from reportlab.lib.pagesizes import A4
from reportlab.lib import colors
from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle
from reportlab.lib.units import cm, mm
from reportlab.platypus import (
    SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle,
    HRFlowable, KeepTogether, PageBreak
)
from reportlab.lib.enums import TA_CENTER, TA_LEFT, TA_JUSTIFY
from reportlab.platypus import Flowable

OUTPUT = "/tmp/workspace/atomic-structure/Atomic_Structure_Complete.pdf"

doc = SimpleDocTemplate(
    OUTPUT,
    pagesize=A4,
    rightMargin=1.8*cm,
    leftMargin=1.8*cm,
    topMargin=2*cm,
    bottomMargin=2*cm,
)

W = A4[0] - 3.6*cm

# ── colour palette ──────────────────────────────────────────────
DARK_BLUE   = colors.HexColor("#1a237e")
MED_BLUE    = colors.HexColor("#1565c0")
LIGHT_BLUE  = colors.HexColor("#e3f2fd")
ACCENT      = colors.HexColor("#ff6f00")
FORMULA_BG  = colors.HexColor("#fff8e1")
FORMULA_BOR = colors.HexColor("#f57f17")
TABLE_HEAD  = colors.HexColor("#283593")
TABLE_ALT   = colors.HexColor("#e8eaf6")
TRAP_BG     = colors.HexColor("#fce4ec")
TRAP_BOR    = colors.HexColor("#c62828")
NOTE_BG     = colors.HexColor("#e8f5e9")
NOTE_BOR    = colors.HexColor("#2e7d32")
WHITE       = colors.white
BLACK       = colors.black
GREY        = colors.HexColor("#546e7a")

# ── styles ───────────────────────────────────────────────────────
styles = getSampleStyleSheet()

def S(name, **kw):
    return ParagraphStyle(name, **kw)

sTitle = S("sTitle",
    fontSize=22, fontName="Helvetica-Bold",
    textColor=WHITE, alignment=TA_CENTER,
    spaceAfter=4, spaceBefore=4)

sSubTitle = S("sSubTitle",
    fontSize=11, fontName="Helvetica",
    textColor=WHITE, alignment=TA_CENTER,
    spaceAfter=2)

sPart = S("sPart",
    fontSize=14, fontName="Helvetica-Bold",
    textColor=WHITE, alignment=TA_LEFT,
    spaceAfter=4, spaceBefore=8,
    leftIndent=6)

sSec = S("sSec",
    fontSize=12, fontName="Helvetica-Bold",
    textColor=MED_BLUE, alignment=TA_LEFT,
    spaceAfter=3, spaceBefore=6)

sSub = S("sSub",
    fontSize=10.5, fontName="Helvetica-Bold",
    textColor=DARK_BLUE, alignment=TA_LEFT,
    spaceAfter=2, spaceBefore=4)

sBody = S("sBody",
    fontSize=9.5, fontName="Helvetica",
    textColor=BLACK, alignment=TA_JUSTIFY,
    spaceAfter=3, leading=14)

sBullet = S("sBullet",
    fontSize=9.5, fontName="Helvetica",
    textColor=BLACK, alignment=TA_LEFT,
    spaceAfter=2, leading=13,
    leftIndent=14, bulletIndent=4)

sFormula = S("sFormula",
    fontSize=10.5, fontName="Helvetica-Bold",
    textColor=colors.HexColor("#e65100"),
    alignment=TA_CENTER,
    spaceAfter=3, spaceBefore=3, leading=16)

sFormulaNote = S("sFormulaNote",
    fontSize=9, fontName="Helvetica",
    textColor=colors.HexColor("#4e342e"),
    alignment=TA_LEFT,
    spaceAfter=2, leading=13)

sTrap = S("sTrap",
    fontSize=9.5, fontName="Helvetica-Bold",
    textColor=colors.HexColor("#b71c1c"),
    alignment=TA_LEFT, spaceAfter=2, leading=13)

sNote = S("sNote",
    fontSize=9.5, fontName="Helvetica",
    textColor=colors.HexColor("#1b5e20"),
    alignment=TA_LEFT, spaceAfter=2, leading=13)

sTableH = S("sTableH",
    fontSize=9, fontName="Helvetica-Bold",
    textColor=WHITE, alignment=TA_CENTER, leading=12)

sTableC = S("sTableC",
    fontSize=8.5, fontName="Helvetica",
    textColor=BLACK, alignment=TA_CENTER, leading=11)

sTableL = S("sTableL",
    fontSize=8.5, fontName="Helvetica",
    textColor=BLACK, alignment=TA_LEFT, leading=11)

# ── helpers ──────────────────────────────────────────────────────

def part_header(text):
    """Dark blue full-width banner for a PART"""
    data = [[Paragraph(text, sPart)]]
    t = Table(data, colWidths=[W])
    t.setStyle(TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), DARK_BLUE),
        ("ROWPADDING", (0,0), (-1,-1), 6),
        ("BOX", (0,0), (-1,-1), 0, WHITE),
    ]))
    return t

def section_header(text):
    return Paragraph(text, sSec)

def sub_header(text):
    return Paragraph(text, sSub)

def body(text):
    return Paragraph(text, sBody)

def bullet(text):
    return Paragraph(f"• {text}", sBullet)

def sp(h=4):
    return Spacer(1, h)

def hr():
    return HRFlowable(width="100%", thickness=0.5, color=colors.HexColor("#90a4ae"))

def formula_box(formula_text, notes=None):
    """Yellow bordered formula box"""
    content = [Paragraph(formula_text, sFormula)]
    if notes:
        for n in notes:
            content.append(Paragraph(n, sFormulaNote))
    inner = Table([[c] for c in content], colWidths=[W-20])
    inner.setStyle(TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), FORMULA_BG),
        ("BOX", (0,0), (-1,-1), 1.5, FORMULA_BOR),
        ("ROWPADDING", (0,0), (-1,-1), 5),
    ]))
    return inner

def trap_box(text):
    t = Table([[Paragraph("⚠ TRAP: " + text, sTrap)]], colWidths=[W])
    t.setStyle(TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), TRAP_BG),
        ("BOX", (0,0), (-1,-1), 1.2, TRAP_BOR),
        ("ROWPADDING", (0,0), (-1,-1), 5),
    ]))
    return t

def note_box(text):
    t = Table([[Paragraph("★ NOTE: " + text, sNote)]], colWidths=[W])
    t.setStyle(TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), NOTE_BG),
        ("BOX", (0,0), (-1,-1), 1.2, NOTE_BOR),
        ("ROWPADDING", (0,0), (-1,-1), 5),
    ]))
    return t

def make_table(headers, rows, col_widths=None, left_cols=None):
    if col_widths is None:
        col_widths = [W / len(headers)] * len(headers)
    left_cols = left_cols or []
    head_row = [Paragraph(h, sTableH) for h in headers]
    data = [head_row]
    for i, row in enumerate(rows):
        styled = []
        for j, cell in enumerate(row):
            st = sTableL if j in left_cols else sTableC
            styled.append(Paragraph(str(cell), st))
        data.append(styled)

    t = Table(data, colWidths=col_widths)
    style = [
        ("BACKGROUND", (0,0), (-1,0), TABLE_HEAD),
        ("ROWPADDING", (0,0), (-1,-1), 4),
        ("GRID", (0,0), (-1,-1), 0.4, colors.HexColor("#b0bec5")),
        ("VALIGN", (0,0), (-1,-1), "MIDDLE"),
    ]
    for i in range(1, len(data)):
        if i % 2 == 0:
            style.append(("BACKGROUND", (0,i), (-1,i), TABLE_ALT))
    t.setStyle(TableStyle(style))
    return t

# ── cover ─────────────────────────────────────────────────────────
def cover():
    data = [[
        Paragraph("ATOMIC STRUCTURE", sTitle),
    ]]
    t = Table(data, colWidths=[W])
    t.setStyle(TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), DARK_BLUE),
        ("ROWPADDING", (0,0), (-1,-1), 18),
        ("BOX", (0,0), (-1,-1), 0, WHITE),
    ]))
    sub_data = [[Paragraph("Complete Chapter | All Formulas | All Topics | Class 11 Chemistry | NEET / JEE", sSubTitle)]]
    sub_t = Table(sub_data, colWidths=[W])
    sub_t.setStyle(TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), MED_BLUE),
        ("ROWPADDING", (0,0), (-1,-1), 8),
    ]))
    return [t, sub_t, sp(10)]

# ═══════════════════════════════════════════════════════════════════
# BUILD STORY
# ═══════════════════════════════════════════════════════════════════
story = []
story += cover()

# ─────────────────────────────────────────────────────────────────
# PART 1 — DISCOVERY OF SUB-ATOMIC PARTICLES
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 1 — DISCOVERY OF SUB-ATOMIC PARTICLES"))
story.append(sp(6))

story.append(section_header("1.1  Cathode Ray Experiment  (J.J. Thomson, 1897)"))
story.append(body("A high-voltage discharge tube (evacuated glass tube with two metal electrodes) was used. Rays travel from cathode (–) to anode (+). These are <b>cathode rays</b>."))
story.append(sp(3))
story.append(sub_header("Observations of Cathode Rays:"))
for b in [
    "Travel in straight lines; cast sharp shadows",
    "Deflect towards the positive plate → carry negative charge",
    "Cause fluorescence on a ZnS screen",
    "Same e/m ratio regardless of cathode material or gas used → electrons are UNIVERSAL",
    "Discovery: the electron",
]:
    story.append(bullet(b))
story.append(sp(4))
story.append(formula_box(
    "e / m_e  =  1.758 × 10¹¹  C/kg",
    ["e = charge of electron = 1.602 × 10⁻¹⁹ C",
     "m_e = mass of electron = 9.109 × 10⁻³¹ kg",
     "This ratio is CONSTANT for cathode rays in ALL gases.",
     "Canal rays (positive ions) have VARYING e/m — different gases give different ion masses."]
))
story.append(sp(4))

story.append(section_header("1.2  Millikan's Oil Drop Experiment  (1909)"))
story.append(body("Measured the charge on an electron by balancing gravitational and electric forces on charged oil drops."))
story.append(formula_box(
    "e  =  1.602 × 10⁻¹⁹  C",
    ["Mass of electron  m_e = e ÷ (e/m) = 9.109 × 10⁻³¹ kg"]
))
story.append(sp(4))

story.append(section_header("1.3  Canal Ray Experiment  (Goldstein, 1886)"))
story.append(body("Cathode with holes (perforations). Rays observed BEHIND the cathode → travel opposite to cathode rays. <b>Discovery: Proton</b> (positively charged particle). The lightest positive ion from hydrogen gas is the proton (H⁺)."))
story.append(sp(3))
story.append(make_table(
    ["Particle", "Charge", "Mass (kg)", "Charge-to-mass (C/kg)"],
    [
        ["Proton (H⁺)", "+1.602 × 10⁻¹⁹ C", "1.673 × 10⁻²⁷", "9.58 × 10⁷"],
    ],
    col_widths=[W*0.25, W*0.25, W*0.25, W*0.25]
))
story.append(sp(4))

story.append(section_header("1.4  Discovery of Neutron  (Chadwick, 1932)"))
story.append(body("Bombarded beryllium with alpha-particles → neutral radiation identified as <b>neutrons</b>."))
story.append(formula_box("Neutron charge = 0   |   m_n = 1.675 × 10⁻²⁷ kg"))
story.append(sp(4))

story.append(section_header("1.5  Sub-Atomic Particles — Summary Table"))
story.append(make_table(
    ["Particle", "Symbol", "Charge", "Mass (kg)", "Mass (amu)", "Discoverer"],
    [
        ["Electron", "e⁻", "–1.602×10⁻¹⁹ C", "9.109×10⁻³¹", "0.000549", "Thomson (1897)"],
        ["Proton",   "p⁺", "+1.602×10⁻¹⁹ C", "1.673×10⁻²⁷", "1.00728",  "Goldstein/Rutherford"],
        ["Neutron",  "n",  "0",               "1.675×10⁻²⁷", "1.00867",  "Chadwick (1932)"],
    ],
    col_widths=[W*0.14, W*0.10, W*0.22, W*0.20, W*0.14, W*0.20],
    left_cols=[5]
))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 2 — ATOMIC MODELS
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 2 — ATOMIC MODELS"))
story.append(sp(6))

story.append(section_header("2.1  Thomson's Plum Pudding Model (1904)"))
for b in [
    "Atom is a uniform positive sphere with electrons embedded like plums in a pudding",
    "Radius ≈ 10⁻¹⁰ m",
    "FAILED — could not explain Rutherford's alpha-scattering results",
]:
    story.append(bullet(b))
story.append(sp(4))

story.append(section_header("2.2  Rutherford's Nuclear Model (1911)"))
story.append(sub_header("Alpha-scattering Experiment Observations:"))
for b in [
    "Most alpha-particles passed straight through → atom is MOSTLY EMPTY SPACE",
    "Few deflected at small angles → small positive charge inside",
    "Very few (1 in 20,000) bounced back at 180° → small, dense, positive NUCLEUS",
]:
    story.append(bullet(b))
story.append(sp(3))
story.append(sub_header("Conclusions:"))
for b in [
    "Tiny, dense, positively charged nucleus at the centre",
    "Electrons revolve around nucleus in circular orbits (like planets around sun)",
    "Nucleus contains protons (and neutrons)",
]:
    story.append(bullet(b))
story.append(sp(4))
story.append(formula_box(
    "Nuclear Radius:  r  =  r₀ × A^(1/3)",
    ["r₀ = nuclear radius constant = 1.2 × 10⁻¹⁵ m = 1.2 fm",
     "A = mass number (number of protons + neutrons)",
     "Nuclear density ≈ 10¹⁷ kg/m³  — CONSTANT for ALL nuclei (independent of A and Z)",
     "1 cm³ of nuclear matter would weigh ~100 million tonnes!"]
))
story.append(sp(4))
story.append(sub_header("Limitations of Rutherford's Model:"))
for b in [
    "Stability problem: Accelerating electron should continuously radiate energy → spiral into nucleus → atom collapses in ~10⁻⁸ s (but atoms are stable!)",
    "Line spectrum problem: A collapsing spiral would give a continuous spectrum, NOT discrete line spectra",
]:
    story.append(bullet(b))
story.append(sp(4))

story.append(section_header("2.3  Nuclear Terminology"))
story.append(formula_box(
    "Mass Number:  A  =  Z  +  N",
    ["A = total nucleons (protons + neutrons)",
     "Z = atomic number = protons = electrons (neutral atom)",
     "N = neutron number = A − Z"]
))
story.append(sp(4))
story.append(make_table(
    ["Term", "Same", "Different", "Example"],
    [
        ["Isotopes",     "Z (same element)",   "A, N",  "¹H, ²H (D), ³H (T)  — all Z=1"],
        ["Isobars",      "A",                  "Z, N",  "¹⁴C and ¹⁴N"],
        ["Isotones",     "N",                  "Z, A",  "³H and ⁴He (both N=2)"],
        ["Isoelectronic","Total electrons",    "—",     "Na⁺, Mg²⁺, Ne, F⁻ (all 10 e⁻)"],
        ["Isodiaphers",  "A−2Z (neutron excess)","—",   "²³⁸U and ²³⁴Th"],
    ],
    col_widths=[W*0.18, W*0.22, W*0.18, W*0.42],
    left_cols=[0,1,2,3]
))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 3 — ELECTROMAGNETIC RADIATION
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 3 — ELECTROMAGNETIC RADIATION & PLANCK'S THEORY"))
story.append(sp(6))

story.append(section_header("3.1  Wave Theory of Light"))
for b in [
    "Light = electromagnetic wave — oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation",
    "All EM waves travel at c = 3 × 10⁸ m/s in vacuum (regardless of frequency)",
    "Do NOT require a medium to propagate",
]:
    story.append(bullet(b))
story.append(sp(4))

story.append(formula_box(
    "Wave Equation:  c  =  ν × λ",
    ["c = speed of light = 3 × 10⁸ m/s",
     "ν (nu) = frequency in Hz (= s⁻¹)",
     "λ (lambda) = wavelength in metres",
     "ν and λ are INVERSELY proportional at constant c",
     "Unit conversions: 1 nm = 10⁻⁹ m  |  1 Å = 10⁻¹⁰ m  |  1 pm = 10⁻¹² m"]
))
story.append(sp(4))

story.append(formula_box(
    "Wave Number:  ν̃  =  1 / λ",
    ["ν̃ = wave number = number of waves per unit length",
     "Units: m⁻¹ or cm⁻¹   (mainly used in IR spectroscopy in cm⁻¹)",
     "CORRECT: ν̃ = 1/λ    WRONG: ν̃ = ν/c  (common mistake)"]
))
story.append(sp(4))

