrt[s(s+1)] x hbar = (sqrt3/2) x hbar [s = 1/2]'), ('z-component of L', 'L_z = m_l x hbar'), ])] story += [sp(2), tbox([ '[TRAP] l goes from 0 to (n-1) ONLY. For n=2: l=0,1 only. For n=3: l=0,1,2 only.', '[TRAP] m_l has (2l+1) values. For l=3: 2(3)+1 = 7 values (-3 to +3).', '[TRAP] m_s = +1/2 or -1/2 ONLY. No other values exist.', '[TRAP] Each orbital holds MAXIMUM 2 electrons (opposite spins -- Pauli exclusion principle).', '[TRAP] 4s orbital: n=4, l=0. 3d orbital: n=3, l=2. 2p orbital: n=2, l=1.', '[TRAP] Angular momentum of s orbital = 0 (NOT hbar -- it is ZERO for s orbital).', '[TRAP] 4th shell: 16 orbitals, max 32 electrons. Subshells: 4s, 4p, 4d, 4f.', '[TRAP] For n=3: total orbitals = 9 (1+3+5 = 9). Max electrons = 18.', ]), sp(3)] # ===== SECTION 9 ===== story.append(S('9. SHAPES OF ORBITALS &amp; NODES')) story.append(SS('9A. Node Formulas')) story.append(ftable([ ('Radial (spherical) nodes', 'n - l - 1'), ('Angular (planar/conical) nodes', 'l'), ('Total nodes', 'n - 1'), ('1s (n=1, l=0)', 'Radial=0, Angular=0, Total=0'), ('2s (n=2, l=0)', 'Radial=1, Angular=0, Total=1'), ('2p (n=2, l=1)', 'Radial=0, Angular=1, Total=1'), ('3s (n=3, l=0)', 'Radial=2, Angular=0, Total=2'), ('3p (n=3, l=1)', 'Radial=1, Angular=1, Total=2'), ('3d (n=3, l=2)', 'Radial=0, Angular=2, Total=2'), ('4s (n=4, l=0)', 'Radial=3, Angular=0, Total=3'), ('4p (n=4, l=1)', 'Radial=2, Angular=1, Total=3'), ('4d (n=4, l=2)', 'Radial=1, Angular=2, Total=3'), ('4f (n=4, l=3)', 'Radial=0, Angular=3, Total=3'), ])) story += [sp(2), SS('9B. Orbital Shapes')] for line in [ ' s ORBITAL (l=0):', ' - Spherically symmetrical. 1s: single sphere. 2s: two spheres (1 radial node). 3s: three regions (2 radial nodes).', ' - All s orbitals have NON-ZERO electron density at nucleus.', ' - Only ONE orientation (m_l = 0 only).', '', ' p ORBITALS (l=1):', ' - Dumbbell (double-lobed) shape along an axis.', ' - THREE p orbitals: px (x-axis), py (y-axis), pz (z-axis). All degenerate.', ' - Each p orbital has ONE angular node (a plane through the nucleus).', ' - p orbitals have ZERO electron density at the nucleus.', ' - 2p: 0 radial nodes. 3p: 1 radial node. 4p: 2 radial nodes.', '', ' d ORBITALS (l=2):', ' - FIVE d orbitals: dxy, dyz, dxz, dx2-y2, dz2.', ' - dxy, dyz, dxz: four-leaf clover shape between axes.', ' - dx2-y2: four-leaf clover along x and y axes.', ' - dz2: UNIQUE -- dumbbell along z-axis WITH a doughnut ring in xy-plane.', ' - All five d orbitals are degenerate -- 2 angular nodes each.', '', ' f ORBITALS (l=3):', ' - SEVEN f orbitals -- complex, multi-lobed shapes. 3 angular nodes each.', ' - f orbitals involved in lanthanides (4f) and actinides (5f) filling.', ]: story.append(P(line)) story += [sp(2), tbox([ '[TRAP] Radial nodes = n-l-1. For 3d (n=3, l=2): 3-2-1 = 0 radial nodes. ZERO, not 1.', '[TRAP] Angular nodes = l. For p (l=1): 1. For d (l=2): 2.', '[TRAP] Total nodes = n-1 ALWAYS. For 3p: 1 radial + 1 angular = 2 total = 3-1=2. Correct.', '[TRAP] 2s and 2p have SAME total nodes (1 each), but different types (radial vs angular).', '[TRAP] dz2 is unique in shape but HAS SAME ENERGY as other 4 d orbitals (degenerate).', '[TRAP] s orbital has NON-ZERO density at nucleus. p, d, f orbitals have ZERO density at nucleus.', ]), sp(3)] # ===== SECTION 10 ===== story.append(S('10. ELECTRONIC CONFIGURATION -- RULES &amp; PRINCIPLES')) story.append(SS('10A. Aufbau Principle -- Filling Order')) for line in [ '- Orbitals filled in order of INCREASING ENERGY (increasing n+l value).', '- If two orbitals have the SAME (n+l) value, fill the one with LOWER n first.', '- Order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p', ]: story.append(P(line)) story += [sp(2), gtable([ ['Orbital','n','l','n+l','Filling Order'], ['1s','1','0','1','1st'], ['2s','2','0','2','2nd'], ['2p','2','1','3','3rd (same n+l as 3s, but n=2 < 3)'], ['3s','3','0','3','4th'], ['3p','3','1','4','5th'], ['4s','4','0','4','6th'], ['3d','3','2','5','7th (same n+l as 4p, n=3 < 4)'], ['4p','4','1','5','8th'], ['5s','5','0','5','9th'], ['4d','4','2','6','10th'], ['5p','5','1','6','11th'], ['6s','6','0','6','12th'], ['4f','4','3','7','13th (same n+l as 5d, n=4 < 5)'], ['5d','5','2','7','14th'], ['6p','6','1','7','15th'], ['7s','7','0','7','16th'], ], cw=[20*mm,14*mm,12*mm,14*mm,106*mm])] story += [sp(2), SS('10B. Pauli\'s Exclusion Principle')] for line in [ '- No two electrons in an atom can have all FOUR quantum numbers (n, l, m_l, m_s) identical.', '- Each orbital is characterised by a UNIQUE set of (n, l, m_l). Two electrons share an orbital only if SPIN is opposite.', '- Maximum 2 electrons per orbital.', '- Max electrons in a subshell: 2(2l+1). s: 2, p: 6, d: 10, f: 14.', f'- Max electrons in n{sup("th")} shell: 2n{sup(2)}. K: 2, L: 8, M: 18, N: 32.', ]: story.append(P(line)) story += [sp(2), SS('10C. Hund\'s Rule of Maximum Multiplicity')] for line in [ '- When filling DEGENERATE orbitals, electrons occupy each orbital SINGLY with PARALLEL SPINS before pairing begins.', '- The state with maximum unpaired electrons has MAXIMUM SPIN MULTIPLICITY = ground state.', '- Spin multiplicity = 2S + 1 where S = total spin = (no. of unpaired electrons) x (1/2).', '- Half-filled (p3, d5, f7) and fully-filled (p6, d10, f14) subshells are EXTRA STABLE.', ' - (a) Symmetrical distribution of electron density.', ' - (b) Maximum exchange energy (more parallel-spin pairs = more stability).', '- Examples: N: 2p3 (up up up). O: 2p4 (up-dn up up). Cr: 3d5.4s1. Cu: 3d10.4s1.', ]: story.append(P(line)) story += [sp(2), tbox([ '[TRAP] 4s fills BEFORE 3d (Aufbau) but 4s is IONISED (removed) BEFORE 3d when forming cations.', '[TRAP] In cations, 3d is lower in energy than 4s -- that is why 4s is removed first.', '[TRAP] Fe: [Ar]3d6.4s2. Fe2+: [Ar]3d6 (removed both 4s). Fe3+: [Ar]3d5 (removed 2 from 4s, 1 from 3d).', '[TRAP] Cr (Z=24): [Ar]3d5.4s1 -- NOT [Ar]3d4.4s2. Half-filled 3d5 is extra stable.', '[TRAP] Cu (Z=29): [Ar]3d10.4s1 -- NOT [Ar]3d9.4s2. Fully-filled 3d10 is extra stable.', '[TRAP] Spin multiplicity: 2S+1. For N (3 unpaired e-): S=3/2, multiplicity=4.', '[TRAP] Exchange energy: more parallel-spin pairs = more exchange energy = more stability.', ]), sp(3)] # ===== SECTION 11 ===== story.append(S('11. ELECTRONIC CONFIGURATIONS -- ALL NEET-IMPORTANT ELEMENTS')) story.append(SS('11A. Elements Z = 1 to 30')) story.append(gtable([ ['Z','Element','Configuration',f'Unpaired e{sup("-")}'], ['1','H (Hydrogen)','1s1','1'], ['2','He (Helium)','1s2','0 (noble gas)'], ['3','Li (Lithium)','[He] 2s1','1'], ['4','Be (Beryllium)','[He] 2s2','0'], ['5','B (Boron)','[He] 2s2.2p1','1'], ['6','C (Carbon)','[He] 2s2.2p2','2'], ['7','N (Nitrogen)','[He] 2s2.2p3','3 (half-filled 2p)'], ['8','O (Oxygen)','[He] 2s2.2p4','2'], ['9','F (Fluorine)','[He] 2s2.2p5','1'], ['10','Ne (Neon)','[He] 2s2.2p6','0 (noble gas)'], ['11','Na (Sodium)','[Ne] 3s1','1'], ['12','Mg (Magnesium)','[Ne] 3s2','0'], ['13','Al (Aluminium)','[Ne] 3s2.3p1','1'], ['14','Si (Silicon)','[Ne] 3s2.3p2','2'], ['15','P (Phosphorus)','[Ne] 3s2.3p3','3 (half-filled 3p)'], ['16','S (Sulphur)','[Ne] 3s2.3p4','2'], ['17','Cl (Chlorine)','[Ne] 3s2.3p5','1'], ['18','Ar (Argon)','[Ne] 3s2.3p6','0 (noble gas)'], ['19','K (Potassium)','[Ar] 4s1','1'], ['20','Ca (Calcium)','[Ar] 4s2','0'], ['21','Sc (Scandium)','[Ar] 3d1.4s2','1'], ['22','Ti (Titanium)','[Ar] 3d2.4s2','2'], ['23','V (Vanadium)','[Ar] 3d3.4s2','3'], ['24','Cr (Chromium)','[Ar] 3d5.4s1 (EXCEPTION)','6 (all unpaired)'], ['25','Mn (Manganese)','[Ar] 3d5.4s2','5'], ['26','Fe (Iron)','[Ar] 3d6.4s2','4'], ['27','Co (Cobalt)','[Ar] 3d7.4s2','3'], ['28','Ni (Nickel)','[Ar] 3d8.4s2','2'], ['29','Cu (Copper)','[Ar] 3d10.4s1 (EXCEPTION)','1'], ['30','Zn (Zinc)','[Ar] 3d10.4s2','0'], ], cw=[12*mm,36*mm,72*mm,46*mm])) story += [sp(2), SS('11B. Important Ions &amp; More Elements')] story.append(gtable([ ['Species','Configuration','Notes'], ['Fe2+ (Z=26)','[Ar] 3d6','Remove 4s2 first, then nothing from 3d'], ['Fe3+ (Z=26)','[Ar] 3d5','Remove 4s2 + 1 from 3d; half-filled 3d5 is stable'], ['Cu+ (Z=29)','[Ar] 3d10','Remove 4s1; get fully-filled 3d10 -- stable'], ['Cu2+ (Z=29)','[Ar] 3d9','Remove 4s1 + 1 from 3d'], ['Zn2+ (Z=30)','[Ar] 3d10','Remove 4s2, keep 3d10'], ['Cr3+ (Z=24)','[Ar] 3d3','Remove 4s1 + 2 from 3d'], ['Mn2+ (Z=25)','[Ar] 3d5','Remove 4s2; half-filled 3d -- extra stable'], ['Pd (Z=46)','[Kr] 4d10','EXCEPTION: no 5s electrons at all'], ['Ag (Z=47)','[Kr] 4d10.5s1','EXCEPTION: fully-filled 4d10'], ['Mo (Z=42)','[Kr] 4d5.5s1','EXCEPTION: half-filled 4d5'], ['Au (Z=79)','[Xe] 4f14.5d10.6s1','EXCEPTION: fully-filled 5d10'], ['Pt (Z=78)','[Xe] 4f14.5d9.6s1','EXCEPTION'], ], cw=[28*mm,50*mm,88*mm])) story += [sp(2), tbox([ '[TRAP] 4s is always EMPTIED before 3d when forming transition metal cations.', '[TRAP] Cr: [Ar]3d5.4s1 has 6 unpaired electrons -- maximum paramagnetism for Period 4 TMs.', '[TRAP] Mn2+ = [Ar]3d5: half-filled 3d -- VERY stable, highest paramagnetism among 2+ ions of Period 4.', '[TRAP] Pd (Z=46): [Kr]4d10 -- NO s electrons at all in valence shell. A common trick question.', '[TRAP] Cu+: [Ar]3d10 -- fully filled -- DIAMAGNETIC. Cu2+: [Ar]3d9 -- PARAMAGNETIC.', '[TRAP] Zn, Cd, Hg: always have 3d10 (or 4d10, 5d10) and are DIAMAGNETIC (no unpaired e-).', '[TRAP] Species with all electrons paired = DIAMAGNETIC. With unpaired = PARAMAGNETIC.', ]), sp(3)] # ===== SECTION 12 ===== story.append(S('12. ISOTOPES, ISOBARS, ISOTONES &amp; ISOELECTRONIC SPECIES')) story.append(gtable([ ['Term','Definition','Examples'], ['Atomic Number (Z)','Z = Number of protons = Number of electrons (neutral atom)',''], ['Mass Number (A)','A = Z + N where N = number of neutrons',''], ['Number of neutrons','N = A - Z',''], ['Isotopes','Same Z, different A (same element, different mass)','1H, 2H(D), 3H(T); 12C, 13C, 14C; 35Cl, 37Cl'], ['Isobars','Same A, different Z (different elements)','40-18-Ar and 40-20-Ca; 31-15-P and 31-16-S'], ['Isotones','Same N, different Z','14C and 14N (both N=8); 31P and 32S (both N=16)'], ['Isoelectronic','Same number of electrons','N3-, O2-, F-, Ne, Na+, Mg2+, Al3+ (all 10 e-)'], ['Isostructural','Same structure/shape','SO4(2-) and PO4(3-) (both tetrahedral)'], ], cw=[32*mm,82*mm,52*mm])) story += [sp(2), tbox([ '[TRAP] Isotopes: SAME chemical properties (same Z), DIFFERENT physical properties.', '[TRAP] Isobars: DIFFERENT elements --> different chemical properties entirely.', '[TRAP] Isotones = same NEUTRON count (often confused with isotopes).', '[TRAP] N3-, O2-, F-, Ne, Na+, Mg2+, Al3+ are all isoelectronic (10 e- each) -- VERY common NEET question.', '[TRAP] CO and N2 are isoelectronic AND isostructural (both have triple bond, bond order 3).', '[TRAP] For 1H: A=1, Z=1, N=0 (no neutrons). Protium has ZERO neutrons.', '[TRAP] Deuterium (2H = D): 1 proton + 1 neutron. Tritium (3H = T): 1 proton + 2 neutrons.', ]), sp(3)] # ===== SECTION 13 ===== story.append(S('13. FAILURES OF BOHR\'S MODEL')) for line in [ '- ZEEMAN EFFECT: Could not explain splitting of spectral lines in a magnetic field.', '- STARK EFFECT: Could not explain splitting of spectral lines in an electric field.', '- FINE STRUCTURE: Could not explain closely spaced doublets/triplets in spectral lines.', '- MULTI-ELECTRON ATOMS: Completely failed for atoms with more than one electron (He, Li, etc.).', '- DE BROGLIE WAVE NATURE: Did not account for the wave nature of the electron.', '- HEISENBERG UNCERTAINTY: Violated the uncertainty principle by assigning definite paths (orbits) to electrons.', '- 3D STRUCTURE OF MOLECULES: Could not explain why atoms form molecules with specific 3D shapes.', '- INTENSITY OF SPECTRAL LINES: Could not predict relative intensities of spectral lines.', ]: story.append(P(line)) story.append(sp(3)) # ===== SECTION 14 ===== story.append(S('14. IMPORTANT CONSTANTS &amp; VALUES (Memorise All)')) story.append(gtable([ ['Constant / Quantity','Value'], ['Planck\'s constant h',f'6.626 x 10{sup(-34)} J.s = 6.626 x 10{sup(-34)} kg.m{sup(2)}.s{sup(-1)}'], ['hbar = h/2pi',f'1.055 x 10{sup(-34)} J.s'], ['Speed of light c',f'2.998 x 10{sup(8)} m/s ~ 3 x 10{sup(8)} m/s'], [f'Mass of electron m{sub("e")}',f'9.109 x 10{sup(-31)} kg = 0.000549 amu'], [f'Mass of proton m{sub("p")}',f'1.673 x 10{sup(-27)} kg = 1.007276 amu'], [f'Mass of neutron m{sub("n")}',f'1.675 x 10{sup(-27)} kg = 1.008665 amu'], ['Charge of electron e',f'1.602 x 10{sup(-19)} C'], ['e/m ratio of electron',f'1.758 x 10{sup(11)} C/kg'], ['Rydberg constant R_H',f'1.097 x 10{sup(7)} m{sup(-1)} = 109677 cm{sup(-1)}'], [f'Bohr radius a{sub(0)}',f'0.529 A = 52.9 pm = 5.29 x 10{sup(-11)} m'], ['1 electron volt (1 eV)',f'1.602 x 10{sup(-19)} J'], ['1 atomic mass unit (1 amu)',f'1.660 x 10{sup(-27)} kg = 931.5 MeV/c{sup(2)}'], [f'Avogadro constant N{sub("A")}',f'6.022 x 10{sup(23)} mol{sup(-1)}'], ['Boltzmann constant k_B',f'1.381 x 10{sup(-23)} J/K'], ['Ionisation energy of H',f'13.6 eV = 1312 kJ/mol = 2.18 x 10{sup(-18)} J'], ['1 Angstrom (A)',f'10{sup(-10)} m = 100 pm = 0.1 nm'], ['1 nanometre (nm)',f'10{sup(-9)} m = 10 A'], ['1 femtometre (fm)',f'10{sup(-15)} m (nuclear scale)'], ], cw=[60*mm,106*mm])) story.append(sp(3)) # ===== SECTION 15 ===== story.append(S('15. MASTER FORMULA QUICK-REFERENCE TABLE')) story.append(gtable([ ['#','Formula Name','Expression','Unit'], ['1','Photon energy','E = hnu = hc/lambda = hc.nu~','J'], ['2','Wave number','nu~ = 1/lambda',f'm{sup(-1)}'], ['3','Bohr radius (nth)',f'r{sub("n")} = 0.529 n{sup(2)}/Z A','A or m'], ['4','Electron velocity',f'v{sub("n")} = 2.18x10{sup(6)} Z/n m/s','m/s'], ['5','Orbital energy (eV)',f'E{sub("n")} = -13.6 Z{sup(2)}/n{sup(2)} eV','eV'], ['6','Orbital energy (J)',f'E{sub("n")} = -2.18x10{sup(-18)} Z{sup(2)}/n{sup(2)} J','J'], ['7','KE in Bohr orbit',f'KE = -E{sub("n")} = +13.6 Z{sup(2)}/n{sup(2)} eV','eV'], ['8','PE in Bohr orbit',f'PE = 2E{sub("n")} = -27.2 Z{sup(2)}/n{sup(2)} eV','eV'], ['9','Angular momentum','mvr = nh/2pi','J.s'], ['10','Rydberg equation',f'1/lambda = R_H x Z{sup(2)}(1/n{sub(1)}{sup(2)} - 1/n{sub(2)}{sup(2)})',f'm{sup(-1)}'], ['11','Spectral lines (n levels)','n(n-1)/2','--'], ['12','de Broglie','lambda = h/mv = h/p','m'], ['13','de Broglie (accelerated)',f'lambda = h/sqrt(2meV) --> 12.27/sqrt(V) A','A'], ['14','Heisenberg','Delta-x . Delta-p >= h/4pi','J.s'], ['15','Radial nodes','n - l - 1','--'], ['16','Angular nodes','l','--'], ['17','Total nodes','n - 1','--'], ['18','Orbitals in shell n',f'n{sup(2)}','--'], ['19','Electrons in shell n',f'2n{sup(2)}','--'], ['20','Orbitals in subshell l','2l + 1','--'], ['21','Electrons in subshell l','2(2l + 1)','--'], ['22','Angular momentum (orbital)','L = sqrt[l(l+1)] x hbar','J.s'], ['23','Nuclear radius',f'r = r{sub(0)} x A{sup("(1/3)")} r{sub(0)} = 1.2x10{sup(-15)} m','m'], ['24','Photoelectric equation',f'hnu = phi + (1/2)m{sub("e")}v{sup(2)} = phi + KE_max','J'], ['25','Work function',f'phi = h.nu{sub(0)}','J'], ['26','Stopping potential',f'e.V{sub(0)} = hnu - phi','V'], ['27','KE (photoelectric)',f'KE = h(nu - nu{sub(0)}) = hnu - phi','J'], ['28','Energy shortcut','E(eV) = 1240 / lambda(nm)','eV'], ['29','Ionisation energy',f'IE = 13.6 Z{sup(2)}/n{sup(2)} eV (from n{sup("th")} level)','eV'], ['30','Spin multiplicity','2S+1 where S = (unpaired e-) x (1/2)','--'], ], cw=[10*mm,44*mm,94*mm,18*mm])) story += [sp(3), HR(), Paragraph('Atomic Structure | Class 11 NEET Complete Revision Sheet | All sections covered | Print-optimised', foot_s)] doc.build(story) print("v2 done") PYEOF

python3 << 'PYEOF' from reportlab.lib.pagesizes import A4 from reportlab.lib.styles import ParagraphStyle from reportlab.lib.units import mm from reportlab.lib import colors from reportlab.platypus import (SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle, HRFlowable) from reportlab.lib.enums import TA_LEFT, TA_CENTER doc = SimpleDocTemplate( '/tmp/workspace/atomic_print/Atomic_Structure_Practice_Problems_v2.pdf', pagesize=A4, leftMargin=20*mm, rightMargin=20*mm, topMargin=18*mm, bottomMargin=18*mm ) BLACK = colors.black; WHITE = colors.white LGREY = colors.HexColor('#F0F0F0'); MGREY = colors.HexColor('#D0D0D0') def sty(name,**kw): base=dict(fontName='Helvetica',fontSize=10,leading=15,spaceBefore=1,spaceAfter=1,textColor=BLACK) base.update(kw); return ParagraphStyle(name,**base) title_s = sty('T', fontName='Helvetica-Bold', fontSize=22, alignment=TA_CENTER, spaceAfter=2, leading=26) subt_s = sty('ST', fontSize=11, alignment=TA_CENTER, spaceAfter=1) sec_s = sty('Sec', fontName='Helvetica-Bold', fontSize=12, alignment=TA_LEFT, spaceBefore=10, spaceAfter=3, textColor=WHITE, backColor=BLACK, leftIndent=5, leading=18) q_s = sty('Q', fontSize=10.5, leftIndent=4, leading=15, spaceBefore=4) opt_s = sty('Opt', fontSize=10, leftIndent=18, leading=14) sh_s = sty('SH', fontName='Helvetica-Bold', fontSize=10.5, spaceBefore=3, spaceAfter=1) sol_s = sty('Sol', fontSize=10, leftIndent=10, leading=14) ans_s = sty('Ans', fontName='Helvetica-Bold', fontSize=11, spaceBefore=2, spaceAfter=3) trap_s = sty('Tr', fontSize=9.5, leftIndent=6, leading=13, textColor=colors.HexColor('#333333')) inst_s = sty('Ins', fontSize=10, leftIndent=6, leading=15, spaceAfter=4) foot_s = sty('Ft', fontSize=8, alignment=TA_CENTER, textColor=colors.grey) def S(t): return Paragraph(f' {t} ', sec_s) def P(t): return Paragraph(t, q_s) def Opt(l,t): return Paragraph(f'<b>({l})</b> {t}', opt_s) def Sol(t): return Paragraph(t, sol_s) def Ans(l,t=''): return Paragraph(f'<b>Answer: ({l}){" -- " + t if t else ""}</b>', ans_s) def SH(t): return Paragraph(f'<b>{t}</b>', sh_s) def Trap(t): return Paragraph(f'<i>[NEET TRAP] {t}</i>', trap_s) def sp(h=2): return Spacer(1, h*mm) def HR(): return HRFlowable(width='100%', thickness=1, color=BLACK) def hr(): return HRFlowable(width='100%', thickness=0.4, color=MGREY) def sup(n): return f'<super>{n}</super>' def sub(n): return f'_{n}' story = [] story += [sp(2), Paragraph('<b>ATOMIC STRUCTURE -- PRACTICE PROBLEMS</b>', title_s), Paragraph('Class 11 | NEET Level | MCQs + Numericals + Assertion-Reason', subt_s), Paragraph('Full Step-by-Step Solutions Included', subt_s), HR(), sp(2)] story.append(S('PART A -- MULTIPLE CHOICE QUESTIONS (15 Questions)')) story.append(sp(1)) def mcq(num, qtext, opts, al, alabel, solns, trap=None): out = [] out.append(P(f'<b>Q{num}.</b> {qtext}')) for l,t in opts: out.append(Opt(l,t)) out.append(sp(1)) out.append(Ans(al, alabel)) out.append(SH('Solution:')) for s in solns: out.append(Sol(s)) if trap: out.append(Trap(trap)) out.append(hr()); out.append(sp(1)) return out story += mcq(1, 'The charge-to-mass (e/m) ratio of cathode rays was measured by J.J. Thomson using hydrogen gas. If the experiment is repeated with helium gas, the e/m ratio will:', [('A','Increase'),('B','Decrease'),('C','Remain the same'),('D','Depend on the voltage applied')], 'C','Remain the same', [f'Cathode rays consist of ELECTRONS -- they are universal particles regardless of the gas used.', f'e = 1.602 x 10{sup(-19)} C and m{sub("e")} = 9.109 x 10{sup(-31)} kg are fixed constants.', f'Therefore e/m = 1.758 x 10{sup(11)} C/kg is ALWAYS the same.', 'Properties of cathode rays are INDEPENDENT of the gas or electrode material.'], 'Canal ray e/m ratio DOES change with gas (depends on the positive ion). Only cathode ray e/m is constant.' ) story += mcq(2, f'An electron in hydrogen atom is in the 3{sup("rd")} orbit (n=3). The ratio of its Kinetic Energy to its Total Energy is:', [('A','-1'),('B','+1'),('C','-2'),('D','+2')], 'A','-1', [f'From Bohr\'s model: KE = -E{sub("n")} (KE is always positive, equal in magnitude to total energy).', f'Total energy E{sub("n")} is NEGATIVE (bound state).', f'Therefore: KE / E{sub("n")} = (-E{sub("n")}) / E{sub("n")} = -1.', f'Verification: KE = +13.6/n{sup(2)} eV; E{sub("n")} = -13.6/n{sup(2)} eV (for H, Z=1).', 'Ratio = (+13.6/n^2) / (-13.6/n^2) = -1. This is INDEPENDENT of n.'], f'Critical relationships: KE = -E{sub("n")}, PE = 2E{sub("n")}, PE/TE = +2, KE/TE = -1. Always hold in Bohr\'s model.' ) story += mcq(3, f'The wavelength of the first line of Lyman series is 121.6 nm. The wavelength of the second line of Balmer series (H-beta) is:', [('A','486.1 nm'),('B','656.3 nm'),('C','97.2 nm'),('D','410.2 nm')], 'A','486.1 nm', [f'Lyman first line: n=2 --> n=1. Balmer second line: n=4 --> n=2.', f'Using Rydberg: 1/lambda = R_H x Z{sup(2)}(1/n{sub(1)}{sup(2)} - 1/n{sub(2)}{sup(2)})', f'For Lyman first line: 1/lambda = R_H(1/1 - 1/4) = R_H x 3/4 => lambda = 121.6 nm (given)', f'For Balmer second line: 1/lambda = R_H(1/4 - 1/16) = R_H x 3/16', f'Ratio lambda_Balmer2 / lambda_Lyman1 = (3/4) / (3/16) = 4', f'lambda_Balmer2 = 4 x 121.6 = 486.4 nm ~ 486.1 nm (H-beta, blue-green).'], 'H-alpha (first Balmer, n=3-->2) = 656.3 nm (RED). H-beta (second Balmer, n=4-->2) = 486.1 nm (BLUE-GREEN).' ) story += mcq(4, f'The ionisation energy of He{sup("+")} ion (Z=2) from its ground state (n=1) is:', [('A','13.6 eV'),('B','27.2 eV'),('C','54.4 eV'),('D','6.8 eV')], 'C','54.4 eV', [f'He{sup("+")} is a hydrogen-like ion with Z = 2.', f'Energy of n{sup("th")} orbit: E{sub("n")} = -13.6 x Z{sup(2)}/n{sup(2)} eV', f'For He{sup("+")} in first orbit (n=1, Z=2): E{sub(1)} = -13.6 x 4/1 = -54.4 eV', f'Ionisation energy = 0 - E{sub(1)} = 0 - (-54.4) = +54.4 eV', f'Quick formula: IE(He{sup("+")}) = Z{sup(2)} x IE(H) = 4 x 13.6 = 54.4 eV'], f'For H-like ions: Energy scales as Z{sup(2)}. He{sup("+")} (Z=2): E = 4x H. Li{sup("2+")} (Z=3): E = 9x H.' ) story += mcq(5, 'An electron is accelerated through a potential difference of 100 V. Its de Broglie wavelength is:', [('A','1.227 Angstroms'),('B','0.123 Angstroms'),('C','12.27 Angstroms'),('D','0.0123 Angstroms')], 'A','1.227 Angstroms', ['For an electron accelerated through V volts: lambda = 12.27 / sqrt(V) Angstroms', 'lambda = 12.27 / sqrt(100) = 12.27 / 10 = 1.227 Angstroms', f'Verification: KE = eV = 1.602x10{sup(-17)} J', f'lambda = h / sqrt(2m{sub("e")}KE) = 6.626x10{sup(-34)} / sqrt(2 x 9.1x10{sup(-31)} x 1.602x10{sup(-17)})', '= 1.227 x 10^-10 m = 1.227 Angstroms (confirmed)'], 'lambda proportional to 1/sqrt(V). Higher voltage --> smaller wavelength. For proton: lambda = 0.286/sqrt(V) Angstroms.' ) story += mcq(6, 'The work function of cesium is 2.0 eV. Light of wavelength 400 nm is incident on it. The maximum kinetic energy of emitted photoelectrons is:', [('A','1.1 eV'),('B','3.1 eV'),('C','2.0 eV'),('D','No emission occurs')], 'A','1.1 eV', ['Energy of photon: E = 1240 / lambda(nm) = 1240 / 400 = 3.1 eV', 'Work function phi = 2.0 eV', 'Since E (3.1 eV) > phi (2.0 eV), photoelectric emission DOES occur.', 'KE_max = E - phi = 3.1 - 2.0 = 1.1 eV'], 'Always check if photon energy > work function before calculating KE. If E < phi, NO emission at any intensity.' ) story += mcq(7, 'Which of the following sets of quantum numbers is NOT possible?', [('A','n=2, l=1, m_l=0, m_s=+1/2'), ('B','n=3, l=2, m_l=-2, m_s=-1/2'), ('C','n=2, l=2, m_l=0, m_s=+1/2'), ('D','n=4, l=3, m_l=+3, m_s=-1/2')], 'C','n=2, l=2 is NOT possible', ['Rule: l can take values from 0 to (n-1) only.', 'For n=2: l can only be 0 or 1 (i.e., l = 0 to n-1 = 1).', 'l=2 is NOT allowed for n=2. This makes option (C) impossible.', 'Check others:', ' (A) n=2, l=1 (valid: l <= 1), m_l=0 (valid), m_s=+1/2 OK', ' (B) n=3, l=2 (valid: l <= 2), m_l=-2 (valid), m_s=-1/2 OK', ' (D) n=4, l=3 (valid: l <= 3), m_l=+3 (valid), m_s=-1/2 OK'], 'l ranges from 0 to (n-1). For n=1: only l=0. For n=2: l=0,1. For n=3: l=0,1,2. Never l=n or higher.' ) story += mcq(8, 'The number of radial nodes in a 3p orbital is:', [('A','0'),('B','1'),('C','2'),('D','3')], 'B','1', ['Radial nodes = n - l - 1', 'For 3p orbital: n=3, l=1 (p orbital)', 'Radial nodes = 3 - 1 - 1 = 1', 'Angular nodes = l = 1 (one nodal plane)', 'Total nodes = n - 1 = 3 - 1 = 2 (confirmed: 1 radial + 1 angular = 2)'], 'For 3d (n=3, l=2): radial nodes = 3-2-1 = 0 (NOT 1 -- common mistake!). For 2s: 2-0-1 = 1 radial node.' ) story += mcq(9, f'If the uncertainty in the position of an electron is 1.0 x 10{sup(-10)} m, the minimum uncertainty in its velocity is approximately: (m{sub("e")} = 9.1 x 10{sup(-31)} kg)', [('A',f'5.8 x 10{sup(5)} m/s'),('B',f'1.2 x 10{sup(5)} m/s'),('C',f'3.6 x 10{sup(5)} m/s'),('D',f'7.3 x 10{sup(5)} m/s')], 'A',f'5.8 x 10{sup(5)} m/s', ['From Heisenberg\'s uncertainty principle: Delta-x . m.Delta-v = h/4pi (minimum)', 'Delta-v = h / (4pi x m x Delta-x)', f'Delta-v = 6.626x10{sup(-34)} / (4 x 3.1416 x 9.1x10{sup(-31)} x 1.0x10{sup(-10)})', f'Delta-v = 6.626x10{sup(-34)} / (1.144x10{sup(-39)})', f'Delta-v = 5.79 x 10{sup(5)} ~ 5.8 x 10{sup(5)} m/s'], 'The "minimum" uncertainty corresponds to equality: Delta-x.Delta-p = h/4pi. For larger Delta-x, Delta-v can be smaller.' ) story += mcq(10, 'The electronic configuration of Cu (Z=29) is [Ar] 3d10.4s1 instead of [Ar] 3d9.4s2. This is because:', [('A','3d10.4s1 has lower energy due to fully-filled 3d subshell stability'), ('B','4s orbital has lower energy than 3d orbital'), ('C','Pauli\'s exclusion principle requires this configuration'), ('D','Aufbau principle directly demands 3d10.4s1')], 'A','Fully-filled 3d subshell stability', ['Expected configuration by simple Aufbau: [Ar] 3d9.4s2', 'Actual configuration: [Ar] 3d10.4s1', 'Fully-filled subshells (d10, f14) are EXTRA STABLE due to:', ' (a) Symmetrical distribution of electron density', ' (b) Maximum exchange energy (more electrons with parallel spins)', 'One electron from 4s promotes to 3d to achieve the fully-filled 3d10 configuration.', 'Similarly Cr (Z=24): [Ar] 3d5.4s1 -- half-filled 3d5 is extra stable.', 'Option (B) is wrong: in neutral atoms, 4s fills BEFORE 3d (Aufbau), but exceptions override.'], 'Cu+: [Ar]3d10 -- DIAMAGNETIC (fully filled). Cu2+: [Ar]3d9 -- PARAMAGNETIC (1 unpaired e-).' ) story += mcq(11, f'The ratio of radii of 1{sup("st")} orbit of H to 1{sup("st")} orbit of He{sup("+")} is:', [('A','1:1'),('B','2:1'),('C','1:2'),('D','4:1')], 'B','2:1', [f'Radius formula: r{sub("n")} = 0.529 x n{sup(2)}/Z Angstroms', 'For H (Z=1, n=1): r_1(H) = 0.529 x 1/1 = 0.529 A', f'For He{sup("+")} (Z=2, n=1): r_1(He+) = 0.529 x 1/2 = 0.2645 