story.append(section_header("3.2  Electromagnetic Spectrum"))
story.append(make_table(
    ["Region", "Wavelength Range", "Frequency Range", "Example / Notes"],
    [
        ["Gamma rays",  "< 0.01 nm",        "> 3×10¹⁹ Hz",           "Nuclear reactions"],
        ["X-rays",      "0.01 – 10 nm",     "3×10¹⁷ – 3×10¹⁹ Hz",   "Medical imaging"],
        ["UV",          "10 – 400 nm",      "7.5×10¹⁴ – 3×10¹⁷ Hz", "Lyman series of H"],
        ["Visible",     "400 – 700 nm",     "4.3×10¹⁴ – 7.5×10¹⁴ Hz","Balmer series of H"],
        ["Infrared (IR)","700 nm – 1 mm",   "3×10¹¹ – 4.3×10¹⁴ Hz", "Paschen/Brackett series"],
        ["Microwaves",  "1 mm – 10 cm",     "3×10⁹ – 3×10¹¹ Hz",    "Radar, cooking"],
        ["Radio waves", "> 10 cm",          "< 3×10⁹ Hz",            "Broadcasting"],
    ],
    col_widths=[W*0.17, W*0.22, W*0.30, W*0.31],
    left_cols=[0,3]
))
story.append(sp(4))

story.append(sub_header("Visible Light — VIBGYOR (increasing λ / decreasing energy):"))
story.append(make_table(
    ["Colour", "λ (approx)", "Energy (eV)"],
    [
        ["Violet", "400 nm", "3.10 eV"],
        ["Indigo", "425 nm", "2.92 eV"],
        ["Blue",   "450 nm", "2.76 eV"],
        ["Green",  "520 nm", "2.38 eV"],
        ["Yellow", "580 nm", "2.14 eV"],
        ["Orange", "620 nm", "2.00 eV"],
        ["Red",    "700 nm", "1.77 eV"],
    ],
    col_widths=[W*0.33, W*0.33, W*0.34]
))
story.append(sp(4))

story.append(section_header("3.3  Planck's Quantum Theory (1900)"))
for b in [
    "Energy is NOT continuous — it is emitted/absorbed in discrete packets called QUANTA (singular: quantum) or PHOTONS",
    "Energy of each quantum is directly proportional to frequency",
]:
    story.append(bullet(b))
story.append(sp(4))
story.append(formula_box(
    "Energy of ONE Photon:  E  =  hν  =  hc/λ  =  hcν̃",
    ["h = Planck's constant = 6.626 × 10⁻³⁴ J·s",
     "ν = frequency (Hz)   |   λ = wavelength (m)   |   ν̃ = wave number (m⁻¹)",
     "E = energy of ONE photon (in Joules or eV)",
     "For n photons:  E_total = n × h × ν",
     "1 eV = 1.602 × 10⁻¹⁹ J"]
))
story.append(sp(4))
story.append(formula_box(
    "Energy–Wavelength Shortcut (fastest for NEET):  E(eV)  =  1240 / λ(nm)",
    ["λ MUST be in nanometres (nm). Answer is in eV.",
     "For Angstroms:  E(eV) = 12400 / λ(Å)",
     "Derived from: hc = 6.626×10⁻³⁴ × 3×10⁸ = 1.988×10⁻²⁵ J·m = 1240 eV·nm"]
))
story.append(sp(4))
story.append(formula_box(
    "Photon Momentum:  p  =  h/λ  =  E/c  =  hν/c",
    ["Photon has ZERO rest mass but has energy E = hν and momentum p = h/λ"]
))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 4 — ATOMIC SPECTRA
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 4 — ATOMIC SPECTRA & SPECTRAL SERIES"))
story.append(sp(6))

story.append(section_header("4.1  Line Spectrum of Hydrogen"))
story.append(body("When hydrogen gas is excited (high voltage), it emits light of only certain wavelengths → <b>line spectrum</b> (not continuous). Each line corresponds to a specific electron transition between energy levels."))
story.append(sp(4))

story.append(section_header("4.2  Spectral Series Table"))
story.append(make_table(
    ["Series", "n₁ (lower)", "n₂ (upper)", "Region", "First Line (λ)"],
    [
        ["Lyman",      "1", "2, 3, 4…",  "UV",         "121.6 nm"],
        ["Balmer",     "2", "3, 4, 5…",  "Visible+UV", "656.3 nm (Hα, red)"],
        ["Paschen",    "3", "4, 5, 6…",  "Near IR",    "1875 nm"],
        ["Brackett",   "4", "5, 6, 7…",  "IR",         "4051 nm"],
        ["Pfund",      "5", "6, 7, 8…",  "Far IR",     "7459 nm"],
        ["Humphreys",  "6", "7, 8, 9…",  "Far IR",     "—"],
    ],
    col_widths=[W*0.18, W*0.14, W*0.20, W*0.18, W*0.30]
))
story.append(sp(4))

story.append(formula_box(
    "Rydberg Equation:  1/λ  =  R_H × Z² × (1/n₁²  −  1/n₂²)",
    ["R_H = Rydberg constant = 1.097 × 10⁷ m⁻¹ = 109677 cm⁻¹",
     "Z = atomic number  (Z=1 for H, Z=2 for He⁺, Z=3 for Li²⁺, etc.)",
     "n₁ = lower orbit  (n₁ determines the SERIES)",
     "n₂ = upper orbit  (n₂ > n₁, must be integer)",
     "First line of each series (longest λ):  n₂ = n₁ + 1",
     "Series limit (shortest λ):  n₂ = ∞  →  1/λ_limit = R_H × Z² / n₁²"]
))
story.append(sp(4))

story.append(formula_box(
    "Number of Spectral Lines (n₂ → n₁):  Lines  =  (n₂ − n₁)(n₂ − n₁ + 1) / 2",
    ["Special case — electron falls to ground state (n₁ = 1):  Lines = n(n−1)/2",
     "Example 1:  n=5 → n=1:  (5×4)/2 = 10 lines",
     "Example 2:  n=5 → n=3:  (2×3)/2 = 3 lines",
     "Example 3:  n=4 → n=2:  (2×3)/2 = 3 lines"]
))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 5 — BOHR'S MODEL
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 5 — BOHR'S ATOMIC MODEL (1913)"))
story.append(sp(6))

story.append(section_header("5.1  Postulates"))
for b in [
    "Electrons revolve in fixed circular orbits called STATIONARY STATES (no energy radiated while in orbit)",
    "Only orbits where angular momentum = whole-number multiple of h/2π are allowed",
    "Energy absorbed or emitted ONLY when electron jumps between orbits",
    "Energy of emitted/absorbed photon = difference in orbital energies:  ΔE = hν",
]:
    story.append(bullet(b))
story.append(sp(4))

story.append(section_header("5.2  Bohr Formulas  (H and H-like ions: He⁺, Li²⁺, Be³⁺…)"))

story.append(sub_header("Formula 1 — Orbital Radius"))
story.append(formula_box(
    "r_n  =  0.529 × n² / Z   Å",
    ["r_n = radius of nth orbit (distance of electron from nucleus)",
     "0.529 Å = a₀ = Bohr radius = radius of 1st orbit of H (n=1, Z=1)",
     "n = principal quantum number = 1, 2, 3, 4…",
     "Z = atomic number",
     "Rules:  r_n ∝ n² (quadruples when n doubles)  |  r_n ∝ 1/Z",
     "To convert to metres: multiply by 10⁻¹⁰   (1 Å = 10⁻¹⁰ m)"]
))
story.append(sp(3))
story.append(make_table(
    ["n", "H (Z=1)", "He⁺ (Z=2)", "Li²⁺ (Z=3)"],
    [
        ["1", "0.529 Å", "0.265 Å", "0.176 Å"],
        ["2", "2.116 Å", "1.058 Å", "0.705 Å"],
        ["3", "4.761 Å", "2.381 Å", "1.587 Å"],
    ],
    col_widths=[W*0.15, W*0.28, W*0.28, W*0.29]
))
story.append(sp(4))

story.append(sub_header("Formula 2 — Orbital Velocity"))
story.append(formula_box(
    "v_n  =  2.18 × 10⁶ × Z / n   m/s",
    ["2.18 × 10⁶ m/s = velocity in 1st orbit of H = c/137 (much less than light speed)",
     "v_n ∝ Z/n   |   Outer electrons move SLOWER (easier to remove)",
     "H (n=1): 2.18×10⁶ m/s   |   H (n=2): 1.09×10⁶ m/s   |   H (n=3): 0.727×10⁶ m/s"]
))
story.append(sp(4))

story.append(sub_header("Formula 3 — Total Energy"))
story.append(formula_box(
    "E_n  =  −13.6 × Z² / n²   eV   =   −2.18×10⁻¹⁸ × Z² / n²   J",
    ["E_n = total energy of electron in nth orbit — ALWAYS NEGATIVE for a bound electron",
     "−13.6 eV = energy in 1st orbit of H (ground state) = ionisation energy of H",
     "Negative sign: electron is BOUND to nucleus",
     "n=1 is most negative = most stable   |   At n=∞:  E=0 (electron free = atom ionised)"]
))
story.append(sp(3))
story.append(make_table(
    ["n", "Energy of H (Z=1)"],
    [
        ["1 (ground)", "−13.6 eV"],
        ["2",          "−3.4 eV"],
        ["3",          "−1.51 eV"],
        ["4",          "−0.85 eV"],
        ["5",          "−0.544 eV"],
        ["∞",          "0 eV (ionised)"],
    ],
    col_widths=[W*0.35, W*0.65]
))
story.append(sp(4))

story.append(sub_header("Formula 4 — Kinetic Energy and Potential Energy"))
story.append(formula_box(
    "KE  =  −E_n  =  +13.6 Z²/n²  eV  (always positive)\n"
    "PE  =  2E_n  =  −27.2 Z²/n²  eV  (always negative)\n"
    "TE  =  KE + PE  =  E_n",
    ["Three golden relationships:   KE = −TE     |     PE = 2×TE     |     PE = −2×KE",
     "Example H (n=1):  KE=+13.6 eV,  PE=−27.2 eV,  TE=−13.6 eV   ✓ (13.6−27.2=−13.6)"]
))
story.append(sp(4))

story.append(sub_header("Formula 5 — Ionisation Energy"))
story.append(formula_box(
    "IE  =  0 − E_n  =  +13.6 × Z² / n²   eV",
    ["IE = energy to remove electron from orbit n to infinity (n → ∞)",
     "IE is ALWAYS positive   |   Decreases as n increases (easier to remove from outer orbits)",
     "H (n=1): 13.6 eV = 1312 kJ/mol   |   He⁺ (Z=2, n=1): 54.4 eV   |   Li²⁺ (Z=3, n=1): 122.4 eV"]
))
story.append(sp(4))

story.append(sub_header("Formula 6 — Energy of Emitted/Absorbed Photon"))
story.append(formula_box(
    "ΔE  =  13.6 × Z² × (1/n₁²  −  1/n₂²)   eV",
    ["n₁ = lower orbit (where electron LANDS after emission) — n₁ < n₂",
     "n₂ = upper orbit (where electron STARTS) — n₂ > n₁",
     "ΔE is always POSITIVE",
     "EMISSION: electron falls n₂ → n₁, photon released",
     "ABSORPTION: electron jumps n₁ → n₂, photon absorbed"]
))
story.append(sp(4))

story.append(sub_header("Formula 7 — Angular Momentum Quantisation (Bohr's Condition)"))
story.append(formula_box(
    "mvr_n  =  nh / 2π  =  nℏ",
    ["m = mass of electron (kg)   |   v = orbital velocity (m/s)   |   r_n = orbital radius (m)",
     "n = principal quantum number   |   h = Planck's constant = 6.626×10⁻³⁴ J·s",
     "ℏ = h/2π = 1.055×10⁻³⁴ J·s  (reduced Planck constant)"]
))
story.append(sp(4))

story.append(sub_header("Formulas 8 & 9 — Time Period and Frequency of Revolution"))
story.append(formula_box(
    "T_n  =  2π r_n / v_n    ∝   n³ / Z²\n"
    "ν_n  =  v_n / (2π r_n)  ∝   Z² / n³",
    ["T_n increases as n³ — if n doubles, T becomes 2³ = 8× longer",
     "ν_n decreases as n³ — outer electrons orbit LESS frequently",
     "NEET trap: If n doubles, time period increases 8 times"]
))
story.append(sp(4))

story.append(section_header("5.3  Limitations of Bohr's Model"))
for b in [
    "Works ONLY for hydrogen and H-like ions (one electron). Fails for multi-electron atoms.",
    "Cannot explain fine structure of spectral lines (Zeeman and Stark effects).",
    "Cannot explain relative intensities of spectral lines.",
    "Violates Heisenberg's Uncertainty Principle — definite orbits imply exact position AND momentum simultaneously.",
    "Does not explain chemical bonding or 3D shapes of molecules.",
]:
    story.append(bullet(b))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 6 — PHOTOELECTRIC EFFECT
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 6 — PHOTOELECTRIC EFFECT"))
story.append(sp(6))

story.append(section_header("6.1  Phenomenon & Observations"))
story.append(body("When light of sufficient frequency falls on a metal surface, electrons are ejected. These ejected electrons are called <b>photoelectrons</b>. Einstein explained this in 1905 using Planck's quantum theory (Nobel Prize 1921)."))
story.append(sp(3))
story.append(sub_header("Observations that Wave Theory CANNOT explain:"))
for b in [
    "Emission is INSTANTANEOUS (wave theory predicts a time delay for energy buildup)",
    "Below threshold frequency ν₀: NO emission regardless of intensity",
    "Above ν₀: KE_max depends on frequency, NOT intensity",
    "More intensity → MORE electrons emitted, NOT faster electrons",
]:
    story.append(bullet(b))
story.append(sp(4))

story.append(sub_header("Formula 10 — Einstein's Photoelectric Equation"))
story.append(formula_box(
    "hν  =  φ  +  KE_max",
    ["hν = energy of incident photon (J or eV)",
     "φ (phi) = work function = minimum energy to eject ONE electron = hν₀  (J or eV)",
     "KE_max = maximum KE of ejected photoelectron = ½m_e v²_max  (J or eV)",
     "If hν < φ:  NO emission at all (even at very high intensity)",
     "If hν = φ:  Emission just starts, KE_max = 0"]
))
story.append(sp(4))

story.append(sub_header("Formula 11 — Work Function"))
story.append(formula_box(
    "φ  =  hν₀",
    ["φ = work function — a fixed property of the metal",
     "ν₀ = threshold frequency — minimum frequency for photoelectric emission"]
))
story.append(sp(3))
story.append(make_table(
    ["Metal", "Work Function φ (eV)", "Threshold λ₀ (nm)", "Responds to"],
    [
        ["Cs",  "2.0 eV", "620 nm", "Visible (red-orange)"],
        ["K",   "2.2 eV", "564 nm", "Visible (yellow)"],
        ["Na",  "2.3 eV", "539 nm", "Visible (green)"],
        ["Al",  "4.3 eV", "288 nm", "UV"],
        ["Zn",  "4.3 eV", "288 nm", "UV"],
        ["Pt",  "5.6 eV", "221 nm", "UV"],
    ],
    col_widths=[W*0.12, W*0.28, W*0.28, W*0.32],
    left_cols=[3]
))
story.append(sp(4))

story.append(sub_header("Formula 12 — Threshold Wavelength"))
story.append(formula_box(
    "λ₀  =  hc / φ  =  c / ν₀     →     λ₀(nm)  =  1240 / φ(eV)",
    ["Light with λ < λ₀ (higher frequency) → emission OCCURS",
     "Light with λ > λ₀ (lower frequency) → NO emission (regardless of intensity)",
     "Example: φ=2.0 eV → λ₀ = 620 nm (red).   φ=4.3 eV → λ₀ = 288 nm (UV)"]
))
story.append(sp(4))

story.append(sub_header("Formula 13 — Stopping Potential"))
story.append(formula_box(
    "eV₀  =  KE_max  =  hν − φ",
    ["e = charge of electron = 1.602×10⁻¹⁹ C",
     "V₀ = stopping potential = minimum REVERSE voltage to stop ALL photoelectrons (Volts)",
     "KE_max in eV numerically equals V₀ in Volts",
     "If KE_max = 2.5 eV  →  V₀ = 2.5 V",
     "More intensity: photocurrent ↑, V₀ UNCHANGED",
     "Higher frequency: V₀ ↑, photocurrent unchanged",
     "V₀ vs ν graph: Slope = h/e = 4.136×10⁻¹⁵ V·s  |  X-intercept = ν₀  |  Y-intercept = −φ/e"]
))
story.append(sp(4))

story.append(sub_header("Formula 14 — Number of Photons per Unit Area per Second"))
story.append(formula_box(
    "n_photons  =  I / hν  =  Iλ / hc",
    ["n_photons = number of photons hitting unit area per second  (s⁻¹·m⁻²)",
     "I = intensity of light = energy per unit area per second  (W/m²)",
     "More intensity = MORE photons = MORE electrons ejected = LARGER photocurrent",
     "Each photon gives its energy to ONE electron — so KE_max is unaffected by intensity"]
))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 7 — de BROGLIE
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 7 — DUAL NATURE OF MATTER  (de Broglie, 1924)"))
story.append(sp(6))

story.append(section_header("7.1  Background & Principle"))
for b in [
    "Louis de Broglie (1924): If light (wave) can behave as particles (photons), then matter (particles) should also show wave properties",
    "Wave-particle duality: all matter has both wave and particle properties",
    "Only observable for microscopic particles (electrons, protons, neutrons) — not for macroscopic objects",
    "Experimental proof: Davisson-Germer experiment (1927) — electron diffraction by nickel crystal confirmed electron wave nature",
]:
    story.append(bullet(b))
story.append(sp(4))

story.append(sub_header("Formula 15 — de Broglie Wavelength (General)"))
story.append(formula_box(
    "λ  =  h / mv  =  h / p",
    ["λ = de Broglie (matter) wavelength (m)",
     "h = Planck's constant = 6.626×10⁻³⁴ J·s",
     "m = mass of particle (kg)   |   v = velocity (m/s)   |   p = mv = momentum (kg·m/s)",
     "Cricket ball (0.1 kg, 30 m/s): λ ~ 2×10⁻³⁴ m — unmeasurably tiny",
     "Electron (9.1×10⁻³¹ kg, 10⁶ m/s): λ ~ 0.7 nm — detectable by X-ray diffraction!"]
))
story.append(sp(4))

story.append(sub_header("Formula 16 — de Broglie Wavelength from Kinetic Energy"))
story.append(formula_box(
    "λ  =  h / √(2m·KE)",
    ["Derived from λ = h/mv and KE = ½mv²  →  mv = √(2m·KE)",
     "KE MUST be in Joules.  Convert:  KE(J) = KE(eV) × 1.602×10⁻¹⁹"]
))
story.append(sp(4))

story.append(sub_header("Formula 17 — de Broglie Wavelength for Accelerated Electron"))
story.append(formula_box(
    "λ  =  12.27 / √V   Å      (electrons only)",
    ["12.27 = constant for ELECTRONS only = h/√(2·m_e·e)  expressed in Å·V^½ units",
     "V = accelerating potential difference in VOLTS   |   λ answer in ANGSTROMS",
     "For proton:  λ = 0.286/√V Å",
     "V=100 V → λ=1.227 Å   |   V=1000 V → λ=0.388 Å   |   V=10000 V → λ=0.123 Å",
     "Used in electron microscopy (λ much smaller than visible light → far higher resolution)"]
))
story.append(sp(4))

story.append(sub_header("Formula 18 — de Broglie and Bohr Connection"))
story.append(formula_box(
    "2π r_n  =  n λ   (circumference = whole-number multiples of λ)",
    ["Bohr's quantisation condition (mvr = nh/2π) is equivalent to the electron's de Broglie wave fitting exactly into the orbit",
     "This gives a wave-mechanical basis to Bohr's model"]
))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 8 — HEISENBERG'S UNCERTAINTY PRINCIPLE
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 8 — HEISENBERG'S UNCERTAINTY PRINCIPLE (1927)"))
story.append(sp(6))

story.append(section_header("8.1  Statement"))
story.append(body("It is impossible to simultaneously determine the EXACT position AND exact momentum (or velocity) of a microscopic particle. This is a fundamental law of nature — NOT due to measurement limitations."))
story.append(sp(4))

story.append(sub_header("Formula 19 — Heisenberg's Uncertainty Principle"))
story.append(formula_box(
    "Δx · Δp  ≥  h / 4π     OR     Δx · m·Δv  ≥  h / 4π",
    ["Δx = uncertainty in position (m)",
     "Δp = uncertainty in momentum (kg·m/s)",
     "Δv = uncertainty in velocity (m/s)",
     "h/4π = minimum allowed product = 5.27×10⁻³⁵ J·s",
     "Equivalent form:  Δx · Δp ≥ ℏ/2  where ℏ = h/2π = 1.055×10⁻³⁴ J·s",
     "Energy-time version:  ΔE · Δt ≥ h/4π"]
))
story.append(sp(4))

story.append(sub_header("Formula 20 — Minimum Uncertainty in Velocity"))
story.append(formula_box(
    "Δv_min  =  h / (4π × m × Δx)",
    ["Use equality sign (=) to get the MINIMUM possible Δv",
     "If Δx = 0 (exact position):  Δp = ∞ (momentum completely unknown)",
     "If Δp = 0 (exact momentum):  Δx = ∞ (position completely unknown)"]
))
story.append(sp(4))
story.append(trap_box("Heisenberg's UP invalidates Bohr's model — definite circular orbits would mean exact position AND velocity simultaneously, which is forbidden by HUP."))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 9 — QUANTUM MECHANICAL MODEL & QUANTUM NUMBERS
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 9 — QUANTUM MECHANICAL MODEL & QUANTUM NUMBERS"))
story.append(sp(6))

story.append(section_header("9.1  Orbital vs Orbit"))
story.append(make_table(
    ["Feature", "Orbit (Bohr)", "Orbital (Quantum Mechanics)"],
    [
        ["Definition",   "Definite circular path", "Region of space where probability of finding electron ≥ 90%"],
        ["Heisenberg",   "Violates HUP",           "Consistent with HUP"],
        ["Dimensions",   "2D circle",              "3D region of space"],
        ["Position",     "Exact position known",   "Only probability density known"],
        ["Stability",    "Cannot explain",         "Fully explains stable atoms"],
    ],
    col_widths=[W*0.18, W*0.30, W*0.52],
    left_cols=[0,1,2]
))
story.append(sp(6))

story.append(section_header("9.2  The Four Quantum Numbers"))
story.append(body("Every electron in an atom is completely described by a UNIQUE set of 4 quantum numbers. No two electrons can have the same set of all 4 (Pauli's Exclusion Principle)."))
story.append(sp(4))

story.append(sub_header("(a) Principal Quantum Number (n)"))
story.append(formula_box(
    "n  =  1, 2, 3, 4, 5, 6, 7…",
    ["Determines ENERGY and SIZE of the orbital",
     "Higher n = larger orbital = higher energy = farther from nucleus",
     "Shell names:  n=1→K,  n=2→L,  n=3→M,  n=4→N"]
))
story.append(sp(3))

story.append(sub_header("(b) Azimuthal Quantum Number (l)  — Subsidiary / Angular Momentum QN"))
story.append(formula_box(
    "l  =  0, 1, 2, …, (n−1)",
    ["Determines SHAPE of orbital and which SUBSHELL",
     "l=0 → s (sphere)   |   l=1 → p (dumbbell)   |   l=2 → d (double-dumbbell)   |   l=3 → f (complex)",
     "For n=1: l=0 only (1s)   |   n=2: l=0,1 (2s, 2p)   |   n=3: l=0,1,2 (3s, 3p, 3d)"]
))
story.append(sp(3))

story.append(sub_header("(c) Magnetic Quantum Number (m_l)"))
story.append(formula_box(
    "m_l  =  −l, −(l−1), …, 0, …, (l−1), +l     →     Total values = 2l+1",
    ["Determines ORIENTATION of orbital in space",
     "s (l=0):  m_l=0 (1 orbital)   |   p (l=1):  m_l=−1,0,+1 (3 orbitals: px, py, pz)",
     "d (l=2):  m_l=−2,−1,0,+1,+2 (5 orbitals)   |   f (l=3):  7 orbitals"]
))
story.append(sp(3))

story.append(sub_header("(d) Spin Quantum Number (m_s)"))
story.append(formula_box(
    "m_s  =  +1/2  (spin up ↑)   or   −1/2  (spin down ↓)     [only these two values]",
    ["Every electron has spin — it is an intrinsic property",
     "Pauli's principle: two electrons in the same orbital MUST have opposite m_s values"]
))
story.append(sp(4))

story.append(make_table(
    ["QN", "Symbol", "Values", "Determines", "Number of values"],
    [
        ["Principal",    "n",   "1, 2, 3, 4…",        "Shell, energy, size",   "Infinite"],
        ["Azimuthal",    "l",   "0 to (n−1)",          "Subshell, shape",       "n values (0 to n−1)"],
        ["Magnetic",     "m_l", "−l to +l",            "Orbital orientation",   "2l+1"],
        ["Spin",         "m_s", "+½ or −½ only",       "Spin direction",        "2"],
    ],
    col_widths=[W*0.16, W*0.12, W*0.20, W*0.28, W*0.24],
    left_cols=[0,3]
))
story.append(sp(6))

story.append(section_header("9.3  Angular Momentum Formulas"))

story.append(sub_header("Formula 21 — Orbital Angular Momentum"))
story.append(formula_box(
    "L  =  √[l(l+1)] · ℏ",
    ["L = magnitude of orbital angular momentum (J·s)",
     "l = azimuthal quantum number   |   ℏ = h/2π = 1.055×10⁻³⁴ J·s",
     "s (l=0): L=0   |   p (l=1): L=√2·ℏ   |   d (l=2): L=√6·ℏ   |   f (l=3): L=2√3·ℏ"]
))
story.append(trap_box("Bohr's model gave L = nℏ (WRONG). Correct QM: L = √[l(l+1)]·ℏ. s orbitals have ZERO orbital angular momentum — NOT ℏ."))
story.append(sp(4))

story.append(sub_header("Formula 22 — z-Component of Angular Momentum"))
story.append(formula_box(
    "L_z  =  m_l · ℏ",
    ["L_z = projection of angular momentum on z-axis",
     "p (l=1):  L_z = −ℏ, 0, +ℏ  (3 orientations)",
     "d (l=2):  L_z = −2ℏ, −ℏ, 0, +ℏ, +2ℏ  (5 orientations)",
     "A magnetic field splits these orientations → Zeeman effect"]
))
story.append(sp(4))

story.append(sub_header("Formula 23 — Spin Angular Momentum"))
story.append(formula_box(
    "S  =  √[s(s+1)] · ℏ  =  (√3/2) · ℏ   [same for ALL electrons]",
    ["s = spin quantum number = ½  (always, for every electron — cannot change)",
     "The MAGNITUDE of spin is fixed for all electrons",
     "Only the DIRECTION (m_s = ±½) can vary"]
))
story.append(sp(6))

story.append(section_header("9.4  Shell/Subshell Count Formulas"))
story.append(formula_box(
    "Orbitals in nth shell  =  n²          Max electrons in nth shell  =  2n²\n"
    "Orbitals in a subshell  =  2l+1       Max electrons in a subshell  =  2(2l+1)",
    ["n=1: 1 orbital, 2 e⁻   |   n=2: 4 orbitals, 8 e⁻   |   n=3: 9 orbitals, 18 e⁻   |   n=4: 16 orbitals, 32 e⁻",
     "s: 1 orbital, 2 e⁻   |   p: 3 orbitals, 6 e⁻   |   d: 5 orbitals, 10 e⁻   |   f: 7 orbitals, 14 e⁻"]
))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 10 — SHAPES OF ORBITALS
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 10 — SHAPES OF ORBITALS"))
story.append(sp(6))

story.append(make_table(
    ["Orbital", "Shape", "Angular Nodes", "Nodal Planes/Regions", "Starts at n"],
    [
        ["s (l=0)", "Sphere", "0", "None — spherical symmetry", "n=1"],
        ["p (l=1)", "Dumbbell (2 lobes)", "1", "px: yz-plane  |  py: xz-plane  |  pz: xy-plane", "n=2"],
        ["d (l=2)", "Double-dumbbell / clover (4 lobes); dz² has donut+dumbbell", "2", "Two nodal planes in each orbital", "n=3"],
        ["f (l=3)", "Complex multi-lobed", "3", "Three nodal regions", "n=4"],
    ],
    col_widths=[W*0.12, W*0.26, W*0.14, W*0.32, W*0.16],
    left_cols=[1,3]
))
story.append(sp(4))
for b in [
    "1s: 1 sphere. 2s: 2 concentric spheres (1 radial node inside). 3s: 3 concentric spheres.",
    "Three p orbitals (px, py, pz) are identical in shape but oriented along different axes — they are DEGENERATE (same energy in absence of field).",
    "Five d orbitals: dxy, dxz, dyz, dx²−y² (clover-leaf in planes) and dz² (unique doughnut + dumbbell along z-axis).",
]:
    story.append(bullet(b))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 11 — NODES
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 11 — NODES"))
story.append(sp(6))

story.append(formula_box(
    "Radial nodes  =  n − l − 1\n"
    "Angular nodes  =  l\n"
    "Total nodes  =  n − 1",
    ["Radial nodes = spherical surfaces INSIDE the orbital where electron density = 0",
     "Angular nodes = flat planes (or cones) through the NUCLEUS where electron probability = 0",
     "Proof:  (n−l−1) + l  =  n−1  ✓  (always true for any orbital)"]
))
story.append(sp(4))

story.append(make_table(
    ["Orbital", "n", "l", "Radial nodes (n−l−1)", "Angular nodes (l)", "Total (n−1)"],
    [
        ["1s", "1", "0", "0",    "0", "0"],
        ["2s", "2", "0", "1",    "0", "1"],
        ["2p", "2", "1", "0",    "1", "1"],
        ["3s", "3", "0", "2",    "0", "2"],
        ["3p", "3", "1", "1",    "1", "2"],
        ["3d", "3", "2", "0 ★",  "2", "2"],
        ["4s", "4", "0", "3",    "0", "3"],
        ["4p", "4", "1", "2",    "1", "3"],
        ["4d", "4", "2", "1",    "2", "3"],
        ["4f", "4", "3", "0",    "3", "3"],
    ],
    col_widths=[W*0.12, W*0.08, W*0.08, W*0.23, W*0.22, W*0.27]
))
story.append(sp(3))
story.append(trap_box("3d has ZERO radial nodes (students often say 1 — that is WRONG)."))
story.append(trap_box("2s and 2p BOTH have 1 total node but DIFFERENT types: 2s has 1 RADIAL node (spherical shell), 2p has 1 ANGULAR node (flat plane)."))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 12 — ELECTRONIC CONFIGURATION
# ─────────────────────────────────────────────────────────────────
story.append(part_header("PART 12 — ELECTRONIC CONFIGURATION"))
story.append(sp(6))

story.append(section_header("12.1  Three Fundamental Rules"))

story.append(sub_header("Rule 1 — Aufbau Principle"))
story.append(body("Fill orbitals in INCREASING order of energy (n+l rule). If two orbitals have the same (n+l), fill the one with <b>lower n</b> first."))
story.append(sp(3))
story.append(formula_box(
    "Filling Order:  1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p",
    ["4s (n+l=4) is filled BEFORE 3d (n+l=5)",
     "4f (n+l=7) is filled BEFORE 5d (n+l=7, but 5d has higher n)"]
))
story.append(sp(4))

story.append(sub_header("Rule 2 — Pauli's Exclusion Principle"))
story.append(body("No two electrons in the same atom can have the <b>same set of all four quantum numbers</b>. Consequence: maximum 2 electrons per orbital, and they must have OPPOSITE spins (one ↑, one ↓)."))
story.append(sp(4))

story.append(sub_header("Rule 3 — Hund's Rule of Maximum Multiplicity"))
story.append(body("In degenerate orbitals (same energy), electrons fill <b>singly first</b> (one per orbital) with <b>parallel spins</b> (same m_s) before any pairing occurs."))
story.append(sp(3))
story.append(note_box("Nitrogen (Z=7): 1s² 2s² 2p³ → 2p orbitals: ↑ | ↑ | ↑  (three singly occupied — CORRECT). NOT: ↑↓ | ↑ | _ (pairing before all singly occupied — WRONG)"))
story.append(sp(6))