A', 'Ratio = 0.529 : 0.2645 = 2 : 1', 'General rule: For same n, radius proportional to 1/Z. H (Z=1) has twice the radius of He+ (Z=2).'], f'For H-like ions: r{sub("n")} proportional to n{sup(2)}/Z. Larger Z --> smaller orbit (electron pulled closer to nucleus).' ) story += mcq(12, 'Which spectral series of hydrogen lies (at least partially) in the VISIBLE region?', [('A','Lyman'),('B','Balmer'),('C','Paschen'),('D','Brackett')], 'B','Balmer (partially)', ['Lyman series: n_1=1 -- all lines in UV region (91.2 nm to 121.6 nm). NOT visible.', 'Balmer series: n_1=2 -- some lines in visible region (400-700 nm):', ' H-alpha = 656.3 nm (red) -- visible', ' H-beta = 486.1 nm (blue-green) -- visible', ' H-gamma = 434.0 nm (violet) -- visible', ' H-delta = 410.2 nm (violet) -- barely visible', ' Series limit = 364.7 nm -- UV (not visible)', 'Paschen, Brackett, Pfund, Humphreys: all in infrared region.'], 'Balmer series is only PARTIALLY visible (400-700 nm). Lines below 400 nm fall in UV. Only 4 lines clearly visible.' ) story += mcq(13, f'The total number of orbitals in the 4{sup("th")} shell (N shell) is:', [('A','9'),('B','16'),('C','12'),('D','32')], 'B','16', [f'Number of orbitals in n{sup("th")} shell = n{sup(2)}', 'For n=4: number of orbitals = 4^2 = 16', 'Breakdown: 4s (1 orbital) + 4p (3 orbitals) + 4d (5 orbitals) + 4f (7 orbitals) = 16 orbitals', f'Maximum electrons = 2n{sup(2)} = 2 x 16 = 32 (each orbital holds 2 electrons)'], f'Do NOT confuse: number of orbitals = n{sup(2)} = 16; maximum electrons = 2n{sup(2)} = 32 (option D is electrons, not orbitals).' ) story += mcq(14, 'Which of the following is an isoelectronic pair?', [('A','CO_2 and NO_2'),('B','N_2 and CO'),('C','O_2 and N_2'),('D','H_2O and H_2S')], 'B','N_2 and CO', ['Isoelectronic species have the SAME number of electrons.', 'N_2: 2 x 7 = 14 electrons', 'CO: 6 + 8 = 14 electrons', 'N_2 and CO are ISOELECTRONIC (14 electrons each) AND isostructural (triple bond, bond order 3).', 'Check others:', ' (A) CO_2: 22 e-; NO_2: 23 e- -- NOT isoelectronic', ' (C) O_2: 16 e-; N_2: 14 e- -- NOT isoelectronic', ' (D) H_2O: 10 e-; H_2S: 18 e- -- NOT isoelectronic'], 'CO and N_2 are the most classic isoelectronic pair in NEET. Both have 14 electrons and triple bond (bond order 3).' ) story += mcq(15, f'The number of spectral lines possible when electrons in hydrogen atoms de-excite from n=5 to n=1 (ground state) is:', [('A','5'),('B','8'),('C','10'),('D','15')], 'C','10', ['When electrons fall from n=5 to n=1, they can land on any intermediate level.', 'Using formula: L = n(n-1)/2 where n = highest level = 5', 'L = 5 x (5-1) / 2 = 5 x 4 / 2 = 10 spectral lines', 'Breakdown by series:', ' Lyman (to n=1): 5->1, 4->1, 3->1, 2->1 = 4 lines', ' Balmer (to n=2): 5->2, 4->2, 3->2 = 3 lines', ' Paschen (to n=3): 5->3, 4->3 = 2 lines', ' Brackett (to n=4): 5->4 = 1 line', ' Total = 4+3+2+1 = 10 lines (confirmed)'], f'Formula L = n(n-1)/2 gives spectral lines from n to ground state. For n{sub(2)} to n{sub(1)}: L = (n{sub(2)}-n{sub(1)})(n{sub(2)}-n{sub(1)}+1)/2.' ) story += [sp(3), S('PART B -- NUMERICAL PROBLEMS (6 Problems)'), sp(1)] def num(n, qtext, given_lines, soln_lines, final_ans): out = [] out.append(P(f'<b>N{n}.</b> {qtext}')) out.append(SH('Given:')) for l in given_lines: out.append(Sol(l)) out.append(SH('Solution:')) for l in soln_lines: out.append(Sol(l)) out.append(Ans('', f'FINAL ANSWER: {final_ans}')) out.append(hr()); out.append(sp(1)) return out story += num(1, 'Calculate the wavelength (in nm) of the photon emitted when an electron in hydrogen transitions from n=4 to n=2.', ['Z=1 (hydrogen)', 'n_1=2 (lower level)', 'n_2=4 (upper level)', f'R_H = 1.097 x 10{sup(7)} m{sup(-1)}'], [f'Rydberg equation: 1/lambda = R_H x Z{sup(2)} x (1/n{sub(1)}{sup(2)} - 1/n{sub(2)}{sup(2)})', '1/lambda = 1.097x10^7 x 1 x (1/4 - 1/16)', '1/lambda = 1.097x10^7 x (4/16 - 1/16)', '1/lambda = 1.097x10^7 x 3/16', '1/lambda = 1.097x10^7 x 0.1875 = 2.057x10^6 m^-1', 'lambda = 1 / (2.057x10^6) = 4.86x10^-7 m = 486 nm', 'This is the H-beta line of the Balmer series (blue-green, visible light).'], 'lambda = 486 nm (H-beta Balmer line, blue-green, visible)' ) story += num(2, 'An electron is accelerated through a potential difference of 25 kV. Calculate its de Broglie wavelength.', ['V = 25 kV = 25,000 V', 'Formula: lambda = 12.27 / sqrt(V) Angstroms'], ['lambda = 12.27 / sqrt(25000)', 'sqrt(25000) = sqrt(25 x 1000) = 5 x sqrt(1000) = 5 x 31.62 = 158.1', 'lambda = 12.27 / 158.1 = 0.0776 Angstroms = 7.76 x 10^-12 m = 7.76 pm', f'Note: This is in the X-ray range -- used in electron microscopy.'], 'lambda = 7.76 x 10^-12 m = 7.76 pm = 0.0776 Angstroms' ) story += num(3, 'The work function of sodium is 2.3 eV. Find (a) threshold frequency and (b) threshold wavelength.', ['phi = 2.3 eV = 2.3 x 1.602x10^-19 J = 3.685x10^-19 J', f'h = 6.626 x 10{sup(-34)} J.s', 'c = 3x10^8 m/s'], [f'(a) Threshold frequency: phi = h.nu{sub(0)} --> nu{sub(0)} = phi/h', 'nu_0 = 3.685x10^-19 / 6.626x10^-34 = 5.56 x 10^14 Hz', '', f'(b) Threshold wavelength: lambda{sub(0)} = c / nu{sub(0)} = hc / phi', 'lambda_0 = 3x10^8 / 5.56x10^14 = 5.40 x 10^-7 m = 540 nm', 'This is the GREEN region of visible spectrum.', 'Any light with lambda < 540 nm (higher frequency) causes photoelectric emission from Na.'], '(a) nu_0 = 5.56 x 10^14 Hz (b) lambda_0 = 540 nm (green)' ) story += num(4, f'Calculate the radius and energy of the 3{sup("rd")} orbit of He{sup("+")} ion.', ['Z=2 (helium)', 'n=3', f'r{sub("n")} = 0.529 x n{sup(2)}/Z Angstroms', f'E{sub("n")} = -13.6 x Z{sup(2)}/n{sup(2)} eV'], [f'Radius: r{sub(3)} = 0.529 x (3){sup(2)} / 2 = 0.529 x 9/2 = 0.529 x 4.5 = 2.38 A', f'r{sub(3)} = 2.38 x 10{sup(-10)} m', '', f'Energy: E{sub(3)} = -13.6 x (2){sup(2)} / (3){sup(2)} = -13.6 x 4/9 = -6.04 eV', f'E{sub(3)} = -6.04 x 1.602x10{sup(-19)} J = -9.68 x 10{sup(-19)} J'], f'r{sub(3)}(He+) = 2.38 Angstroms E{sub(3)}(He+) = -6.04 eV' ) story += num(5, f'The stopping potential for a metal is 1.2 V when light of frequency 6.0 x 10{sup(14)} Hz is used. Calculate the work function.', [f'V{sub(0)} = 1.2 V', f'nu = 6.0 x 10{sup(14)} Hz', f'h = 6.626 x 10{sup(-34)} J.s', f'1 eV = 1.602 x 10{sup(-19)} J'], ['From Einstein\'s equation: h.nu = phi + e.V_0', 'phi = h.nu - e.V_0', 'h.nu = 6.626x10^-34 x 6.0x10^14 = 3.976x10^-19 J = 2.48 eV', 'e.V_0 = 1.2 eV (stopping potential directly gives KE_max in eV)', 'phi = 2.48 - 1.2 = 1.28 eV', '', 'Using h/e = 4.136x10^-15 eV.s:', 'phi = (h/e).nu - V_0 = 4.136x10^-15 x 6.0x10^14 - 1.2 = 2.48 - 1.2 = 1.28 eV (confirmed)'], 'Work function phi = 1.28 eV (slope of V_0 vs nu graph = h/e = 4.136x10^-15 eV.s)' ) story += num(6, 'Calculate the minimum uncertainty in the velocity of an electron (m_e = 9.1x10^-31 kg) if its position is measured within 0.1 nm.', ['Delta-x = 0.1 nm = 1.0x10^-10 m', f'm{sub("e")} = 9.1 x 10{sup(-31)} kg', f'h = 6.626 x 10{sup(-34)} J.s'], ['Heisenberg\'s Uncertainty Principle: Delta-x . m.Delta-v >= h/4pi', 'Minimum uncertainty: Delta-x . m.Delta-v = h/4pi', 'Delta-v = h / (4pi x m x Delta-x)', 'Delta-v = 6.626x10^-34 / (4 x 3.1416 x 9.1x10^-31 x 1.0x10^-10)', 'Delta-v = 6.626x10^-34 / 1.144x10^-39', 'Delta-v = 5.79 x 10^5 m/s', 'This is about 0.2% of the speed of light -- shows why definite orbits are impossible!'], 'Delta-v_min = 5.79 x 10^5 m/s ~ 5.8 x 10^5 m/s' ) story += [sp(3), S('PART C -- ASSERTION-REASON QUESTIONS (5 Questions)'), sp(1)] story.append(Paragraph( '<b>Instructions:</b> Choose:<br/>' '(A) Both Assertion (A) and Reason (R) are TRUE, and R is the correct explanation of A.<br/>' '(B) Both Assertion (A) and Reason (R) are TRUE, but R is NOT the correct explanation of A.<br/>' '(C) Assertion (A) is TRUE, but Reason (R) is FALSE.<br/>' '(D) Assertion (A) is FALSE, but Reason (R) is TRUE.', inst_s)) story.append(hr()) def ar(n, assertion, reason, al, expl): out = [] out.append(P(f'<b>AR{n}.