story.append(section_header("12.2  Electronic Configurations of Z = 1 to 30"))
story.append(make_table(
    ["Z", "Element", "Configuration", "Unpaired e⁻"],
    [
        ["1",  "H",  "1s¹",                  "1"],
        ["2",  "He", "1s²",                  "0"],
        ["3",  "Li", "[He] 2s¹",             "1"],
        ["4",  "Be", "[He] 2s²",             "0"],
        ["5",  "B",  "[He] 2s² 2p¹",         "1"],
        ["6",  "C",  "[He] 2s² 2p²",         "2"],
        ["7",  "N",  "[He] 2s² 2p³",         "3"],
        ["8",  "O",  "[He] 2s² 2p⁴",         "2"],
        ["9",  "F",  "[He] 2s² 2p⁵",         "1"],
        ["10", "Ne", "[He] 2s² 2p⁶",         "0"],
        ["11", "Na", "[Ne] 3s¹",             "1"],
        ["12", "Mg", "[Ne] 3s²",             "0"],
        ["13", "Al", "[Ne] 3s² 3p¹",         "1"],
        ["14", "Si", "[Ne] 3s² 3p²",         "2"],
        ["15", "P",  "[Ne] 3s² 3p³",         "3"],
        ["16", "S",  "[Ne] 3s² 3p⁴",         "2"],
        ["17", "Cl", "[Ne] 3s² 3p⁵",         "1"],
        ["18", "Ar", "[Ne] 3s² 3p⁶",         "0"],
        ["19", "K",  "[Ar] 4s¹",             "1"],
        ["20", "Ca", "[Ar] 4s²",             "0"],
        ["21", "Sc", "[Ar] 3d¹ 4s²",         "1"],
        ["22", "Ti", "[Ar] 3d² 4s²",         "2"],
        ["23", "V",  "[Ar] 3d³ 4s²",         "3"],
        ["24", "Cr ★", "[Ar] 3d⁵ 4s¹  (EXCEPTION)", "6"],
        ["25", "Mn", "[Ar] 3d⁵ 4s²",         "5"],
        ["26", "Fe", "[Ar] 3d⁶ 4s²",         "4"],
        ["27", "Co", "[Ar] 3d⁷ 4s²",         "3"],
        ["28", "Ni", "[Ar] 3d⁸ 4s²",         "2"],
        ["29", "Cu ★", "[Ar] 3d¹⁰ 4s¹  (EXCEPTION)", "1"],
        ["30", "Zn", "[Ar] 3d¹⁰ 4s²",        "0"],
    ],
    col_widths=[W*0.07, W*0.13, W*0.60, W*0.20],
    left_cols=[2]
))
story.append(sp(4))
story.append(trap_box("Cr (Z=24): Expected [Ar]3d⁴4s² — Actual [Ar]3d⁵4s¹ (half-filled d⁵ is extra stable).  Cu (Z=29): Expected [Ar]3d⁹4s² — Actual [Ar]3d¹⁰4s¹ (fully-filled d¹⁰ is extra stable)."))
story.append(note_box("Reason for exceptions: Half-filled (d⁵) and fully-filled (d¹⁰) subshells have extra stability due to: (1) Symmetrical distribution of electrons, and (2) Maximum exchange energy."))
story.append(sp(6))

story.append(section_header("12.3  Magnetic Properties & Spin Multiplicity"))

story.append(sub_header("Formula 31 — Spin Multiplicity"))
story.append(formula_box(
    "Spin multiplicity  =  2S + 1     where  S  =  (number of unpaired electrons) / 2",
    ["Multiplicity = 1 (singlet): all electrons paired → DIAMAGNETIC (repelled by magnetic field)",
     "Multiplicity > 1: unpaired electrons → PARAMAGNETIC (attracted by magnetic field)",
     "Higher multiplicity = more unpaired electrons = stronger paramagnetism"]
))
story.append(sp(3))
story.append(make_table(
    ["Unpaired e⁻", "S", "Multiplicity", "Type", "Example"],
    [
        ["0", "0",   "1 (singlet)",  "Diamagnetic",   "He, Ne, Zn, Be"],
        ["1", "½",   "2 (doublet)",  "Paramagnetic",  "H, F, Na"],
        ["2", "1",   "3 (triplet)",  "Paramagnetic",  "C, O, Ni²⁺"],
        ["3", "3/2", "4 (quartet)",  "Paramagnetic",  "N, Co²⁺, Cr³⁺"],
        ["4", "2",   "5 (quintet)",  "Paramagnetic",  "Fe²⁺, Cr²⁺"],
        ["5", "5/2", "6 (sextet)",   "Paramagnetic",  "Mn²⁺, Fe³⁺"],
    ],
    col_widths=[W*0.14, W*0.10, W*0.20, W*0.18, W*0.38],
    left_cols=[4]
))
story.append(sp(4))

story.append(sub_header("Formula 32 — Magnetic Moment"))
story.append(formula_box(
    "μ  =  √[n(n+2)]   BM   (Bohr Magneton)",
    ["n = number of unpaired electrons",
     "1 BM (Bohr Magneton) = 9.274×10⁻²⁴ J/T",
     "1 unpaired: μ = √3 ≈ 1.73 BM  (Cu²⁺, Ti³⁺)",
     "2 unpaired: μ = √8 ≈ 2.83 BM  (Ni²⁺)",
     "3 unpaired: μ = √15 ≈ 3.87 BM (Co²⁺, Cr³⁺)",
     "4 unpaired: μ = √24 ≈ 4.90 BM (Fe²⁺)",
     "5 unpaired: μ = √35 ≈ 5.92 BM (Mn²⁺, Fe³⁺)"]
))
story.append(sp(8))

# ─────────────────────────────────────────────────────────────────
# PART 13 — CONSTANTS & MASTER FORMULA LIST
# ─────────────────────────────────────────────────────────────────
story.append(PageBreak())
story.append(part_header("PART 13 — COMPLETE CONSTANTS REFERENCE"))
story.append(sp(6))
story.append(make_table(
    ["Symbol", "Name", "Value", "Unit"],
    [
        ["h",    "Planck's constant",            "6.626 × 10⁻³⁴",  "J·s"],
        ["ℏ",    "Reduced Planck (h/2π)",         "1.055 × 10⁻³⁴",  "J·s"],
        ["c",    "Speed of light",                "3 × 10⁸",         "m/s"],
        ["e",    "Elementary charge",             "1.602 × 10⁻¹⁹",  "C"],
        ["m_e",  "Mass of electron",              "9.109 × 10⁻³¹",  "kg"],
        ["m_p",  "Mass of proton",                "1.673 × 10⁻²⁷",  "kg"],
        ["m_n",  "Mass of neutron",               "1.675 × 10⁻²⁷",  "kg"],
        ["a₀",   "Bohr radius (1st orbit of H)",  "0.529 Å = 5.29×10⁻¹¹", "m"],
        ["R_H",  "Rydberg constant",              "1.097 × 10⁷ m⁻¹ = 109677 cm⁻¹", "m⁻¹"],
        ["r₀",   "Nuclear radius constant",        "1.2 × 10⁻¹⁵ = 1.2 fm", "m"],
        ["1 eV", "In Joules",                     "1.602 × 10⁻¹⁹",  "J"],
        ["1 amu","In kg",                         "1.66 × 10⁻²⁷",   "kg"],
        ["1 Å",  "In metres",                     "10⁻¹⁰",           "m"],
        ["1 nm", "In metres",                     "10⁻⁹",            "m"],
        ["1 pm", "In metres",                     "10⁻¹²",           "m"],
        ["1 fm", "In metres",                     "10⁻¹⁵",           "m"],
    ],
    col_widths=[W*0.12, W*0.38, W*0.30, W*0.20],
    left_cols=[1]
))
story.append(sp(8))

story.append(PageBreak())
story.append(part_header("MASTER FORMULA SHEET — ALL 41 FORMULAS AT A GLANCE"))
story.append(sp(6))
story.append(make_table(
    ["#", "Formula Name", "Expression"],
    [
        ["1",  "Orbital radius",             "r_n = 0.529 × n²/Z  Å"],
        ["2",  "Orbital velocity",           "v_n = 2.18×10⁶ × Z/n  m/s"],
        ["3",  "Total energy",               "E_n = −13.6 × Z²/n²  eV"],
        ["4",  "Kinetic energy",             "KE = −E_n = +13.6 Z²/n²  eV"],
        ["5",  "Potential energy",           "PE = 2E_n = −27.2 Z²/n²  eV"],
        ["6",  "Ionisation energy",          "IE = +13.6 × Z²/n²  eV"],
        ["7",  "Photon energy (transition)", "ΔE = 13.6 Z² (1/n₁² − 1/n₂²)  eV"],
        ["8",  "Rydberg equation",           "1/λ = R_H Z² (1/n₁² − 1/n₂²)"],
        ["9",  "Angular momentum (Bohr)",    "mvr_n = nh/2π  (= nℏ)"],
        ["10", "Time period",                "T_n ∝ n³/Z²"],
        ["11", "Revolution frequency",       "ν_n ∝ Z²/n³"],
        ["12", "Spectral lines count",       "(n₂−n₁)(n₂−n₁+1)/2"],
        ["13", "Wave equation",              "c = νλ"],
        ["14", "Wave number",                "ν̃ = 1/λ  (m⁻¹ or cm⁻¹)"],
        ["15", "Photon energy",              "E = hν = hc/λ = hcν̃"],
        ["16", "Energy shortcut",            "E(eV) = 1240/λ(nm)"],
        ["17", "Photon momentum",            "p = h/λ = E/c"],
        ["18", "Photoelectric equation",     "hν = φ + KE_max"],
        ["19", "Work function",              "φ = hν₀"],
        ["20", "Threshold wavelength",       "λ₀(nm) = 1240/φ(eV)"],
        ["21", "Stopping potential",         "eV₀ = KE_max = hν − φ"],
        ["22", "Photon count (intensity)",   "n = I/hν = Iλ/hc"],
        ["23", "de Broglie (general)",       "λ = h/mv = h/p"],
        ["24", "de Broglie (from KE)",       "λ = h/√(2m·KE)"],
        ["25", "de Broglie (electron, V)",   "λ = 12.27/√V  Å"],
        ["26", "Heisenberg's UP",            "Δx·Δp ≥ h/4π"],
        ["27", "Min. velocity uncertainty",  "Δv_min = h/(4π·m·Δx)"],
        ["28", "Orbital angular momentum",   "L = √[l(l+1)]·ℏ"],
        ["29", "L z-component",              "L_z = m_l·ℏ"],
        ["30", "Spin angular momentum",      "S = (√3/2)·ℏ  [ALL electrons]"],
        ["31", "Orbitals per shell",         "n²"],
        ["32", "Max e⁻ per shell",           "2n²"],
        ["33", "Orbitals per subshell",      "2l+1"],
        ["34", "Max e⁻ per subshell",        "2(2l+1)"],
        ["35", "Radial nodes",               "n − l − 1"],
        ["36", "Angular nodes",              "l"],
        ["37", "Total nodes",                "n − 1"],
        ["38", "Spin multiplicity",          "2S+1  where  S=(unpaired e⁻)/2"],
        ["39", "Magnetic moment",            "μ = √[n(n+2)]  BM"],
        ["40", "Nuclear radius",             "r = r₀ × A^(1/3)"],
        ["41", "e/m ratio (electron)",       "1.758 × 10¹¹  C/kg"],
    ],
    col_widths=[W*0.06, W*0.36, W*0.58],
    left_cols=[1,2]
))
story.append(sp(6))

# footer note
story.append(HRFlowable(width="100%", thickness=1, color=DARK_BLUE))
story.append(sp(4))
story.append(Paragraph(
    "Atomic Structure | Class 11 Chemistry | Complete Chapter | All 41 Formulas | NEET / JEE",
    S("footer", fontSize=8, fontName="Helvetica", textColor=GREY, alignment=TA_CENTER)
))

# ─────────────────────────────────────────────────────────────────
doc.build(story)
print(f"PDF created: {OUTPUT}")

"""
Atomic Structure - Complete Chapter PDF
Black & White theme, Unicode fonts (DroidSans), print-optimised large fonts
No colour fills, no placeholder squares
"""
from reportlab.pdfbase import pdfmetrics
from reportlab.pdfbase.ttfonts import TTFont
from reportlab.lib.pagesizes import A4
from reportlab.lib import colors
from reportlab.lib.styles import ParagraphStyle
from reportlab.lib.units import cm
from reportlab.lib.enums import TA_CENTER, TA_LEFT, TA_JUSTIFY
from reportlab.platypus import (
    SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle,
    HRFlowable, PageBreak, KeepTogether
)

# ── Register Unicode fonts ─────────────────────────────────────────
pdfmetrics.registerFont(TTFont('DS',  '/usr/share/fonts/google-droid-sans-fonts/DroidSans.ttf'))
pdfmetrics.registerFont(TTFont('DSB', '/usr/share/fonts/google-droid-sans-fonts/DroidSans-Bold.ttf'))

OUTPUT = "/tmp/workspace/atomic-structure/Atomic_Structure_BW.pdf"

doc = SimpleDocTemplate(
    OUTPUT,
    pagesize=A4,
    rightMargin=2.0*cm,
    leftMargin=2.0*cm,
    topMargin=2.2*cm,
    bottomMargin=2.2*cm,
)
W = A4[0] - 4.0*cm   # usable width

# ── Unicode constants (no rendering squares) ───────────────────────
SUP = {
    '0':'\u2070','1':'\u00b9','2':'\u00b2','3':'\u00b3',
    '4':'\u2074','5':'\u2075','6':'\u2076','7':'\u2077',
    '8':'\u2078','9':'\u2079','+':'\u207a','-':'\u207b',
    'n':'\u207f',
}
SUB = {
    '0':'\u2080','1':'\u2081','2':'\u2082','3':'\u2083',
    '4':'\u2084','5':'\u2085','6':'\u2086','7':'\u2087',
    '8':'\u2088','9':'\u2089',
}

NU   = '\u03bd'        # nu
LAM  = '\u03bb'        # lambda
PHI  = '\u03c6'        # phi
DEL  = '\u0394'        # Delta
PI   = '\u03c0'        # pi
SQRT = '\u221a'        # sqrt
INF  = '\u221e'        # infinity
PROP = '\u221d'        # proportional
HBAR = '\u0127'        # hbar (h-bar)
ANG  = '\u212b'        # Angstrom symbol
MU   = '\u03bc'        # mu
TILD = '\u0303'        # combining tilde (for nu-tilde)
GEQ  = '\u2265'        # >=
LEQ  = '\u2264'        # <=
ARR  = '\u2192'        # ->
PM   = '\u00b1'        # plus-minus
TIMES= '\u00d7'        # times
CDOT = '\u00b7'        # middle dot
NEQL = '\u2260'        # not equal
UP   = '\u2191'        # up arrow
DOWN = '\u2193'        # down arrow
STAR = '\u2605'        # black star
WARN = '\u26a0'        # warning sign
CHECK= '\u2713'        # checkmark
BULL = '\u2022'        # bullet

# Shorthand for common chemical notation (pure ASCII-safe Unicode)
def sup(s): return ''.join(SUP.get(c, c) for c in str(s))
def sub(s): return ''.join(SUB.get(c, c) for c in str(s))

# Frequently used fragments
N1 = 'n' + sub('1')
N2 = 'n' + sub('2')
NU_TILDE = NU + '\u0304'   # nu with macron as wave-number symbol

# ── Styles ─────────────────────────────────────────────────────────
BLACK = colors.black
WHITE = colors.white
LT_GREY = colors.HexColor("#d0d0d0")
MID_GREY = colors.HexColor("#808080")
DARK_GREY = colors.HexColor("#303030")

def S(name, **kw):
    return ParagraphStyle(name, **kw)

sTitle = S("sTitle",
    fontName="DSB", fontSize=22, textColor=WHITE,
    alignment=TA_CENTER, spaceAfter=4, spaceBefore=4, leading=28)

sSubtitle = S("sSubtitle",
    fontName="DS", fontSize=11, textColor=WHITE,
    alignment=TA_CENTER, spaceAfter=2, leading=16)

sPart = S("sPart",
    fontName="DSB", fontSize=14, textColor=WHITE,
    alignment=TA_LEFT, spaceAfter=4, spaceBefore=6,
    leftIndent=6, leading=20)

sSec = S("sSec",
    fontName="DSB", fontSize=13, textColor=BLACK,
    alignment=TA_LEFT, spaceAfter=4, spaceBefore=8, leading=18)

sSub = S("sSub",
    fontName="DSB", fontSize=11.5, textColor=BLACK,
    alignment=TA_LEFT, spaceAfter=3, spaceBefore=5, leading=16)

sBody = S("sBody",
    fontName="DS", fontSize=11, textColor=BLACK,
    alignment=TA_JUSTIFY, spaceAfter=4, leading=16)

sBullet = S("sBullet",
    fontName="DS", fontSize=11, textColor=BLACK,
    alignment=TA_LEFT, spaceAfter=3, leading=15,
    leftIndent=16, bulletIndent=4)

sFormLabel = S("sFormLabel",
    fontName="DSB", fontSize=11, textColor=BLACK,
    alignment=TA_LEFT, spaceAfter=2, spaceBefore=2, leading=15)

sFormula = S("sFormula",
    fontName="DSB", fontSize=12.5, textColor=BLACK,
    alignment=TA_CENTER, spaceAfter=3, spaceBefore=3, leading=19)

sFormNote = S("sFormNote",
    fontName="DS", fontSize=10.5, textColor=DARK_GREY,
    alignment=TA_LEFT, spaceAfter=2, leading=15, leftIndent=4)

sTrap = S("sTrap",
    fontName="DSB", fontSize=11, textColor=BLACK,
    alignment=TA_LEFT, spaceAfter=2, leading=15)

sNote = S("sNote",
    fontName="DS", fontSize=11, textColor=BLACK,
    alignment=TA_LEFT, spaceAfter=2, leading=15)

sTableH = S("sTableH",
    fontName="DSB", fontSize=10, textColor=WHITE,
    alignment=TA_CENTER, leading=13)

sTableC = S("sTableC",
    fontName="DS", fontSize=10, textColor=BLACK,
    alignment=TA_CENTER, leading=13)

sTableL = S("sTableL",
    fontName="DS", fontSize=10, textColor=BLACK,
    alignment=TA_LEFT, leading=13)

sFooter = S("sFooter",
    fontName="DS", fontSize=9, textColor=MID_GREY,
    alignment=TA_CENTER, leading=12)

# ── Helper flowables ───────────────────────────────────────────────

def sp(h=5):
    return Spacer(1, h)

def hr(thick=0.8):
    return HRFlowable(width="100%", thickness=thick, color=BLACK)

def thinhr():
    return HRFlowable(width="100%", thickness=0.4, color=MID_GREY)

def body(text):
    return Paragraph(text, sBody)

def blt(text):
    return Paragraph(BULL + "  " + text, sBullet)

def part_header(text):
    data = [[Paragraph(text, sPart)]]
    t = Table(data, colWidths=[W])
    t.setStyle(TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), BLACK),
        ("ROWPADDING", (0,0), (-1,-1), 8),
    ]))
    return t

def sec(text):
    return Paragraph(text, sSec)

def sub_h(text):
    return Paragraph(text, sSub)

def formula_box(main_text, notes=None):
    """Box with thick border, no fill (white bg), formula centered, notes left."""
    elems = [Paragraph(main_text, sFormula)]
    if notes:
        elems.append(HRFlowable(width="100%", thickness=0.5, color=LT_GREY))
        for n in notes:
            elems.append(Paragraph(n, sFormNote))
    rows = [[e] for e in elems]
    inner = Table(rows, colWidths=[W - 24])
    inner.setStyle(TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), WHITE),
        ("ROWPADDING", (0,0), (-1,-1), 5),
    ]))
    outer = Table([[inner]], colWidths=[W])
    outer.setStyle(TableStyle([
        ("BOX", (0,0), (-1,-1), 2, BLACK),
        ("ROWPADDING", (0,0), (-1,-1), 6),
        ("BACKGROUND", (0,0), (-1,-1), WHITE),
    ]))
    return outer

def trap_box(text):
    t = Table([[Paragraph(WARN + "  NEET TRAP: " + text, sTrap)]], colWidths=[W])
    t.setStyle(TableStyle([
        ("BOX",        (0,0), (-1,-1), 1.5, BLACK),
        ("ROWPADDING", (0,0), (-1,-1), 6),
        ("BACKGROUND", (0,0), (-1,-1), colors.HexColor("#f0f0f0")),
    ]))
    return t

def note_box(text):
    t = Table([[Paragraph(STAR + "  NOTE: " + text, sNote)]], colWidths=[W])
    t.setStyle(TableStyle([
        ("BOX",        (0,0), (-1,-1), 1, BLACK),
        ("ROWPADDING", (0,0), (-1,-1), 6),
        ("BACKGROUND", (0,0), (-1,-1), WHITE),
    ]))
    return t

def make_table(headers, rows, col_widths=None, left_cols=None):
    if col_widths is None:
        col_widths = [W / len(headers)] * len(headers)
    left_cols = left_cols or []
    head_row = [Paragraph(h, sTableH) for h in headers]
    data = [head_row]
    for row in rows:
        styled = []
        for j, cell in enumerate(row):
            st = sTableL if j in left_cols else sTableC
            styled.append(Paragraph(str(cell), st))
        data.append(styled)
    t = Table(data, colWidths=col_widths)
    style_cmds = [
        ("BACKGROUND",  (0,0), (-1,0), BLACK),
        ("ROWPADDING",  (0,0), (-1,-1), 5),
        ("GRID",        (0,0), (-1,-1), 0.5, MID_GREY),
        ("VALIGN",      (0,0), (-1,-1), "MIDDLE"),
        ("LINEBELOW",   (0,0), (-1,0),  1.0, BLACK),
    ]
    for i in range(1, len(data)):
        if i % 2 == 0:
            style_cmds.append(("BACKGROUND", (0,i), (-1,i), colors.HexColor("#f4f4f4")))
    t.setStyle(TableStyle(style_cmds))
    return t

# ══════════════════════════════════════════════════════════════════
# STORY
# ══════════════════════════════════════════════════════════════════
story = []

# ── COVER ─────────────────────────────────────────────────────────
cover_title = Table([[Paragraph("ATOMIC STRUCTURE", sTitle)]], colWidths=[W])
cover_title.setStyle(TableStyle([
    ("BACKGROUND", (0,0), (-1,-1), BLACK),
    ("ROWPADDING", (0,0), (-1,-1), 20),
]))
cover_sub = Table([[Paragraph(
    "Complete Chapter  |  All 41 Formulas  |  All Topics  |  Class 11 Chemistry  |  NEET / JEE",
    sSubtitle)]], colWidths=[W])
cover_sub.setStyle(TableStyle([
    ("BACKGROUND", (0,0), (-1,-1), DARK_GREY),
    ("ROWPADDING", (0,0), (-1,-1), 10),
]))
story += [cover_title, cover_sub, sp(12)]

# ══════════════════════════════════════════════════════════════════
# PART 1 — DISCOVERY OF SUB-ATOMIC PARTICLES
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 1 — DISCOVERY OF SUB-ATOMIC PARTICLES"), sp(8)]

story += [sec("1.1  Cathode Ray Experiment  (J.J. Thomson, 1897)")]
story += [body("High-voltage discharge tube (evacuated glass tube with two metal electrodes). "
               "Rays travel from cathode (-) to anode (+). These are cathode rays.")]
story += [sp(3), sub_h("Observations:")]
for b in [
    "Travel in straight lines; cast sharp shadows",
    "Deflect towards the positive plate  " + ARR + "  carry NEGATIVE charge",
    "Cause fluorescence on a ZnS screen",
    "Same e/m ratio regardless of cathode material or gas used  " + ARR + "  electrons are universal",
    "Discovery: the ELECTRON",
]:
    story.append(blt(b))
story += [sp(5),
    formula_box(
        "e / m" + sub('e') + "  =  1.758 " + TIMES + " 10" + sup('11') + "  C/kg",
        [
            "e = charge of electron = 1.602 " + TIMES + " 10" + sup('-19') + " C",
            "m" + sub('e') + " = mass of electron = 9.109 " + TIMES + " 10" + sup('-31') + " kg",
            "Ratio is CONSTANT for cathode rays in ALL gases (same electron everywhere in matter).",
            "Canal rays (positive ions) have VARYING e/m  --  different gases give different ion masses.",
        ]
    ), sp(6)]

story += [sec("1.2  Millikan's Oil Drop Experiment  (1909)")]
story += [body("Balanced gravitational and electric forces on charged oil droplets to measure electron charge."),
    formula_box(
        "e  =  1.602 " + TIMES + " 10" + sup('-19') + "  C",
        ["From e and e/m:   m" + sub('e') + " = e / (e/m) = 9.109 " + TIMES + " 10" + sup('-31') + " kg"]
    ), sp(6)]

story += [sec("1.3  Canal Ray Experiment  (Goldstein, 1886)")]
story += [body("Cathode with holes (perforations). Rays travel BEHIND the cathode -- opposite to cathode rays. "
               "Discovery: PROTON (positively charged particle). "
               "The lightest positive ion from hydrogen gas is the proton (H" + sup('+') + ")."), sp(6)]

story += [sec("1.4  Discovery of Neutron  (Chadwick, 1932)")]
story += [body("Bombarded beryllium with " + "\u03b1" + "-particles  " + ARR + "  neutral radiation identified as NEUTRONS."),
    formula_box("Neutron charge = 0     m" + sub('n') + " = 1.675 " + TIMES + " 10" + sup('-27') + " kg"),
    sp(6)]

story += [sec("1.5  Sub-Atomic Particles -- Summary")]
story.append(make_table(
    ["Particle","Symbol","Charge","Mass (kg)","Mass (amu)","Discoverer"],
    [
        ["Electron","e" + sup('-'),"-1.602" + TIMES + "10" + sup('-19') + " C","9.109" + TIMES + "10" + sup('-31'),"0.000549","Thomson (1897)"],
        ["Proton",  "p" + sup('+'),"+1.602" + TIMES + "10" + sup('-19') + " C","1.673" + TIMES + "10" + sup('-27'),"1.00728", "Goldstein / Rutherford"],
        ["Neutron", "n","0","1.675" + TIMES + "10" + sup('-27'),"1.00867","Chadwick (1932)"],
    ],
    col_widths=[W*0.13,W*0.10,W*0.23,W*0.20,W*0.13,W*0.21],
    left_cols=[5]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 2 — ATOMIC MODELS
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 2 — ATOMIC MODELS"), sp(8)]

story += [sec("2.1  Thomson's Plum Pudding Model (1904)")]
for b in [
    "Atom = uniform positive sphere with electrons embedded like plums in a pudding",
    "Radius ~ 10" + sup('-10') + " m",
    "FAILED -- could not explain Rutherford's alpha-scattering results",
]:
    story.append(blt(b))
story.append(sp(6))

story += [sec("2.2  Rutherford's Nuclear Model (1911)")]
story += [sub_h("Alpha-Particle Scattering Observations:")]
for b in [
    "Most " + "\u03b1" + "-particles passed straight through  " + ARR + "  atom is MOSTLY EMPTY SPACE",
    "Few deflected at small angles  " + ARR + "  small positive charge inside",
    "Very few (1 in 20,000) bounced back at 180 degrees  " + ARR + "  small, dense, positive NUCLEUS",
]:
    story.append(blt(b))
story += [sp(4),
    formula_box(
        "Nuclear Radius:   r  =  r" + sub('0') + "  " + TIMES + "  A" + sup('1/3'),
        [
            "r" + sub('0') + " = nuclear radius constant = 1.2 " + TIMES + " 10" + sup('-15') + " m  =  1.2 fm",
            "A = mass number (total protons + neutrons)",
            "Nuclear density " + "\u2248" + " 10" + sup('17') + " kg/m" + sup('3') + "  -- CONSTANT for ALL nuclei (independent of A and Z)",
            "1 cm" + sup('3') + " of nuclear matter would weigh ~100 million tonnes!",
        ]
    ), sp(4)]
story += [sub_h("Limitations:")]
for b in [
    "STABILITY: Accelerating electron should continuously radiate energy " + ARR + " spiral into nucleus " + ARR + " collapse in ~10" + sup('-8') + " s  (but atoms ARE stable!)",
    "LINE SPECTRA: A spiralling electron would emit a CONTINUOUS spectrum, not discrete line spectra",
]:
    story.append(blt(b))
story.append(sp(6))

story += [sec("2.3  Nuclear Terminology")]
story.append(formula_box(
    "Mass Number:   A  =  Z  +  N",
    [
        "A = total nucleons (protons + neutrons)",
        "Z = atomic number = number of protons = electrons in neutral atom",
        "N = neutron number = A - Z",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["Term","Same","Different","Example"],
    [
        ["Isotopes","Z (same element)","A, N","" + sup('1') + "H,  " + sup('2') + "H (D),  " + sup('3') + "H (T)  -- all Z=1"],
        ["Isobars","A","Z, N","" + sup('14') + sub('6') + "C  and  " + sup('14') + sub('7') + "N"],
        ["Isotones","N","Z, A","" + sup('3') + sub('1') + "H  and  " + sup('4') + sub('2') + "He  (both N=2)"],
        ["Isoelectronic","Total electrons","--","Na" + sup('+') + ", Mg" + sup('2+') + ", Ne, F" + sup('-') + "  (all 10 e" + sup('-') + ")"],
    ],
    col_widths=[W*0.18,W*0.22,W*0.18,W*0.42],
    left_cols=[0,1,2,3]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 3 — EM RADIATION
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 3 — ELECTROMAGNETIC RADIATION & PLANCK'S THEORY"), sp(8)]

story += [sec("3.1  Wave Theory of Light")]
for b in [
    "Light = electromagnetic wave  --  oscillating electric and magnetic fields perpendicular to each other and to direction of travel",
    "All EM waves travel at c = 3 " + TIMES + " 10" + sup('8') + " m/s in vacuum (all frequencies, always)",
    "Do NOT require a medium to propagate",
]:
    story.append(blt(b))
story.append(sp(5))
story.append(formula_box(
    "Wave Equation:   c  =  " + NU + "  " + TIMES + "  " + LAM,
    [
        "c = speed of light = 3 " + TIMES + " 10" + sup('8') + " m/s",
        NU + " (nu) = frequency  in Hz (= s" + sup('-1') + ")",
        LAM + " (lambda) = wavelength  in metres",
        NU + " and " + LAM + " are INVERSELY proportional at constant c",
        "Conversions:  1 nm = 10" + sup('-9') + " m  |  1 " + ANG + " = 10" + sup('-10') + " m  |  1 pm = 10" + sup('-12') + " m",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Wave Number:   " + NU + "\u0303  =  1 / " + LAM,
    [
        "Units: m" + sup('-1') + " or cm" + sup('-1') + "  (mainly used in IR spectroscopy in cm" + sup('-1') + ")",
        "CORRECT: wave number = 1/" + LAM + "   |   WRONG: " + NU + "/c  (common mistake)",
    ]
))
story.append(sp(6))

story += [sec("3.2  Electromagnetic Spectrum")]
story.append(make_table(
    ["Region","Wavelength Range","Frequency Range","Notes"],
    [
        ["Gamma rays","< 0.01 nm","> 3" + TIMES + "10" + sup('19') + " Hz","Nuclear reactions"],
        ["X-rays","0.01 - 10 nm","3" + TIMES + "10" + sup('17') + " - 3" + TIMES + "10" + sup('19') + " Hz","Medical imaging"],
        ["UV","10 - 400 nm","7.5" + TIMES + "10" + sup('14') + " - 3" + TIMES + "10" + sup('17') + " Hz","Lyman series of H"],
        ["Visible","400 - 700 nm","4.3" + TIMES + "10" + sup('14') + " - 7.5" + TIMES + "10" + sup('14') + " Hz","Balmer series of H"],
        ["Infrared","700 nm - 1 mm","3" + TIMES + "10" + sup('11') + " - 4.3" + TIMES + "10" + sup('14') + " Hz","Paschen, Brackett series"],
        ["Microwaves","1 mm - 10 cm","3" + TIMES + "10" + sup('9') + " - 3" + TIMES + "10" + sup('11') + " Hz","Radar, cooking"],
        ["Radio waves","> 10 cm","< 3" + TIMES + "10" + sup('9') + " Hz","Broadcasting"],
    ],
    col_widths=[W*0.16,W*0.24,W*0.33,W*0.27],
    left_cols=[3]
))
story.append(sp(4))
story += [sub_h("Visible Light -- VIBGYOR (increasing wavelength, decreasing energy):")]
story.append(make_table(
    ["Colour","Wavelength","Energy"],
    [
        ["Violet","400 nm","3.10 eV"],
        ["Indigo","425 nm","2.92 eV"],
        ["Blue",  "450 nm","2.76 eV"],
        ["Green", "520 nm","2.38 eV"],
        ["Yellow","580 nm","2.14 eV"],
        ["Orange","620 nm","2.00 eV"],
        ["Red",   "700 nm","1.77 eV"],
    ],
    col_widths=[W*0.33,W*0.33,W*0.34]
))
story.append(sp(6))