</b>')) out.append(P(f'<b>Assertion (A):</b> {assertion}')) out.append(P(f'<b>Reason (R):</b> {reason}')) out.append(sp(1)) out.append(Ans(al)) out.append(SH('Explanation:')) for l in expl: out.append(Sol(l)) out.append(hr()); out.append(sp(1)) return out story += ar(1, f'The e/m ratio of cathode rays is the same regardless of the gas used in the discharge tube.', 'Cathode rays consist of electrons, which are identical subatomic particles present in all atoms.', 'A', ['Both A and R are TRUE, and R correctly explains A.', f'Cathode rays = streams of electrons. e = 1.602x10{sup(-19)} C and m = 9.109x10{sup(-31)} kg are constants.', f'Therefore e/m = 1.758x10{sup(11)} C/kg is ALWAYS the same regardless of gas used.', 'J.J. Thomson proved that electrons are universal to all matter.'] ) story += ar(2, 'Bohr\'s model is applicable only to hydrogen and hydrogen-like species (He+, Li2+, etc.).', 'Bohr\'s model fails to account for electron-electron repulsion in multi-electron atoms.', 'A', ['Both A and R are TRUE, and R correctly explains A.', 'Bohr\'s model assumes a SINGLE electron orbiting the nucleus -- no electron-electron repulsion term.', 'For multi-electron atoms (He, Li, etc.), electron repulsion significantly changes energy levels.', 'The model cannot handle these interactions, so it fails completely for atoms with 2+ electrons.', 'Works perfectly for H (1 e-), He+ (1 e-), Li2+ (1 e-), Be3+ (1 e-), etc.'] ) story += ar(3, 'The kinetic energy of photoelectrons does not depend on the intensity of incident light.', 'Kinetic energy of photoelectrons depends only on the frequency of light, not its intensity.', 'A', ['Both A and R are TRUE, and R correctly explains A.', 'Intensity = number of photons per unit area per second. More intensity = more photons = more electrons emitted.', 'Each photon has energy E = h.nu, which depends only on FREQUENCY (nu), not intensity.', 'Each photon ejects one electron. KE_max = h.nu - phi (depends only on nu and phi).', 'More intensity --> more electrons emitted (more photocurrent), NOT more KE per electron.'] ) story += ar(4, '4s orbital is filled before the 3d orbital in the ground state of potassium (Z=19).', 'In cations of transition metals, the 3d electrons are removed before 4s electrons.', 'B', ['Both A and R are TRUE, but R is NOT a correct explanation of A.', 'Assertion: TRUE -- Aufbau principle states 4s (n+l = 4+0 = 4) fills before 3d (n+l = 3+2 = 5).', 'Reason: TRUE -- when transition metals form cations, 4s is ionised first (3d is lower in energy in cations).', 'However, R does NOT explain A. The reason 4s fills before 3d is the n+l rule (Aufbau principle).', 'The ionisation order (R) is a completely different phenomenon caused by energy changes in cations.'] ) story += ar(5, 'The dz2 orbital has a unique shape compared to other d orbitals but has the same energy as them.', 'All five d orbitals in the same subshell are degenerate (same energy) in the absence of external fields.', 'A', ['Both A and R are TRUE, and R correctly explains A.', 'dz2 has a distinctive shape: dumbbell along z-axis + a doughnut (torus) ring in the xy-plane.', 'Other d orbitals (dxy, dxz, dyz, dx2-y2) have a four-leaf clover shape.', 'Despite different shapes, all five d orbitals in the same subshell have SAME ENERGY (degenerate)', '-- in the absence of any external electric or magnetic field.', 'Degeneracy is broken in presence of external fields (Zeeman effect/Stark effect).'] ) story += [sp(2), HR(), Paragraph('Atomic Structure Practice Problems | Class 11 NEET Level | 15 MCQs + 6 Numericals + 5 Assertion-Reason | Full Solutions', foot_s)] doc.build(story) print("Practice Problems v2 done") PYEOF

python3 << 'PYEOF' from reportlab.lib.pagesizes import A4 from reportlab.lib.styles import ParagraphStyle from reportlab.lib.units import mm from reportlab.lib import colors from reportlab.platypus import (SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle, HRFlowable, KeepTogether) from reportlab.lib.enums import TA_LEFT, TA_CENTER doc = SimpleDocTemplate( '/tmp/workspace/atomic_print/Atomic_Structure_Formula_Explanations.pdf', pagesize=A4, leftMargin=20*mm, rightMargin=20*mm, topMargin=18*mm, bottomMargin=18*mm ) BLACK = colors.black WHITE = colors.white LGREY = colors.HexColor('#F0F0F0') DGREY = colors.HexColor('#D0D0D0') FBOX = colors.HexColor('#F7F7F7') def sty(name, **kw): base = dict(fontName='Helvetica', fontSize=10, leading=15, spaceBefore=1, spaceAfter=1, textColor=BLACK) base.update(kw) return ParagraphStyle(name, **base) title_s = sty('T', fontName='Helvetica-Bold', fontSize=22, alignment=TA_CENTER, leading=26) subt_s = sty('ST', fontSize=11, alignment=TA_CENTER, spaceAfter=1) sec_s = sty('Sec',fontName='Helvetica-Bold', fontSize=12, alignment=TA_LEFT, spaceBefore=10, spaceAfter=3, textColor=WHITE, backColor=BLACK, leftIndent=5, leading=18) subsec_s = sty('SS', fontName='Helvetica-Bold', fontSize=11, spaceBefore=6, spaceAfter=2, leading=15) form_s = sty('F', fontName='Helvetica-Bold', fontSize=11, spaceBefore=4, spaceAfter=1, leftIndent=4, leading=15, backColor=LGREY) exp_s = sty('E', fontSize=10, leftIndent=10, leading=15, spaceBefore=1, spaceAfter=1) use_s = sty('U', fontSize=9.5, leftIndent=10, leading=13, spaceBefore=0, spaceAfter=2, textColor=colors.HexColor('#222222')) note_s = sty('N', fontSize=9.5, leftIndent=10, leading=13, spaceBefore=0, spaceAfter=3, textColor=colors.HexColor('#444444')) th_s = sty('TH', fontName='Helvetica-Bold', fontSize=9.5, textColor=WHITE, leading=13) td_s = sty('TD', fontSize=9.5, leading=13) foot_s = sty('Ft', fontSize=8, alignment=TA_CENTER, textColor=colors.grey) def S(t): return Paragraph(f' {t} ', sec_s) def SS(t): return Paragraph(f'<b>{t}</b>', subsec_s) def F(t): return Paragraph(f' FORMULA: {t}', form_s) def E(t): return Paragraph(t, exp_s) def U(t): return Paragraph(f'<i>USE: {t}</i>', use_s) def N(t): return Paragraph(f'<i>NOTE: {t}</i>', note_s) def sp(h=2): return Spacer(1, h*mm) def HR(): return HRFlowable(width='100%', thickness=1, color=BLACK) def hr(): return HRFlowable(width='100%', thickness=0.4, color=DGREY) def thr(): return HRFlowable(width='100%', thickness=0.2, color=LGREY) def sup(n): return f'<super>{n}</super>' def sub(n): return f'_{n}' # Formula explanation block def fblock(formula_str, terms, use_str, note_str=None): """Returns a KeepTogether block for one formula""" items = [] items.append(F(formula_str)) items.append(E('<b>Where:</b>')) for sym, meaning in terms: items.append(E(f' <b>{sym}</b> = {meaning}')) items.append(U(use_str)) if note_str: items.append(N(note_str)) items.append(thr()) return KeepTogether(items) story = [] # ===== TITLE ===== story += [sp(2), Paragraph('<b>ATOMIC STRUCTURE</b>', title_s), Paragraph('Section 16 -- Formula Explanations', subt_s), Paragraph('Every Formula | Every Symbol Explained | When &amp; How to Use', subt_s), HR(), sp(2)] story.append(Paragraph( 'This section explains EVERY formula in Atomic Structure. For each formula you will find: ' 'the formula itself, what every symbol/letter means, the units, when to apply it, ' 'and key tips to avoid mistakes in NEET.', sty('Intro', fontSize=10, leading=15, leftIndent=4, spaceAfter=6))) story.append(hr()) story.append(sp(2)) # ============================================================ # GROUP 1 -- BOHR'S MODEL # ============================================================ story.append(S('GROUP 1 -- BOHR\'S MODEL FORMULAS')) story.append(sp(1)) story.append(fblock( f'r{sub("n")} = 0.529 x n{sup(2)} / Z Angstroms (radius of n{sup("th")} orbit)', [ (f'r{sub("n")}', 'radius of the nth orbit (distance of electron from nucleus) -- in Angstroms (A)'), ('0.529 A', f'Bohr radius a{sub(0)} -- radius of 1st orbit of hydrogen (n=1, Z=1) -- a fixed constant'), ('n', 'principal quantum number = 1, 2, 3, 4 ... (shell number)'), ('Z', 'atomic number of the element (number of protons in nucleus)'), ], f'Use this to find the orbital radius of any H-like ion (H, He+, Li2+, Be3+...) in any orbit n. ' f'For n=1, Z=1 (hydrogen): r = 0.529 A. For n=2, Z=1: r = 0.529 x 4 = 2.116 A.', f'Radius increases as n{sup(2)} (quadruples when n doubles). Radius decreases as Z increases ' f'(He+ has half the radius of H for same n). Units: A (Angstroms) or convert to m (1 A = 10{sup(-10)} m).' )) story.append(fblock( f'v{sub("n")} = 2.18 x 10{sup(6)} x Z / n m/s (velocity of electron in n{sup("th")} orbit)', [ (f'v{sub("n")}', 'speed of the electron in the nth orbit -- in m/s'), (f'2.18 x 10{sup(6)} m/s', f'velocity of electron in 1st orbit of H (v{sub(1)} for n=1, Z=1) -- a constant'), ('Z', 'atomic number'), ('n', 'principal quantum number (orbit number)'), ], f'Use to find orbital speed. As n increases, v decreases (outer orbits are slower). ' f'As Z increases, v increases (stronger nuclear pull speeds the electron up).', f'v{sub("n")} proportional to Z/n. For H (n=1): v = 2.18 x 10{sup(6)} m/s ~ c/137 (much less than speed of light). ' f'Velocity decreases as orbit number increases -- opposite to what you might expect.' )) story.append(fblock( f'E{sub("n")} = -13.6 x Z{sup(2)} / n{sup(2)} eV (energy of electron in n{sup("th")} orbit)', [ (f'E{sub("n")}', 'total energy of the electron in the nth orbit -- always NEGATIVE for bound electron -- in eV'), ('-13.6 eV', f'energy of electron in 1st orbit of H (E{sub(1)} for n=1, Z=1) -- a constant (also = -13.6 eV = ionisation energy)'), ('Z', 'atomic number'), ('n', 'principal quantum number'), ], f'Most important formula in Bohr\'s