story += [sec("3.3  Planck's Quantum Theory (1900)")]
for b in [
    "Energy is NOT continuous -- emitted/absorbed in discrete packets called QUANTA (photons)",
    "Energy of each quantum is directly proportional to frequency",
]:
    story.append(blt(b))
story.append(sp(4))
story.append(formula_box(
    "Energy of ONE Photon:   E  =  h" + NU + "  =  hc/" + LAM + "  =  hc" + NU + "\u0303",
    [
        "h = Planck's constant = 6.626 " + TIMES + " 10" + sup('-34') + " J" + CDOT + "s",
        NU + " = frequency (Hz)   |   " + LAM + " = wavelength (m)   |   " + NU + "\u0303 = wave number (m" + sup('-1') + ")",
        "E = energy of ONE photon  (in Joules or eV)   |   For n photons:  E_total = n " + TIMES + " h" + NU,
        "Conversion:  1 eV = 1.602 " + TIMES + " 10" + sup('-19') + " J",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Energy-Wavelength Shortcut:   E(eV)  =  1240 / " + LAM + "(nm)",
    [
        LAM + " MUST be in nanometres.  Answer in eV.",
        "For Angstroms:  E(eV) = 12400 / " + LAM + "(" + ANG + ")",
        "Derived from:  hc = 1.988" + TIMES + "10" + sup('-25') + " J" + CDOT + "m = 1240 eV" + CDOT + "nm",
        "Examples:  400 nm " + ARR + " 3.1 eV  |  500 nm " + ARR + " 2.48 eV  |  700 nm " + ARR + " 1.77 eV",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Photon Momentum:   p  =  h/" + LAM + "  =  E/c",
    ["Photon has ZERO rest mass but has energy E=h" + NU + " and momentum p=h/" + LAM]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 4 — ATOMIC SPECTRA
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 4 — ATOMIC SPECTRA & SPECTRAL SERIES"), sp(8)]

story += [sec("4.1  Line Spectrum of Hydrogen")]
story += [body("When hydrogen gas is excited (high voltage), it emits light of only certain wavelengths -- "
               "a LINE SPECTRUM (not continuous). Each spectral line corresponds to one specific electron transition.")]
story.append(sp(6))

story += [sec("4.2  Spectral Series of Hydrogen")]
story.append(make_table(
    ["Series","n" + sub('1') + " (lower)","n" + sub('2') + " (upper)","Region","First Line (" + LAM + ")"],
    [
        ["Lyman",     "1","2, 3, 4...","UV","121.6 nm"],
        ["Balmer",    "2","3, 4, 5...","Visible + UV","656.3 nm  (H" + "\u03b1" + ",  red)"],
        ["Paschen",   "3","4, 5, 6...","Near IR","1875 nm"],
        ["Brackett",  "4","5, 6, 7...","IR","4051 nm"],
        ["Pfund",     "5","6, 7, 8...","Far IR","7459 nm"],
        ["Humphreys", "6","7, 8, 9...","Far IR","--"],
    ],
    col_widths=[W*0.17,W*0.15,W*0.17,W*0.18,W*0.33]
))
story.append(sp(5))
story.append(formula_box(
    "Rydberg Equation:   1/" + LAM + "  =  R" + sub('H') + "  " + TIMES + "  Z" + sup('2') + "  " + TIMES + "  ( 1/n" + sub('1') + sup('2') + "  -  1/n" + sub('2') + sup('2') + " )",
    [
        "R" + sub('H') + " = Rydberg constant = 1.097 " + TIMES + " 10" + sup('7') + " m" + sup('-1') + " = 109677 cm" + sup('-1'),
        "Z = atomic number  (Z=1 for H,  Z=2 for He" + sup('+') + ",  Z=3 for Li" + sup('2+') + ")",
        "n" + sub('1') + " = lower orbit  (determines the SERIES)   |   n" + sub('2') + " = upper orbit  (n" + sub('2') + " > n" + sub('1') + ")",
        "First line of each series (longest " + LAM + "):   n" + sub('2') + " = n" + sub('1') + " + 1",
        "Series limit (shortest " + LAM + "):   n" + sub('2') + " = " + INF + "   " + ARR + "   1/" + LAM + " = R" + sub('H') + " " + TIMES + " Z" + sup('2') + " / n" + sub('1') + sup('2'),
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Number of Spectral Lines  (n" + sub('2') + " " + ARR + " n" + sub('1') + "):   Lines  =  (n" + sub('2') + " - n" + sub('1') + ") (n" + sub('2') + " - n" + sub('1') + " + 1) / 2",
    [
        "Special case -- electron falls to GROUND STATE (n" + sub('1') + " = 1):   Lines = n(n-1)/2",
        "Example 1:  n=5 " + ARR + " n=1:   5" + TIMES + "4/2 = 10 lines",
        "Example 2:  n=5 " + ARR + " n=3:   (2)(3)/2 = 3 lines",
        "Example 3:  n=4 " + ARR + " n=2:   (2)(3)/2 = 3 lines",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 5 — BOHR'S MODEL
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 5 — BOHR'S ATOMIC MODEL (1913)"), sp(8)]

story += [sec("5.1  Postulates of Bohr's Model")]
for b in [
    "Electrons revolve in fixed circular orbits called STATIONARY STATES (no energy radiated while in orbit)",
    "Only orbits where angular momentum = whole-number multiple of h/2" + PI + " are allowed",
    "Energy absorbed or emitted ONLY when electron jumps between orbits",
    "Energy of emitted/absorbed photon = difference in orbital energies:   " + DEL + "E = h" + NU,
]:
    story.append(blt(b))
story.append(sp(8))

story += [sec("5.2  Bohr Model Formulas  (H and H-like ions: He" + sup('+') + ", Li" + sup('2+') + ", Be" + sup('3+') + "...)")]

story.append(sub_h("Formula 1 -- Orbital Radius"))
story.append(formula_box(
    "r" + sub('n') + "  =  0.529  " + TIMES + "  n" + sup('2') + " / Z     " + ANG,
    [
        "r" + sub('n') + " = radius of nth orbit  (distance of electron from nucleus)",
        "0.529 " + ANG + " = a" + sub('0') + " = Bohr radius = radius of 1st orbit of H  (n=1, Z=1)  -- fixed constant",
        "n = principal quantum number = 1, 2, 3, 4...   |   Z = atomic number",
        "Rule: r" + sub('n') + " " + PROP + " n" + sup('2') + "  (quadruples when n doubles)   |   r" + sub('n') + " " + PROP + " 1/Z",
        "Convert to metres: multiply by 10" + sup('-10') + "   (1 " + ANG + " = 10" + sup('-10') + " m)",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["n","H  (Z=1)","He" + sup('+') + "  (Z=2)","Li" + sup('2+') + "  (Z=3)"],
    [
        ["1","0.529 " + ANG,"0.265 " + ANG,"0.176 " + ANG],
        ["2","2.116 " + ANG,"1.058 " + ANG,"0.705 " + ANG],
        ["3","4.761 " + ANG,"2.381 " + ANG,"1.587 " + ANG],
    ],
    col_widths=[W*0.15,W*0.28,W*0.28,W*0.29]
))
story.append(sp(6))

story.append(sub_h("Formula 2 -- Orbital Velocity"))
story.append(formula_box(
    "v" + sub('n') + "  =  2.18 " + TIMES + " 10" + sup('6') + "  " + TIMES + "  Z / n     m/s",
    [
        "2.18 " + TIMES + " 10" + sup('6') + " m/s = velocity in 1st orbit of H  =  c/137  (much less than light speed)",
        "v" + sub('n') + " " + PROP + " Z/n   |   Outer electrons move SLOWER  (easier to remove)",
        "H (n=1): 2.18" + TIMES + "10" + sup('6') + " m/s   |   H (n=2): 1.09" + TIMES + "10" + sup('6') + " m/s   |   H (n=3): 0.727" + TIMES + "10" + sup('6') + " m/s",
    ]
))
story.append(sp(6))

story.append(sub_h("Formula 3 -- Total Energy"))
story.append(formula_box(
    "E" + sub('n') + "  =  -13.6  " + TIMES + "  Z" + sup('2') + " / n" + sup('2') + "     eV     =     -2.18" + TIMES + "10" + sup('-18') + "  " + TIMES + "  Z" + sup('2') + "/n" + sup('2') + "     J",
    [
        "E" + sub('n') + " = total energy of electron in nth orbit -- ALWAYS NEGATIVE for a bound electron",
        "-13.6 eV = energy in 1st orbit of H  (ground state)  =  ionisation energy of H",
        "Negative sign: electron is BOUND to nucleus",
        "n=1 is most negative = most stable   |   At n=" + INF + ":  E=0  (electron free = atom ionised)",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["n","Energy of H (Z=1)"],
    [
        ["1  (ground state)","-13.6 eV"],
        ["2","-3.4 eV"],
        ["3","-1.51 eV"],
        ["4","-0.85 eV"],
        ["5","-0.544 eV"],
        ["" + INF + "  (ionised)","0 eV"],
    ],
    col_widths=[W*0.40,W*0.60]
))
story.append(sp(6))

story.append(sub_h("Formula 4 -- Kinetic Energy, Potential Energy, Total Energy"))
story.append(formula_box(
    "KE  =  -E" + sub('n') + "  =  +13.6 Z" + sup('2') + "/n" + sup('2') + "  eV   (always positive)\n"
    "PE  =  2E" + sub('n') + "  =  -27.2 Z" + sup('2') + "/n" + sup('2') + "  eV   (always negative)\n"
    "TE  =  KE + PE  =  E" + sub('n'),
    [
        "Three golden relationships:   KE = -TE    |    PE = 2" + TIMES + "TE    |    PE = -2" + TIMES + "KE",
        "Example H (n=1):  KE=+13.6 eV,  PE=-27.2 eV,  TE=-13.6 eV     " + CHECK + "  (13.6-27.2 = -13.6)",
    ]
))
story.append(sp(6))

story.append(sub_h("Formula 5 -- Ionisation Energy"))
story.append(formula_box(
    "IE  =  0 - E" + sub('n') + "  =  +13.6  " + TIMES + "  Z" + sup('2') + " / n" + sup('2') + "     eV",
    [
        "IE = energy to remove electron from orbit n to infinity (n " + ARR + " " + INF + ")",
        "IE is ALWAYS positive   |   Decreases as n increases (easier to remove from outer orbits)",
        "H (n=1): 13.6 eV = 1312 kJ/mol   |   He" + sup('+') + " (Z=2): 54.4 eV   |   Li" + sup('2+') + " (Z=3): 122.4 eV",
    ]
))
story.append(sp(6))

story.append(sub_h("Formula 6 -- Energy of Emitted/Absorbed Photon"))
story.append(formula_box(
    DEL + "E  =  13.6  " + TIMES + "  Z" + sup('2') + "  " + TIMES + "  ( 1/n" + sub('1') + sup('2') + "  -  1/n" + sub('2') + sup('2') + " )     eV",
    [
        "n" + sub('1') + " = lower orbit  (electron LANDS here after emission)   |   n" + sub('2') + " = upper orbit  (electron starts here)",
        "n" + sub('1') + " < n" + sub('2') + " always   |   " + DEL + "E is always POSITIVE",
        "EMISSION: electron falls n" + sub('2') + " " + ARR + " n" + sub('1') + ",  photon released",
        "ABSORPTION: electron jumps n" + sub('1') + " " + ARR + " n" + sub('2') + ",  photon absorbed",
    ]
))
story.append(sp(6))

story.append(sub_h("Formula 7 -- Angular Momentum Quantisation (Bohr's Condition)"))
story.append(formula_box(
    "mv" + sub('n') + "r" + sub('n') + "  =  nh / 2" + PI + "  =  n" + HBAR,
    [
        "m = mass of electron (kg)   |   v = orbital velocity (m/s)   |   r" + sub('n') + " = orbital radius (m)",
        "n = principal quantum number   |   h = Planck's constant = 6.626" + TIMES + "10" + sup('-34') + " J" + CDOT + "s",
        HBAR + " = h/2" + PI + " = 1.055" + TIMES + "10" + sup('-34') + " J" + CDOT + "s  (reduced Planck constant)",
    ]
))
story.append(sp(6))

story.append(sub_h("Formulas 8 & 9 -- Time Period and Frequency of Revolution"))
story.append(formula_box(
    "T" + sub('n') + "  =  2" + PI + "r" + sub('n') + "/v" + sub('n') + "     " + PROP + "     n" + sup('3') + "/Z" + sup('2') + "\n"
    NU + sub('n') + "  =  v" + sub('n') + " / (2" + PI + "r" + sub('n') + ")     " + PROP + "     Z" + sup('2') + "/n" + sup('3'),
    [
        "T" + sub('n') + " " + PROP + " n" + sup('3') + "  --  if n doubles, T becomes 2" + sup('3') + " = 8 times longer",
        NU + sub('n') + " " + PROP + " 1/n" + sup('3') + "  --  outer electrons orbit LESS frequently",
    ]
))
story.append(sp(4))
story.append(trap_box("If n doubles, time period increases by 2" + sup('3') + " = 8 times."))
story.append(sp(6))

story += [sec("5.3  Limitations of Bohr's Model")]
for b in [
    "Works ONLY for hydrogen and H-like ions (one electron). Fails for multi-electron atoms.",
    "Cannot explain fine structure of spectral lines (Zeeman and Stark effects).",
    "Cannot explain relative intensities of spectral lines.",
    "Violates Heisenberg's Uncertainty Principle -- definite orbits imply exact position AND momentum simultaneously.",
    "Does not explain chemical bonding or 3D shapes of molecules.",
]:
    story.append(blt(b))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 6 — PHOTOELECTRIC EFFECT
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 6 — PHOTOELECTRIC EFFECT"), sp(8)]

story += [sec("6.1  Phenomenon & Why Wave Theory Fails")]
story += [body("When light of sufficient frequency falls on a metal surface, electrons are ejected (photoelectrons). "
               "Einstein explained this in 1905 using Planck's quantum theory  (Nobel Prize 1921).")]
story += [sp(3), sub_h("Observations that Wave Theory CANNOT explain:")]
for b in [
    "Emission is INSTANTANEOUS  (wave theory predicts time delay for energy buildup)",
    "Below threshold frequency " + NU + sub('0') + ":  NO emission regardless of intensity",
    "Above " + NU + sub('0') + ":  KE_max depends on FREQUENCY, NOT intensity",
    "More intensity " + ARR + " MORE electrons emitted  (not faster electrons)",
]:
    story.append(blt(b))
story.append(sp(5))

story.append(sub_h("Formula 10 -- Einstein's Photoelectric Equation"))
story.append(formula_box(
    "h" + NU + "  =  " + PHI + "  +  KE_max",
    [
        "h" + NU + " = energy of incident photon (J or eV)",
        PHI + " (phi) = work function = minimum energy to eject ONE electron = h" + NU + sub('0') + "  (J or eV)",
        "KE_max = maximum KE of ejected photoelectron = (1/2)m" + sub('e') + "v" + sup('2') + "_max  (J or eV)",
        "If h" + NU + " < " + PHI + ":  NO emission at all (even at very high intensity)",
        "If h" + NU + " = " + PHI + ":  Emission just starts,  KE_max = 0",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 11 -- Work Function"))
story.append(formula_box(
    PHI + "  =  h" + NU + sub('0'),
    [
        PHI + " = work function -- a fixed property of the metal surface",
        NU + sub('0') + " = threshold frequency -- minimum frequency for photoelectric emission",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["Metal",PHI + " (eV)","Threshold " + LAM + sub('0') + " (nm)","Responds to"],
    [
        ["Cs","2.0","620 nm","Visible light (red-orange)"],
        ["K", "2.2","564 nm","Visible light (yellow)"],
        ["Na","2.3","539 nm","Visible light (green)"],
        ["Al","4.3","288 nm","UV only"],
        ["Zn","4.3","288 nm","UV only"],
        ["Pt","5.6","221 nm","UV only"],
    ],
    col_widths=[W*0.12,W*0.18,W*0.26,W*0.44],
    left_cols=[3]
))
story.append(sp(5))

story.append(sub_h("Formula 12 -- Threshold Wavelength"))
story.append(formula_box(
    LAM + sub('0') + "  =  hc / " + PHI + "  =  c / " + NU + sub('0') + "     " + ARR + "     " + LAM + sub('0') + "(nm)  =  1240 / " + PHI + "(eV)",
    [
        "Light with " + LAM + " < " + LAM + sub('0') + "  (higher frequency)  " + ARR + "  emission OCCURS",
        "Light with " + LAM + " > " + LAM + sub('0') + "  (lower frequency)  " + ARR + "  NO emission  (regardless of intensity)",
        "Example:  " + PHI + "=2.0 eV  " + ARR + "  " + LAM + sub('0') + "=620 nm (red)     " + PHI + "=4.3 eV  " + ARR + "  " + LAM + sub('0') + "=288 nm (UV)",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 13 -- Stopping Potential"))
story.append(formula_box(
    "eV" + sub('0') + "  =  KE_max  =  h" + NU + "  -  " + PHI,
    [
        "e = 1.602" + TIMES + "10" + sup('-19') + " C   |   V" + sub('0') + " = stopping potential  (minimum reverse voltage to stop ALL photoelectrons)  in Volts",
        "KE_max in eV numerically equals V" + sub('0') + " in Volts  --  if KE_max=2.5 eV then V" + sub('0') + "=2.5 V",
        "More INTENSITY:  photocurrent " + UP + ",  V" + sub('0') + " UNCHANGED",
        "Higher FREQUENCY:  V" + sub('0') + " " + UP + ",  photocurrent unchanged",
        "V" + sub('0') + " vs " + NU + " graph:  Slope = h/e = 4.136" + TIMES + "10" + sup('-15') + " V" + CDOT + "s   |   x-intercept = " + NU + sub('0') + "   |   y-intercept = -" + PHI + "/e",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 14 -- Number of Photons per Unit Area per Second"))
story.append(formula_box(
    "n_photons  =  I / h" + NU + "  =  I" + LAM + " / hc",
    [
        "n_photons = number of photons hitting unit area per second  (s" + sup('-1') + CDOT + "m" + sup('-2') + ")",
        "I = intensity = energy per unit area per second  (W/m" + sup('2') + ")",
        "More intensity = MORE photons = MORE electrons ejected = LARGER photocurrent",
        "Each photon gives energy to ONE electron -- so KE_max is unaffected by intensity",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 7 — de BROGLIE
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 7 — DUAL NATURE OF MATTER  (de Broglie, 1924)"), sp(8)]

story += [sec("7.1  Background")]
for b in [
    "Louis de Broglie (1924): If light (wave) can behave as particles (photons), matter (particles) should also show wave properties",
    "Wave-particle duality: all matter has both wave and particle properties",
    "Only observable for MICROSCOPIC particles (electrons, protons)  --  not for macroscopic objects",
    "Experimental proof: Davisson-Germer experiment (1927)  --  electron diffraction by nickel crystal confirmed electron wave nature",
]:
    story.append(blt(b))
story.append(sp(5))

story.append(sub_h("Formula 15 -- de Broglie Wavelength (General)"))
story.append(formula_box(
    LAM + "  =  h / mv  =  h / p",
    [
        LAM + " = de Broglie (matter) wavelength (m)",
        "h = Planck's constant = 6.626" + TIMES + "10" + sup('-34') + " J" + CDOT + "s   |   m = mass of particle (kg)   |   v = velocity (m/s)",
        "p = mv = momentum (kg" + CDOT + "m/s)",
        "Cricket ball (0.1 kg, 30 m/s):   " + LAM + " ~ 2" + TIMES + "10" + sup('-34') + " m   --  unmeasurably tiny",
        "Electron (9.1" + TIMES + "10" + sup('-31') + " kg, 10" + sup('6') + " m/s):   " + LAM + " ~ 0.7 nm   --  detectable by X-ray diffraction!",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 16 -- de Broglie Wavelength from Kinetic Energy"))
story.append(formula_box(
    LAM + "  =  h / " + SQRT + "(2m" + CDOT + "KE)",
    [
        "Derived from " + LAM + " = h/mv and KE = (1/2)mv" + sup('2') + "   " + ARR + "   mv = " + SQRT + "(2m" + CDOT + "KE)",
        "KE MUST be in Joules.  Convert:  KE(J) = KE(eV) " + TIMES + " 1.602" + TIMES + "10" + sup('-19'),
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 17 -- de Broglie Wavelength for Accelerated Electron"))
story.append(formula_box(
    LAM + "  =  12.27 / " + SQRT + "V     " + ANG + "       (electrons only)",
    [
        "12.27 = constant for ELECTRONS only = h/" + SQRT + "(2" + CDOT + "m" + sub('e') + CDOT + "e)  in " + ANG + CDOT + "V" + sup('1/2') + " units",
        "V = accelerating potential difference in VOLTS   |   Answer in ANGSTROMS",
        "For PROTON:   " + LAM + " = 0.286/" + SQRT + "V  " + ANG,
        "V=100 V " + ARR + " " + LAM + "=1.227 " + ANG + "   |   V=1000 V " + ARR + " " + LAM + "=0.388 " + ANG + "   |   V=10000 V " + ARR + " " + LAM + "=0.123 " + ANG,
        "Used in electron microscopy  (" + LAM + " much smaller than visible light " + ARR + " far higher resolution)",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 18 -- de Broglie and Bohr Connection"))
story.append(formula_box(
    "2" + PI + "r" + sub('n') + "  =  n" + LAM + "   (circumference of orbit = whole-number multiples of " + LAM + ")",
    [
        "Bohr's quantisation condition (mvr = nh/2" + PI + ") is equivalent to the electron's de Broglie wave fitting exactly into the orbit.",
        "This gives a wave-mechanical basis to Bohr's model.",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 8 — HEISENBERG
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 8 — HEISENBERG'S UNCERTAINTY PRINCIPLE (1927)"), sp(8)]

story += [sec("8.1  Statement")]
story += [body("It is impossible to simultaneously determine the EXACT position AND exact momentum (or velocity) "
               "of a microscopic particle. This is a fundamental law of nature -- NOT due to measurement error.")]
story.append(sp(5))

story.append(sub_h("Formula 19 -- Heisenberg's Uncertainty Principle"))
story.append(formula_box(
    DEL + "x  " + CDOT + "  " + DEL + "p  " + GEQ + "  h / 4" + PI + "         OR         "
    + DEL + "x  " + CDOT + "  m" + DEL + "v  " + GEQ + "  h / 4" + PI,
    [
        DEL + "x = uncertainty in position (m)   |   " + DEL + "p = uncertainty in momentum (kg" + CDOT + "m/s)",
        DEL + "v = uncertainty in velocity (m/s)   |   h/4" + PI + " = 5.27" + TIMES + "10" + sup('-35') + " J" + CDOT + "s",
        "Equivalent form:   " + DEL + "x " + CDOT + " " + DEL + "p  " + GEQ + "  " + HBAR + "/2       where  " + HBAR + " = h/2" + PI + " = 1.055" + TIMES + "10" + sup('-34') + " J" + CDOT + "s",
        "Energy-time version:   " + DEL + "E " + CDOT + " " + DEL + "t  " + GEQ + "  h/4" + PI,
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 20 -- Minimum Uncertainty in Velocity"))
story.append(formula_box(
    DEL + "v_min  =  h / (4" + PI + "  " + TIMES + "  m  " + TIMES + "  " + DEL + "x)",
    [
        "If " + DEL + "x = 0 (exact position):   " + DEL + "p = " + INF + "  (momentum completely unknown)",
        "If " + DEL + "p = 0 (exact momentum):   " + DEL + "x = " + INF + "  (position completely unknown)",
        "Applies to ALL microscopic particles -- not due to experimental limitations",
    ]
))
story.append(sp(4))
story.append(trap_box("Heisenberg's UP INVALIDATES Bohr's model -- definite circular orbits would mean exact position AND velocity simultaneously, which is FORBIDDEN by the UP."))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 9 — QUANTUM NUMBERS
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 9 — QUANTUM MECHANICAL MODEL & QUANTUM NUMBERS"), sp(8)]

story += [sec("9.1  Orbital vs Orbit")]
story.append(make_table(
    ["Feature","Orbit (Bohr)","Orbital (Quantum Mechanics)"],
    [
        ["Definition","Definite circular path","Region of space where probability of finding electron is 90% or more"],
        ["Heisenberg","VIOLATES HUP","Consistent with HUP"],
        ["Dimensions","2D circle","3D region of space"],
        ["Position","Exact position known","Only probability density known"],
    ],
    col_widths=[W*0.18,W*0.28,W*0.54],
    left_cols=[0,1,2]
))
story.append(sp(8))

story += [sec("9.2  The Four Quantum Numbers")]
story += [body("Every electron in an atom is described by a UNIQUE set of 4 quantum numbers. "
               "No two electrons can have the same set of all 4  (Pauli's Exclusion Principle).")]
story.append(sp(5))

story.append(sub_h("(a) Principal Quantum Number  (n)"))
story.append(formula_box(
    "n  =  1,  2,  3,  4,  5,  6,  7  ...",
    [
        "Determines ENERGY and SIZE of the orbital",
        "Higher n = larger orbital = higher energy = farther from nucleus",
        "Shell names:  n=1 " + ARR + " K    n=2 " + ARR + " L    n=3 " + ARR + " M    n=4 " + ARR + " N",
    ]
))
story.append(sp(5))

story.append(sub_h("(b) Azimuthal Quantum Number  (l)  --  Subsidiary / Angular Momentum QN"))
story.append(formula_box(
    "l  =  0,  1,  2,  ...,  (n-1)",
    [
        "Determines SHAPE of orbital and SUBSHELL",
        "l=0 " + ARR + " s (sphere)   |   l=1 " + ARR + " p (dumbbell)   |   l=2 " + ARR + " d (double dumbbell)   |   l=3 " + ARR + " f (complex)",
        "For n=1: l=0 only (1s)   |   n=2: l=0,1 (2s, 2p)   |   n=3: l=0,1,2 (3s, 3p, 3d)",
    ]
))
story.append(sp(5))

story.append(sub_h("(c) Magnetic Quantum Number  (m" + sub('l') + ")"))
story.append(formula_box(
    "m" + sub('l') + "  =  -l,  -(l-1),  ...,  0,  ...,  (l-1),  +l     " + ARR + "     Total values = 2l+1",
    [
        "Determines ORIENTATION of orbital in space",
        "s (l=0):  m" + sub('l') + "=0  (1 orbital)   |   p (l=1):  m" + sub('l') + "=-1,0,+1  (3 orbitals: px, py, pz)",
        "d (l=2):  m" + sub('l') + "=-2,-1,0,+1,+2  (5 orbitals)   |   f (l=3):  7 orbitals",
    ]
))
story.append(sp(5))

story.append(sub_h("(d) Spin Quantum Number  (m" + sub('s') + ")"))
story.append(formula_box(
    "m" + sub('s') + "  =  +1/2  (spin up " + UP + ")     or     -1/2  (spin down " + DOWN + ")",
    [
        "Only two possible values -- cannot change",
        "Pauli's principle: two electrons in the same orbital MUST have opposite m" + sub('s') + " values",
    ]
))
story.append(sp(8))

story += [sec("9.3  Angular Momentum Formulas")]

story.append(sub_h("Formula 21 -- Orbital Angular Momentum"))
story.append(formula_box(
    "L  =  " + SQRT + "[l(l+1)]  " + CDOT + "  " + HBAR,
    [
        "L = magnitude of orbital angular momentum (J" + CDOT + "s)",
        "l = azimuthal quantum number   |   " + HBAR + " = h/2" + PI + " = 1.055" + TIMES + "10" + sup('-34') + " J" + CDOT + "s",
        "s (l=0): L=0   |   p (l=1): L=" + SQRT + "2 " + CDOT + HBAR + "   |   d (l=2): L=" + SQRT + "6 " + CDOT + HBAR + "   |   f (l=3): L=2" + SQRT + "3 " + CDOT + HBAR,
    ]
))
story.append(trap_box("Bohr's model gave L=n" + HBAR + "  (WRONG). Correct QM formula: L=" + SQRT + "[l(l+1)]" + CDOT + HBAR + ". s orbitals have ZERO orbital angular momentum -- NOT " + HBAR + "."))
story.append(sp(5))

story.append(sub_h("Formula 22 -- z-Component of Angular Momentum"))
story.append(formula_box(
    "L" + sub('z') + "  =  m" + sub('l') + "  " + CDOT + "  " + HBAR,
    [
        "L" + sub('z') + " = projection of angular momentum on z-axis",
        "p (l=1):  L" + sub('z') + "=-" + HBAR + ", 0, +" + HBAR + "  (3 orientations)",
        "d (l=2):  L" + sub('z') + "=-2" + HBAR + ", -" + HBAR + ", 0, +" + HBAR + ", +2" + HBAR + "  (5 orientations)",
        "A magnetic field splits these orientations  " + ARR + "  Zeeman effect",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 23 -- Spin Angular Momentum"))
story.append(formula_box(
    "S  =  " + SQRT + "[s(s+1)]  " + CDOT + "  " + HBAR + "  =  (" + SQRT + "3/2)  " + CDOT + "  " + HBAR + "     [same for ALL electrons]",
    [
        "s = spin quantum number = 1/2 always (intrinsic property of electron -- cannot change)",
        "The MAGNITUDE of spin is fixed for all electrons; only DIRECTION (m" + sub('s') + " = " + PM + "1/2) can vary",
    ]
))
story.append(sp(8))

story += [sec("9.4  Shell / Subshell Count Formulas")]
story.append(formula_box(
    "Orbitals in n" + sup('th') + " shell  =  n" + sup('2') + "                Max electrons in n" + sup('th') + " shell  =  2n" + sup('2') + "\n"
    "Orbitals in a subshell  =  2l+1          Max electrons in a subshell  =  2(2l+1)",
    [
        "n=1: 1 orbital, 2 e" + sup('-') + "   |   n=2: 4 orbitals, 8 e" + sup('-') + "   |   n=3: 9 orbitals, 18 e" + sup('-') + "   |   n=4: 16 orbitals, 32 e" + sup('-'),
        "s: 1 orbital, 2 e" + sup('-') + "   |   p: 3 orbitals, 6 e" + sup('-') + "   |   d: 5 orbitals, 10 e" + sup('-') + "   |   f: 7 orbitals, 14 e" + sup('-'),
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 10 — SHAPES OF ORBITALS
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 10 — SHAPES OF ORBITALS"), sp(8)]
story.append(make_table(
    ["Orbital","Shape","Angular Nodes","Nodal Planes","Starts at n"],
    [
        ["s (l=0)","Sphere","0","None (spherical symmetry)","n=1"],
        ["p (l=1)","Dumbbell (2 lobes)","1","px: yz-plane  |  py: xz-plane  |  pz: xy-plane","n=2"],
        ["d (l=2)","Double dumbbell / clover (4 lobes); dz" + sup('2') + " has donut+dumbbell","2","Two nodal planes per orbital","n=3"],
        ["f (l=3)","Complex multi-lobed","3","Three nodal regions","n=4"],
    ],
    col_widths=[W*0.12,W*0.30,W*0.14,W*0.30,W*0.14],
    left_cols=[1,3]
))
story.append(sp(4))
for b in [
    "1s: 1 sphere.  2s: 2 concentric spheres (1 radial node inside).  3s: 3 concentric spheres.",
    "Three p orbitals (px, py, pz) are identical in shape but oriented along different axes -- DEGENERATE (same energy in absence of a field).",
    "Five d orbitals: dxy, dxz, dyz, dx" + sup('2') + "-y" + sup('2') + " (clover-leaf) and dz" + sup('2') + " (unique doughnut + dumbbell along z-axis).",
]:
    story.append(blt(b))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 11 — NODES
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 11 — NODES"), sp(8)]
story.append(formula_box(
    "Radial nodes  =  n - l - 1\n"
    "Angular nodes  =  l\n"
    "Total nodes  =  n - 1",
    [
        "Radial nodes = spherical surfaces INSIDE the orbital where electron density = 0",
        "Angular nodes = flat planes (or cones) through the NUCLEUS where electron probability = 0",
        "Proof:  (n-l-1) + l  =  n-1     " + CHECK + "  (always true for any orbital)",
    ]
))
story.append(sp(5))
story.append(make_table(
    ["Orbital","n","l","Radial (n-l-1)","Angular (l)","Total (n-1)"],
    [
        ["1s","1","0","0","0","0"],
        ["2s","2","0","1","0","1"],
        ["2p","2","1","0","1","1"],
        ["3s","3","0","2","0","2"],
        ["3p","3","1","1","1","2"],
        ["3d","3","2","0  " + WARN,"2","2"],
        ["4s","4","0","3","0","3"],
        ["4p","4","1","2","1","3"],
        ["4d","4","2","1","2","3"],
        ["4f","4","3","0","3","3"],
    ],
    col_widths=[W*0.12,W*0.08,W*0.08,W*0.24,W*0.22,W*0.26]
))
story.append(sp(3))
story.append(trap_box("3d has ZERO radial nodes  (students often say 1 -- that is WRONG)."))
story.append(trap_box("2s and 2p BOTH have 1 total node but DIFFERENT types:  2s has 1 RADIAL node (spherical shell),  2p has 1 ANGULAR node (flat plane)."))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 12 — ELECTRONIC CONFIGURATION
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 12 — ELECTRONIC CONFIGURATION"), sp(8)]