model. Use to find energy, energy difference between orbits, ' f'ionisation energy, and spectral line wavelengths.', f'Energy is NEGATIVE because electron is BOUND (has lower energy than a free electron at E=0). ' f'More negative = more stable = harder to remove. n=1 is most stable (most negative energy). ' f'As n increases, E{sub("n")} becomes less negative (increases towards 0). ' f'At n = infinity: E = 0 (electron is free = ionised). ' f'In SI units: E{sub("n")} = -2.18 x 10{sup(-18)} x Z{sup(2)}/n{sup(2)} Joules.' )) story.append(fblock( f'KE = -E{sub("n")} = +13.6 Z{sup(2)}/n{sup(2)} eV (kinetic energy)', [ ('KE', 'kinetic energy of electron in nth orbit -- always POSITIVE'), (f'-E{sub("n")}', f'negative of the total energy -- since E{sub("n")} is negative, KE = -E{sub("n")} is positive'), ], 'KE is always positive and equals the magnitude of total energy. KE = -TE always.', f'Critical: KE = +13.6 Z{sup(2)}/n{sup(2)} eV. PE = -27.2 Z{sup(2)}/n{sup(2)} eV. TE = -13.6 Z{sup(2)}/n{sup(2)} eV. ' f'Relationships: KE = -TE, PE = 2TE, PE = -2KE. These come up CONSTANTLY in NEET MCQs.' )) story.append(fblock( f'IE = +13.6 x Z{sup(2)} / n{sup(2)} eV (ionisation energy from orbit n)', [ ('IE', 'ionisation energy = energy required to completely remove the electron from orbit n to infinity'), ('+13.6 eV', 'ionisation energy of H from ground state (n=1, Z=1)'), ('Z', 'atomic number'), ('n', 'orbit from which electron is being removed'), ], f'IE = 0 - E{sub("n")} = 0 - (-13.6 Z{sup(2)}/n{sup(2)}) = +13.6 Z{sup(2)}/n{sup(2)} eV. ' f'For H from ground state: IE = 13.6 eV = 1312 kJ/mol.', f'IE is always positive. IE decreases as n increases (easier to remove from outer orbits). ' f'IE increases as Z increases (harder to remove when nucleus has more protons). ' f'For He+ (Z=2, n=1): IE = 13.6 x 4 / 1 = 54.4 eV.' )) story.append(fblock( f'Delta-E = 13.6 Z{sup(2)} (1/n{sub(1)}{sup(2)} - 1/n{sub(2)}{sup(2)}) eV (energy of photon emitted/absorbed)', [ ('Delta-E', 'energy of the photon emitted or absorbed during electron transition -- always POSITIVE'), ('13.6 eV', 'Rydberg energy for H-like ions'), ('Z', 'atomic number of H-like ion'), (f'n{sub(1)}', 'lower energy orbit (smaller n) -- where electron lands after emission'), (f'n{sub(2)}', f'higher energy orbit (larger n, n{sub(2)} > n{sub(1)}) -- where electron starts before emission'), ], f'Use when asked for energy of photon emitted/absorbed in a transition. ' f'For EMISSION: electron goes from n{sub(2)} (higher) to n{sub(1)} (lower) and releases a photon. ' f'For ABSORPTION: electron goes from n{sub(1)} (lower) to n{sub(2)} (higher) and absorbs a photon.', f'Always keep n{sub(1)} < n{sub(2)} (n{sub(1)} = lower orbit, n{sub(2)} = upper orbit). ' f'Positive result = energy of photon. Use Delta-E = h.nu = hc/lambda to get wavelength.' )) story.append(fblock( f'1/lambda = R_H x Z{sup(2)} x (1/n{sub(1)}{sup(2)} - 1/n{sub(2)}{sup(2)}) (Rydberg equation)', [ ('1/lambda', f'wave number nu~ = reciprocal of wavelength -- unit: m{sup(-1)} or cm{sup(-1)}'), ('lambda', 'wavelength of the emitted/absorbed spectral line -- in metres'), ('R_H', f'Rydberg constant = 1.097 x 10{sup(7)} m{sup(-1)} = 109677 cm{sup(-1)} -- a fixed constant'), ('Z', 'atomic number (Z=1 for H, Z=2 for He+, etc.)'), (f'n{sub(1)}', f'lower orbit (integer, n{sub(1)} = 1 for Lyman, 2 for Balmer, 3 for Paschen...)'), (f'n{sub(2)}', f'upper orbit (integer, n{sub(2)} > n{sub(1)})'), ], f'THE most used formula for spectral lines. Gives wavelength of any spectral line of any H-like ion. ' f'n{sub(1)} identifies the series (1=Lyman, 2=Balmer, 3=Paschen, 4=Brackett, 5=Pfund). ' f'First line of each series: n{sub(2)} = n{sub(1)}+1. Series limit: n{sub(2)} = infinity.', f'This gives 1/lambda (NOT lambda directly). Always invert at the end to get lambda. ' f'Series limit wavelength (shortest in series, highest frequency): set n{sub(2)} = infinity, so 1/lambda = R_H x Z{sup(2)}/n{sub(1)}{sup(2)}.' )) story.append(fblock( f'T{sub("n")} proportional to n{sup(3)} / Z{sup(2)} and nu{sub("n")} proportional to Z{sup(2)} / n{sup(3)} (time period and frequency of revolution)', [ (f'T{sub("n")}', 'time period of revolution of electron in nth orbit (time for one complete revolution) -- in seconds'), (f'nu{sub("n")}', 'frequency of revolution = number of revolutions per second = 1/T_n -- in Hz'), ('n', 'orbit number'), ('Z', 'atomic number'), ], f'Use for MCQs asking about how T or nu changes as orbit changes. ' f'T{sub("n")} = 2pi.r{sub("n")} / v{sub("n")} (circumference / speed). ' f'nu{sub("n")} = v{sub("n")} / (2pi.r{sub("n")}).', f'T increases RAPIDLY with n (as n{sup(3)}): outer orbits take much longer per revolution. ' f'nu decreases as n increases. Both scale with Z. ' f'NEET loves asking: if n doubles, T becomes 8x (2{sup(3)}=8); nu becomes 1/8th.' )) story.append(sp(2)) # ============================================================ # GROUP 2 -- EM RADIATION & PLANCK # ============================================================ story.append(S('GROUP 2 -- ELECTROMAGNETIC RADIATION &amp; PLANCK\'S QUANTUM THEORY')) story.append(sp(1)) story.append(fblock( 'c = nu x lambda (wave equation for EM radiation)', [ ('c', f'speed of light in vacuum = 3 x 10{sup(8)} m/s -- a universal constant'), ('nu', 'frequency of radiation -- in Hz (hertz) = cycles per second = s{sup(-1)}'), ('lambda', 'wavelength of radiation -- in metres (or nm, A)'), ], 'Use to convert between frequency and wavelength. Given lambda, find nu = c/lambda. Given nu, find lambda = c/nu.', f'nu and lambda are INVERSELY proportional (higher frequency = shorter wavelength). ' f'Speed of light is CONSTANT in vacuum for all EM radiation. ' f'Conversions: 1 nm = 10{sup(-9)} m. 1 A = 10{sup(-10)} m.' )) story.append(fblock( 'E = h.nu = hc/lambda = hc.nu~ (energy of one photon -- Planck-Einstein relation)', [ ('E', 'energy of ONE photon -- in Joules (J) or electron-volts (eV)'), ('h', f'Planck\'s constant = 6.626 x 10{sup(-34)} J.s -- a universal constant'), ('nu', 'frequency of radiation -- in Hz'), ('lambda', 'wavelength of radiation -- in metres'), ('nu~', f'wave number = 1/lambda -- in m{sup(-1)} or cm{sup(-1)}'), ], 'Use for all photon energy calculations. Three equivalent forms -- use whichever you are given. ' f'SHORTCUT: E(eV) = 1240 / lambda(nm). This is the most useful form for NEET.', f'E is proportional to nu (not lambda). Higher frequency = higher energy. ' f'For n photons: E_total = n.h.nu. ' f'Photon has ZERO rest mass but has energy E = h.nu and momentum p = h/lambda = E/c.' )) story.append(fblock( f'E(eV) = 1240 / lambda(nm) (energy-wavelength shortcut)', [ ('E(eV)', 'energy of photon in electron-volts (eV)'), ('1240', 'a derived constant = hc in eV.nm units'), ('lambda(nm)', 'wavelength of photon in NANOMETRES (nm)'), ], 'FASTEST way to find photon energy in NEET. Visible light: 400-700 nm = 3.1-1.77 eV. ' 'UV has higher energy, IR has lower energy than visible.', 'Remember: lambda MUST be in nm, answer comes in eV. ' 'Examples: 400 nm --> 3.1 eV (violet). 500 nm --> 2.48 eV. 600 nm --> 2.07 eV. 700 nm --> 1.77 eV (red).' )) story.append(fblock( f'nu~ = 1/lambda (wave number)', [ ('nu~', f'wave number = number of wave cycles per unit length -- units: m{sup(-1)} or cm{sup(-1)}'), ('lambda', 'wavelength in same units as 1/nu~'), ], 'Used mainly in infrared spectroscopy. Wave number increases as wavelength decreases (higher energy = larger wave number).', f'nu~ = nu/c is WRONG. nu~ = 1/lambda is correct. ' f'In spectroscopy: unit is cm{sup(-1)} (wavenumber per centimetre). In SI: m{sup(-1)}.' )) story.append(sp(2)) # ============================================================ # GROUP 3 -- PHOTOELECTRIC EFFECT # ============================================================ story.append(S('GROUP 3 -- PHOTOELECTRIC EFFECT FORMULAS')) story.append(sp(1)) story.append(fblock( f'h.nu = phi + KE_max = phi + (1/2).m{sub("e")}.v{sup(2)} (Einstein\'s photoelectric equation)', [ ('h.nu', 'energy of the incident photon -- in Joules or eV'), ('phi', f'work function = minimum energy to eject electron from metal surface = h.nu{sub(0)} -- in J or eV'), ('KE_max', 'maximum kinetic energy of ejected photoelectron -- in J or eV'), (f'(1/2).m{sub("e")}.v{sup(2)}', f'classical KE formula where m{sub("e")} = electron mass = 9.1 x 10{sup(-31)} kg, v = max velocity'), ], 'Use for ALL photoelectric effect problems. Given photon energy and work function, find KE_max. ' 'Given KE_max and work function, find photon energy/frequency/wavelength.', f'KE_max = h.nu - phi = h(nu - nu{sub(0)}). KE is ZERO when nu = nu{sub(0)} (threshold). ' f'KE is NEGATIVE is impossible -- if h.nu < phi, NO emission occurs. ' f'Increasing INTENSITY increases number of electrons but NOT their KE. ' f'Increasing FREQUENCY increases KE but NOT the number of electrons.' )) story.append(fblock( f'phi = h.nu{sub(0)} (work function)', [ ('phi', 'work function of the metal -- minimum energy needed to eject one electron -- in J or eV'), ('h', f'Planck\'s constant = 6.626 x 10{sup(-34)} J.s'), (f'nu{sub(0)}', 'threshold frequency = minimum frequency needed for photoelectric emission -- in Hz'), ], f'Work function is a property of the METAL -- it is different for different metals. ' f'Higher phi = harder to eject electrons = needs higher frequency light.', f'Work functions: Na = 2.3 eV, K = 2.2 eV, Al = 4.3 eV, Zn = 4.3 eV, Pt = 5.6 eV. ' f'Lower work function metals (Na, K, Cs) respond to visible light. ' f'Higher work function metals need UV light.' )) story.append(fblock( f'e.V{sub(0)} = KE_max = h.nu - phi (stopping potential)', [ ('e', f'charge of electron = 1.602 x 10{sup(-19)} C'), (f'V{sub(0)}', 'stopping potential -- the MINIMUM reverse voltage needed to stop ALL photoelectrons -- in Volts'), ('KE_max', 'maximum kinetic energy of emitted photoelectrons -- in J or eV'), ], f'Stopping potential equals KE_max in eV. If KE_max = 2.5 eV, then V{sub(0)} = 2.5 V. ' f'Increasing frequency increases V{sub(0)}. Increasing intensity does NOT change V{sub(0)}.', f'V{sub(0)} = (h/e).nu - phi/e. This is a linear equation in nu. ' f'Slope of V{sub(0)} vs nu graph = h/e = 4.136 x 10{sup(-15)} V.s = 4.136 x 10{sup(-15)} eV.s -- gives Planck\'s constant! ' f'Y-intercept = -phi/e. X-intercept = nu{sub(0)} (threshold frequency).' )) story.append(fblock( f'lambda{sub(0)} = hc / phi = c / nu{sub(0)} (threshold wavelength)', [ (f'lambda{sub(0)}', 'threshold wavelength = maximum wavelength that can cause photoelectric emission -- in metres'), ('hc', f'h x c = 6.626x10{sup(-34)} x 3x10{sup(8)} = 1.988 x 10{sup(-25)} J.m'), ('phi', 'work function in Joules'), (f'nu{sub(0)}', 'threshold frequency in Hz'), ], 'Wavelengths SHORTER than threshold (lambda < lambda_0, higher frequency) will cause emission. ' 'Wavelengths LONGER than threshold (lambda > lambda_0, lower frequency) will NOT cause emission.', f'For phi in eV: lambda{sub(0)} = 1240/phi(eV) nm. Example: phi=2.0 eV --> lambda{sub(0)} = 1240/2.0 = 620 nm.' )) story.append(sp(2)) # ============================================================ # GROUP 4 -- DE BROGLIE & HEISENBERG # ============================================================ story.append(S('GROUP 4 -- de BROGLIE &amp; HEISENBERG FORMULAS')) story.append(sp(1)) story.append(fblock( 'lambda = h / mv = h / p (de Broglie wavelength)', [ ('lambda', 'de Broglie wavelength of the moving particle -- in metres'), ('h', f'Planck\'s constant = 6.626 x 10{sup(-34)} J.s'), ('m', 'mass of the particle -- in kg'), ('v', 'velocity of the particle -- in m/s'), ('p', 'momentum = mv -- in kg.m/s'), ], 'Use for ANY moving particle (electron, proton, neutron, ball, etc.). ' 'Heavier and faster particles have smaller wavelengths. ' 'Very significant only for microscopic particles (electrons, protons).', f'Lambda is INVERSELY proportional to both m and v. ' f'For a cricket ball (0.1 kg, 30 m/s): lambda ~ 10{sup(-34)} m -- undetectably small. ' f'For an electron (9.1x10{sup(-31)} kg, 10{sup(6)} m/s): lambda ~ 10{sup(-9)} m = 1 nm -- detectable by diffraction!' )) story.append(fblock( 'lambda = h / sqrt(2m.KE) (de Broglie wavelength from kinetic energy)', [ ('lambda', 'de Broglie wavelength -- in metres'), ('h', f'Planck\'s constant = 6.626 x 10{sup(-34)} J.s'), ('m', 'mass of particle -- in kg'), ('KE', 'kinetic energy of particle -- in Joules (J) NOTE: NOT in eV!'), ], 'Use when given kinetic energy instead of velocity. Derive from lambda = h/mv and KE = (1/2)mv^2.', f'KE must be in JOULES, not eV. Convert: 1 eV = 1.602 x 10{sup(-19)} J. ' f'This form leads to the accelerated-particle formula when KE = qV.' )) story.append(fblock( 'lambda = 12.27 / sqrt(V) Angstroms (de Broglie wavelength for accelerated electron)', [ ('lambda', 'de Broglie wavelength of the ELECTRON -- in Angstroms (A)'), ('12.27', f'a derived constant for electrons only = h / sqrt(2.m{sub("e")}.e) in A.V{sup("1/2")} units'), ('V', 'accelerating potential difference -- in VOLTS (V)'), ], 'FASTEST formula for NEET problems on electron wavelength. Always check units: V must be in Volts, answer is in Angstroms.', f'Derived: KE = e.V = (1/2)m{sub("e")}v{sup(2)} --> lambda = h/sqrt(2.m{sub("e")}.e.V). ' f'Numerically this gives 12.27/sqrt(V) A. For proton: lambda = 0.286/sqrt(V) A. ' f'Higher voltage --> smaller wavelength (electrons move faster).' )) story.append(fblock( 'Delta-x . Delta-p >= h / 4pi (Heisenberg\'s uncertainty principle)', [ ('Delta-x', 'uncertainty in position of the particle -- in metres'), ('Delta-p', 'uncertainty in momentum (p = mv) of the particle -- in kg.m/s'), ('h', f'Planck\'s constant = 6.626 x 10{sup(-34)} J.s'), ('4pi', '4 x 3.1416 = 12.566'), ('>= (greater or equal)', 'the product of uncertainties can be GREATER than h/4pi, but NEVER less'), ], 'If you know the uncertainty in position (Delta-x), find minimum uncertainty in momentum: ' 'Delta-p_min = h/(4pi.Delta-x). Then Delta-v = Delta-p/m.', f'Equivalently: Delta-x . Delta-p >= hbar/2 where hbar = h/2pi = 1.055 x 10{sup(-34)} J.s. ' f'Minimum uncertainty = equality: Delta-x . Delta-p = h/4pi = hbar/2. ' f'Energy-time version: Delta-E . Delta-t >= h/4pi. ' f'This is NOT experimental error -- it is a fundamental law of nature from wave-particle duality.' )) story.append(sp(2)) # ============================================================ # GROUP 5 -- QUANTUM NUMBERS # ============================================================ story.append(S('GROUP 5 -- QUANTUM NUMBER FORMULAS')) story.append(sp(1)) story.append(fblock( 'L = sqrt[l(l+1)] x hbar (orbital angular momentum of electron)', [ ('L', 'magnitude of the orbital angular momentum of the electron -- in J.s'), ('l', 'azimuthal quantum number = 0, 1, 2, 3 ... (n-1)'), ('hbar', f'h/2pi = 1.055 x 10{sup(-34)} J.s'), ('sqrt[l(l+1)]', 'the numerical factor that depends on the orbital type'), ], 'Use to find angular momentum of electron in a given orbital. l=0 (s): L=0. l=1 (p): L=sqrt(2).hbar. l=2 (d): L=sqrt(6).hbar.', f'NOTE: The Bohr model gives L = n.hbar (WRONG). Quantum mechanics gives L = sqrt[l(l+1)].hbar (CORRECT). ' f's orbitals have ZERO angular momentum (L=0), which Bohr\'s model could not predict. ' f'This is one of the failures of Bohr\'s model.' )) story.append(fblock( 'L_z = m_l x hbar (z-component of orbital angular momentum)', [ ('L_z', 'component of angular momentum along z-axis (chosen axis) -- in J.s'), ('m_l', 'magnetic quantum number = -l, -(l-1), ..., 0, ..., (l-1), +l'), ('hbar', f'h/2pi = 1.055 x 10{sup(-34)} J.s'), ], 'Tells you how the orbital is oriented relative to an external field. Different m_l values = different orientations.', 'L_z can be positive, negative, or zero. The number of possible L_z values = 2l+1 (same as number of m_l values). ' 'This is why a p subshell has 3 orientations (m_l = -1, 0, +1) and d subshell has 5 (m_l = -2,-1,0,+1,+2).' )) story.append(fblock( 'S = sqrt[s(s+1)] x hbar = (sqrt3/2) x hbar (spin angular momentum)', [ ('S', 'spin angular momentum of the electron -- in J.s -- ALWAYS the same value for electron'), ('s', 'spin quantum number = 1/2 for all electrons (fixed, not variable)'), ('sqrt[s(s+1)]', 'for s=1/2: sqrt[(1/2)(3/2)] = sqrt(3/4) = sqrt(3)/2'), ('hbar', f'h/2pi = 1.055 x 10{sup(-34)} J.s'), ], 'Electron spin is a fixed quantity -- you cannot change the spin angular momentum of an electron. ' 'The spin projection (m_s = +1/2 or -1/2) tells you if electron spins up or down.', 'm_s = +1/2 (spin up, arrow pointing up) OR m_s = -1/2 (spin down, arrow pointing down). ' 'Only TWO values for electron. Spin multiplicity = 2s+1 = 2(1/2)+1 = 2 for single electron.' )) story.append(fblock( f'Number of orbitals in n{sup("th")} shell = n{sup(2)} Max electrons in n{sup("th")} shell = 2n{sup(2)}', [ (f'n{sup(2)}', 'total number of distinct orbitals in the nth shell'), (f'2n{sup(2)}', 'maximum number of electrons that can fill the nth shell'), ('n', 'principal quantum number'), ], f'Quick check: n=1 --> 1 orbital, 2 e-. n=2 --> 4 orbitals, 8 e-. n=3 --> 9 orbitals, 18 e-. n=4 --> 16 orbitals, 32 e-.', f'Each orbital holds 2 electrons (one spin up, one spin down -- Pauli\'s principle). ' f'So max electrons = 2 x number of orbitals = 2n{sup(2)}. ' f'Within a shell: number of subshells = n, orbitals per subshell l = (2l+1).' )) story.append(sp(2)) # ============================================================ # GROUP 6 -- NODES # ============================================================ story.append(S('GROUP 6 -- NODE FORMULAS FOR ORBITALS')) story.append(sp(1)) story.append(fblock( 'Radial nodes = n - l - 1', [ ('n', 'principal quantum number (shell number)'), ('l', 'azimuthal quantum number (0 for s, 1 for p, 2 for d, 3 for f)'), ('Radial nodes', 'spherical surfaces where the electron density = 0 (psi = 0). ' 'These are shells WITHIN the orbital where there is ZERO probability of finding the electron.'), ], 'Calculate radial nodes for any orbital. Examples: 1s: 1-0-1=0. 2s: 2-0-1=1. 2p: 2-1-1=0. ' '3s: 3-0-1=2. 3p: 3-1-1=1. 3d: 3-2-1=0. 4s: 4-0-1=3.', 'As n increases (same l), more radial nodes appear. s orbitals have more radial nodes than p,d,f for same n. ' 'Radial nodes give the orbital a multi-layered appearance (like onion layers for s orbitals).' )) story.append(fblock( 'Angular nodes = l', [ ('l', 'azimuthal quantum number'), ('Angular nodes', 'flat planes (or cones) passing through the nucleus where electron density = 0. ' 'These determine the SHAPE of the orbital.'), ], 'l=0 (s): 0 angular nodes (sphere, no flat regions). l=1 (p): 1 angular node (one nodal plane). ' 'l=2 (d): 2 angular nodes (two nodal planes). l=3 (f): 3 angular nodes.', 'Angular nodes = l for ALL orbitals -- it is just the azimuthal quantum number. ' 'p orbital: 1 plane passes through nucleus (e.g., for pz: xy-plane is the node). ' 'd orbital: 2 planes pass through nucleus (this is why d orbitals look like 4-leaf clovers).' )) story.append(fblock( 'Total nodes = n - 1', [ ('n', 'principal quantum number'), ('Total nodes', 'sum of radial and angular nodes = n-1 for any orbital'), ], 'Quick check for ANY orbital: total nodes = n-1. Verify: radial (n-l-1) + angular (l) = n-l-1+l = n-1. Confirmed!', 'Examples: 1s: 0 total nodes. 2s: 1 node. 2p: 1 node. 3s: 2 nodes. 3p: 2 nodes. 3d: 2 nodes. 4f: 3 nodes. ' 'NOTE: 2s and 2p BOTH have 1 total node -- but 2s has 1 radial node (spherical shell) while 2p has 1 angular node (flat plane).' )) story.append(sp(2)) # ============================================================ # GROUP 7 -- ELECTRONIC CONFIGURATION # ============================================================ story.append(S('GROUP 7 -- ELECTRONIC CONFIGURATION FORMULAS')) story.append(sp(1)) story.append(fblock( 'Spin multiplicity = 2S + 1', [ ('S', 'total spin quantum number = sum of all unpaired electron spins = (number of unpaired electrons) x (1/2)'), ('2S+1', 'spin multiplicity -- a measure of how many unpaired electrons the atom has'), ], 'Use to find the spin multiplicity of an atom/ion from its ground state configuration. ' 'Count unpaired electrons, multiply by 1/2 to get S, then 2S+1.', 'Examples: H (1 unpaired e-): S=1/2, multiplicity=2 (doublet). ' 'N (3 unpaired e-): S=3/2, multiplicity=4 (quartet). ' 'C (2 unpaired e-): S=1, multiplicity=3 (triplet). ' 'High spin multiplicity = high paramagnetism. ' 'Multiplicity=1 (singlet) = all electrons paired = DIAMAGNETIC.' )) story.append(fblock( f'Max electrons in subshell l = 2(2l + 1)', [ ('l', 'azimuthal quantum number (l=0 for s, l=1 for p, l=2 for d, l=3 for f)'), ('(2l+1)', 'number of orbitals in subshell l'), ('2(2l+1)', 'max electrons (2 per orbital)'), ], 'l=0 (s): 2(1)=2 electrons. l=1 (p): 2(3)=6 electrons. l=2 (d): 2(5)=10 electrons. l=3 (f): 2(7)=14 electrons.', 'Derived from: number of orbitals = 2l+1. Each orbital holds 2 electrons (Pauli). So max = 2(2l+1).' )) story.append(sp(2)) # ============================================================ # GROUP 8 -- NUCLEAR/ATOMIC STRUCTURE # ============================================================ story.append(S('GROUP 8 -- NUCLEAR &amp; ATOMIC STRUCTURE FORMULAS')) story.append(sp(1)) story.append(fblock( f'r = r{sub(0)} x A{sup("(1/3)")} (nuclear radius formula)', [ ('r', 'radius of the atomic nucleus -- in metres or femtometres (fm)'), (f'r{sub(0)}', f'empirical constant = 1.2 x 10{sup(-15)} m = 1.2 fm'), ('A', 'mass number = total number of protons + neutrons in the nucleus'), ('A^(1/3)', 'cube root of the mass number'), ], 'Use to estimate the radius of any nucleus. Nuclear radius depends on MASS NUMBER (A), NOT atomic number (Z).', f'Key consequences: Nuclear VOLUME = (4/3)pi.r{sup(3)} proportional to A (volume proportional to mass number). ' f'Nuclear DENSITY = constant for all nuclei (does not depend on A or Z). ' f'Nuclear density ~ 10{sup(17)} kg/m{sup(3)} -- extremely high (1 cm{sup(3)} of nuclear matter would weigh 100 million tonnes!).' )) story.append(fblock( 'A = Z + N (mass number)', [ ('A', 'mass number = total number of nucleons (protons + neutrons) in the nucleus'), ('Z', 'atomic number = number of protons in the nucleus = number of electrons in neutral atom'), ('N', 'neutron number = number of neutrons in the nucleus = A - Z'), ], 'Fundamental definition. Use to find number of neutrons: N = A-Z. ' 'Example: Chlorine-35: A=35, Z=17, N=35-17=18 neutrons.', 'Isotopes: same Z, different A (different N). ' 'Isobars: same A, different Z. ' 'Isotones: same N, different Z and A. ' 'Isoelectronic: same total number of ELECTRONS (related to Z and charge, not A).' )) story.append(sp(2)) # ============================================================ # SYMBOL REFERENCE TABLE # ============================================================ story.append(S('SYMBOL &amp; CONSTANT REFERENCE TABLE')) story.append(sp(1)) story.append(Paragraph('Quick reference for every symbol used in Atomic Structure formulas:', exp_s)) story.append(sp(1)) sym_data = [ ['Symbol', 'Full Name', 'Value / Typical Range', 'Units'], ['n', 'Principal quantum number', '1, 2, 3, 4, 5, 6, 7 ...', 'dimensionless (integer)'], ['l', 'Azimuthal quantum number', '0, 1, 2, ..., (n-1)', 'dimensionless (integer)'], ['m_l', 'Magnetic quantum number', '-l, ..., 0, ..., +l', 'dimensionless (integer)'], ['m_s', 'Spin quantum number', '+1/2 or -1/2 only', 'dimensionless'], ['Z', 'Atomic number', '1, 2, 3, ... (protons in nucleus)', 'dimensionless (integer)'], ['A', 'Mass number', 'Z + N (nucleons in nucleus)', 'dimensionless (integer)'], ['N', 'Neutron number', 'A - Z', 'dimensionless (integer)'], ['h', 'Planck\'s constant', f'6.626 x 10{sup(-34)}', 'J.s'], ['hbar', 'h-bar (h/2pi)', f'1.055 x 10{sup(-34)}', 'J.s'], ['c', 'Speed of light', f'3 x 10{sup(8)}', 'm/s'], ['e', 'Elementary charge', f'1.602 x 10{sup(-19)}', 'C (Coulombs)'], ['m_e', 'Mass of electron', f'9.109 x 10{sup(-31)}', 'kg'], ['m_p', 'Mass of proton', f'1.673 x 10{sup(-27)}', 'kg'], ['m_n', 'Mass of neutron', f'1.675 x 10{sup(-27)}', 'kg'], ['a_0', 'Bohr radius', f'0.529 A = 5.29 x 10{sup(-11)}', 'm'], ['R_H', 'Rydberg constant', f'1.097 x 10{sup(7)}', f'm{sup(-1)}'], ['phi', 'Work function', 'varies by metal (2-6 eV typical)', 'eV or J'], ['nu_0', 'Threshold frequency', 'varies by metal', 'Hz'], ['lambda_0', 'Threshold wavelength', 'varies by metal', 'm or nm'], ['V_0', 'Stopping potential', 'varies with photon energy and phi', 'V (Volts)'], ['r_0', 'Nuclear radius constant', f'1.2 x 10{sup(-15)}', 'm = fm'], ['E_n', 'Orbital energy', '-13.6 Z^2/n^2 eV (always negative)', 'eV or J'], ['IE', 'Ionisation energy', '+13.6 Z^2/n^2 eV (always positive)', 'eV or kJ/mol'], ['KE', 'Kinetic energy', '+13.6 Z^2/n^2 eV (always positive)', 'eV or J'], ['PE', 'Potential energy', '-27.2 Z^2/n^2 eV (always negative)', 'eV or J'], ['lambda', 'Wavelength', '1 A to 10^8 m (full EM spectrum)', 'm, nm, or A'], ['nu', 'Frequency', f'10{sup(4)} to 10{sup(24)} Hz (full EM spectrum)', 'Hz = s^-1'], ['nu~', 'Wave number', '1/lambda', f'm{sup(-1)} or cm{sup(-1)}'], ['L', 'Orbital angular momentum', 'sqrt[l(l+1)] x hbar', 'J.s'], ['S', 'Spin angular momentum', '(sqrt3/2) x hbar (for electron)', 'J.s'], ['T_n', 'Time period of revolution', 'proportional to n^3/Z^2', 's'], ['v_n', 'Orbital velocity', 'proportional to Z/n', 'm/s'], ['r_n', 'Orbital radius', '0.529 n^2/Z A', 'A or m'], ] prows = [] for ri, row in enumerate(sym_data): st = th_s if ri == 0 else td_s prows.append([Paragraph(str(c), st) for c in row]) t = Table(prows, colWidths=[18*mm, 44*mm, 58*mm, 46*mm], repeatRows=1) t.setStyle(TableStyle([ ('GRID', (0,0), (-1,-1), 0.5, BLACK), ('BACKGROUND', (0,0), (-1,0), BLACK), ('VALIGN', (0,0), (-1,-1), 'TOP'), ('LEFTPADDING', (0,0), (-1,-1), 4), ('RIGHTPADDING', (0,0), (-1,-1), 4), ('TOPPADDING', (0,0), (-1,-1), 2), ('BOTTOMPADDING', (0,0), (-1,-1), 2), ] + [('BACKGROUND', (0,i), (-1,i), LGREY) for i in range(1, len(sym_data), 2)])) story.append(t) story.append(sp(3)) story += [HR(), Paragraph('Atomic Structure | Formula Explanations | All symbols defined | All formulas explained | NEET Class 11', foot_s)] doc.build(story) print("Formula Explanations PDF done!") PYEOF