story += [sec("12.1  Three Fundamental Rules")]

story.append(sub_h("Rule 1 -- Aufbau Principle"))
story += [body("Fill orbitals in INCREASING order of energy (n+l rule). "
               "If two orbitals have the same (n+l), fill the one with LOWER n first.")]
story.append(sp(3))
story.append(formula_box(
    "Filling order:  1s " + ARR + " 2s " + ARR + " 2p " + ARR + " 3s " + ARR + " 3p " + ARR + " 4s " + ARR + " 3d " + ARR + " 4p " + ARR + " 5s " + ARR + " 4d " + ARR + " 5p " + ARR + " 6s " + ARR + " 4f " + ARR + " 5d " + ARR + " 6p",
    [
        "4s (n+l=4) is filled BEFORE 3d (n+l=5)",
        "4f (n+l=7) is filled BEFORE 5d (n+l=7, but 5d has higher n)",
    ]
))
story.append(sp(5))

story.append(sub_h("Rule 2 -- Pauli's Exclusion Principle"))
story += [body("No two electrons in the same atom can have the SAME SET of all four quantum numbers. "
               "Consequence: maximum 2 electrons per orbital with OPPOSITE spins (one " + UP + ", one " + DOWN + ").")]
story.append(sp(5))

story.append(sub_h("Rule 3 -- Hund's Rule of Maximum Multiplicity"))
story += [body("In degenerate orbitals (same energy), electrons fill SINGLY first (one per orbital) "
               "with PARALLEL spins before any pairing occurs.")]
story.append(sp(3))
story.append(note_box("Nitrogen (Z=7):  1s" + sup('2') + " 2s" + sup('2') + " 2p" + sup('3') + "   " + ARR + "   2p orbitals:  " + UP + " | " + UP + " | " + UP + "   (singly occupied -- CORRECT)     NOT:  " + UP + DOWN + " | " + UP + " | _ (pairing before all singly occupied -- WRONG)"))
story.append(sp(8))

story += [sec("12.2  Electronic Configurations  Z = 1 to 30")]
story.append(make_table(
    ["Z","Element","Configuration","Unpaired e" + sup('-')],
    [
        ["1","H","1s" + sup('1'),"1"],
        ["2","He","1s" + sup('2'),"0"],
        ["3","Li","[He] 2s" + sup('1'),"1"],
        ["4","Be","[He] 2s" + sup('2'),"0"],
        ["5","B","[He] 2s" + sup('2') + " 2p" + sup('1'),"1"],
        ["6","C","[He] 2s" + sup('2') + " 2p" + sup('2'),"2"],
        ["7","N","[He] 2s" + sup('2') + " 2p" + sup('3'),"3"],
        ["8","O","[He] 2s" + sup('2') + " 2p" + sup('4'),"2"],
        ["9","F","[He] 2s" + sup('2') + " 2p" + sup('5'),"1"],
        ["10","Ne","[He] 2s" + sup('2') + " 2p" + sup('6'),"0"],
        ["11","Na","[Ne] 3s" + sup('1'),"1"],
        ["12","Mg","[Ne] 3s" + sup('2'),"0"],
        ["13","Al","[Ne] 3s" + sup('2') + " 3p" + sup('1'),"1"],
        ["14","Si","[Ne] 3s" + sup('2') + " 3p" + sup('2'),"2"],
        ["15","P","[Ne] 3s" + sup('2') + " 3p" + sup('3'),"3"],
        ["16","S","[Ne] 3s" + sup('2') + " 3p" + sup('4'),"2"],
        ["17","Cl","[Ne] 3s" + sup('2') + " 3p" + sup('5'),"1"],
        ["18","Ar","[Ne] 3s" + sup('2') + " 3p" + sup('6'),"0"],
        ["19","K","[Ar] 4s" + sup('1'),"1"],
        ["20","Ca","[Ar] 4s" + sup('2'),"0"],
        ["21","Sc","[Ar] 3d" + sup('1') + " 4s" + sup('2'),"1"],
        ["22","Ti","[Ar] 3d" + sup('2') + " 4s" + sup('2'),"2"],
        ["23","V","[Ar] 3d" + sup('3') + " 4s" + sup('2'),"3"],
        ["24 " + WARN,"Cr  (EXCEPTION)","[Ar] 3d" + sup('5') + " 4s" + sup('1') + "   (NOT 3d" + sup('4') + " 4s" + sup('2') + ")","6"],
        ["25","Mn","[Ar] 3d" + sup('5') + " 4s" + sup('2'),"5"],
        ["26","Fe","[Ar] 3d" + sup('6') + " 4s" + sup('2'),"4"],
        ["27","Co","[Ar] 3d" + sup('7') + " 4s" + sup('2'),"3"],
        ["28","Ni","[Ar] 3d" + sup('8') + " 4s" + sup('2'),"2"],
        ["29 " + WARN,"Cu  (EXCEPTION)","[Ar] 3d" + sup('10') + " 4s" + sup('1') + "   (NOT 3d" + sup('9') + " 4s" + sup('2') + ")","1"],
        ["30","Zn","[Ar] 3d" + sup('10') + " 4s" + sup('2'),"0"],
    ],
    col_widths=[W*0.12,W*0.18,W*0.54,W*0.16],
    left_cols=[2]
))
story.append(sp(4))
story.append(note_box(
    "Reason for Cr and Cu exceptions:  Half-filled (d" + sup('5') + ") and fully-filled (d" + sup('10') + ") "
    "subshells have extra stability due to  (1) Symmetrical distribution of electrons,  "
    "(2) Maximum exchange energy."
))
story.append(sp(8))

story += [sec("12.3  Magnetic Properties")]

story.append(sub_h("Formula 31 -- Spin Multiplicity"))
story.append(formula_box(
    "Spin multiplicity  =  2S + 1         where  S  =  (number of unpaired electrons) / 2",
    [
        "Multiplicity = 1 (singlet):  all electrons paired  " + ARR + "  DIAMAGNETIC (repelled by magnetic field)",
        "Multiplicity > 1:  unpaired electrons  " + ARR + "  PARAMAGNETIC (attracted by magnetic field)",
        "Higher multiplicity = more unpaired electrons = stronger paramagnetism",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["Unpaired e" + sup('-'),"S","Multiplicity","Type","Example"],
    [
        ["0","0","1  (singlet)","Diamagnetic","He, Ne, Zn, Be, Mg"],
        ["1","1/2","2  (doublet)","Paramagnetic","H, F, Na, Cu" + sup('2+')],
        ["2","1","3  (triplet)","Paramagnetic","C, O, Ni" + sup('2+')],
        ["3","3/2","4  (quartet)","Paramagnetic","N, Co" + sup('2+') + ", Cr" + sup('3+')],
        ["4","2","5  (quintet)","Paramagnetic","Fe" + sup('2+') + ", Cr" + sup('2+')],
        ["5","5/2","6  (sextet)","Paramagnetic","Mn" + sup('2+') + ", Fe" + sup('3+')],
    ],
    col_widths=[W*0.14,W*0.10,W*0.22,W*0.18,W*0.36],
    left_cols=[4]
))
story.append(sp(5))

story.append(sub_h("Formula 32 -- Magnetic Moment"))
story.append(formula_box(
    MU + "  =  " + SQRT + "[n(n+2)]     BM   (Bohr Magneton)",
    [
        "n = number of unpaired electrons   |   1 BM (Bohr Magneton) = 9.274" + TIMES + "10" + sup('-24') + " J/T",
        "1 unpaired: " + MU + "=" + SQRT + "3 " + "\u2248" + " 1.73 BM  (Cu" + sup('2+') + ", Ti" + sup('3+') + ")",
        "2 unpaired: " + MU + "=" + SQRT + "8 " + "\u2248" + " 2.83 BM  (Ni" + sup('2+') + ")",
        "3 unpaired: " + MU + "=" + SQRT + "15 " + "\u2248" + " 3.87 BM  (Co" + sup('2+') + ", Cr" + sup('3+') + ")",
        "4 unpaired: " + MU + "=" + SQRT + "24 " + "\u2248" + " 4.90 BM  (Fe" + sup('2+') + ")",
        "5 unpaired: " + MU + "=" + SQRT + "35 " + "\u2248" + " 5.92 BM  (Mn" + sup('2+') + ", Fe" + sup('3+') + ")",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 13 — CONSTANTS
# ══════════════════════════════════════════════════════════════════
story.append(PageBreak())
story += [part_header("PART 13 — COMPLETE CONSTANTS REFERENCE"), sp(8)]
story.append(make_table(
    ["Symbol","Name","Value","Unit"],
    [
        ["h","Planck's constant","6.626 " + TIMES + " 10" + sup('-34'),"J" + CDOT + "s"],
        [HBAR,"Reduced Planck (h/2" + PI + ")","1.055 " + TIMES + " 10" + sup('-34'),"J" + CDOT + "s"],
        ["c","Speed of light","3 " + TIMES + " 10" + sup('8'),"m/s"],
        ["e","Elementary charge","1.602 " + TIMES + " 10" + sup('-19'),"C"],
        ["m" + sub('e'),"Mass of electron","9.109 " + TIMES + " 10" + sup('-31'),"kg"],
        ["m" + sub('p'),"Mass of proton","1.673 " + TIMES + " 10" + sup('-27'),"kg"],
        ["m" + sub('n'),"Mass of neutron","1.675 " + TIMES + " 10" + sup('-27'),"kg"],
        ["a" + sub('0'),"Bohr radius (1st orbit of H)","0.529 " + ANG + " = 5.29" + TIMES + "10" + sup('-11'),"m"],
        ["R" + sub('H'),"Rydberg constant","1.097" + TIMES + "10" + sup('7') + " m" + sup('-1') + " = 109677 cm" + sup('-1'),"m" + sup('-1')],
        ["r" + sub('0'),"Nuclear radius constant","1.2 " + TIMES + " 10" + sup('-15') + " = 1.2 fm","m"],
        ["1 eV","In Joules","1.602 " + TIMES + " 10" + sup('-19'),"J"],
        ["1 amu","In kg","1.66 " + TIMES + " 10" + sup('-27'),"kg"],
        ["1 " + ANG,"In metres","10" + sup('-10'),"m"],
        ["1 nm","In metres","10" + sup('-9'),"m"],
        ["1 pm","In metres","10" + sup('-12'),"m"],
        ["1 fm","In metres","10" + sup('-15'),"m"],
    ],
    col_widths=[W*0.13,W*0.40,W*0.32,W*0.15],
    left_cols=[1]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# MASTER FORMULA SHEET
# ══════════════════════════════════════════════════════════════════
story.append(PageBreak())
story += [part_header("MASTER FORMULA SHEET -- ALL 41 FORMULAS AT A GLANCE"), sp(8)]
story.append(make_table(
    ["#","Formula Name","Expression"],
    [
        ["1","Orbital radius","r" + sub('n') + " = 0.529 " + TIMES + " n" + sup('2') + "/Z  " + ANG],
        ["2","Orbital velocity","v" + sub('n') + " = 2.18" + TIMES + "10" + sup('6') + " " + TIMES + " Z/n  m/s"],
        ["3","Total energy","E" + sub('n') + " = -13.6 " + TIMES + " Z" + sup('2') + "/n" + sup('2') + "  eV"],
        ["4","Kinetic energy","KE = -E" + sub('n') + " = +13.6 Z" + sup('2') + "/n" + sup('2') + "  eV"],
        ["5","Potential energy","PE = 2E" + sub('n') + " = -27.2 Z" + sup('2') + "/n" + sup('2') + "  eV"],
        ["6","Ionisation energy","IE = +13.6 " + TIMES + " Z" + sup('2') + "/n" + sup('2') + "  eV"],
        ["7","Photon energy (transition)",DEL + "E = 13.6 Z" + sup('2') + " (1/n" + sub('1') + sup('2') + " - 1/n" + sub('2') + sup('2') + ")  eV"],
        ["8","Rydberg equation","1/" + LAM + " = R" + sub('H') + " Z" + sup('2') + " (1/n" + sub('1') + sup('2') + " - 1/n" + sub('2') + sup('2') + ")"],
        ["9","Angular momentum (Bohr)","mv" + sub('n') + "r" + sub('n') + " = nh/2" + PI + " = n" + HBAR],
        ["10","Time period","T" + sub('n') + " " + PROP + " n" + sup('3') + "/Z" + sup('2')],
        ["11","Revolution frequency",NU + sub('n') + " " + PROP + " Z" + sup('2') + "/n" + sup('3')],
        ["12","Spectral lines count","(n" + sub('2') + "-n" + sub('1') + ")(n" + sub('2') + "-n" + sub('1') + "+1)/2"],
        ["13","Wave equation","c = " + NU + LAM],
        ["14","Wave number",NU + "\u0303 = 1/" + LAM + "  (m" + sup('-1') + " or cm" + sup('-1') + ")"],
        ["15","Photon energy","E = h" + NU + " = hc/" + LAM + " = hc" + NU + "\u0303"],
        ["16","Energy shortcut","E(eV) = 1240/" + LAM + "(nm)"],
        ["17","Photon momentum","p = h/" + LAM + " = E/c"],
        ["18","Photoelectric equation","h" + NU + " = " + PHI + " + KE_max"],
        ["19","Work function",PHI + " = h" + NU + sub('0')],
        ["20","Threshold wavelength",LAM + sub('0') + "(nm) = 1240/" + PHI + "(eV)"],
        ["21","Stopping potential","eV" + sub('0') + " = KE_max = h" + NU + " - " + PHI],
        ["22","Photon count (intensity)","n = I/h" + NU + " = I" + LAM + "/hc"],
        ["23","de Broglie (general)",LAM + " = h/mv = h/p"],
        ["24","de Broglie (from KE)",LAM + " = h/" + SQRT + "(2m" + CDOT + "KE)"],
        ["25","de Broglie (electron, V)",LAM + " = 12.27/" + SQRT + "V  " + ANG],
        ["26","Heisenberg's UP",DEL + "x" + CDOT + DEL + "p " + GEQ + " h/4" + PI],
        ["27","Min velocity uncertainty",DEL + "v_min = h/(4" + PI + CDOT + "m" + CDOT + DEL + "x)"],
        ["28","Orbital angular momentum","L = " + SQRT + "[l(l+1)]" + CDOT + HBAR],
        ["29","L z-component","L" + sub('z') + " = m" + sub('l') + CDOT + HBAR],
        ["30","Spin angular momentum","S = (" + SQRT + "3/2)" + CDOT + HBAR + "  [all electrons]"],
        ["31","Orbitals per shell","n" + sup('2')],
        ["32","Max e" + sup('-') + " per shell","2n" + sup('2')],
        ["33","Orbitals per subshell","2l+1"],
        ["34","Max e" + sup('-') + " per subshell","2(2l+1)"],
        ["35","Radial nodes","n - l - 1"],
        ["36","Angular nodes","l"],
        ["37","Total nodes","n - 1"],
        ["38","Spin multiplicity","2S+1   where S=(unpaired e" + sup('-') + ")/2"],
        ["39","Magnetic moment",MU + " = " + SQRT + "[n(n+2)]  BM"],
        ["40","Nuclear radius","r = r" + sub('0') + " " + TIMES + " A" + sup('1/3')],
        ["41","e/m ratio (electron)","1.758 " + TIMES + " 10" + sup('11') + "  C/kg"],
    ],
    col_widths=[W*0.06,W*0.36,W*0.58],
    left_cols=[1,2]
))
story.append(sp(8))

# Footer
story.append(thinhr())
story.append(sp(4))
story.append(Paragraph(
    "Atomic Structure  |  Class 11 Chemistry  |  Complete Chapter  |  All 41 Formulas  |  NEET / JEE",
    sFooter
))

# ── Build ──────────────────────────────────────────────────────────
doc.build(story)
print("PDF created:", OUTPUT)

Successfully replaced 1 instance(s) of the string in '/tmp/workspace/atomic-structure/generate_bw.py'

"""
Atomic Structure - Complete Chapter PDF
Black & White, DroidSans Unicode font, ReportLab <sub>/<super> markup,
NO placeholder squares, larger fonts, print-optimised.
"""
from reportlab.pdfbase import pdfmetrics
from reportlab.pdfbase.ttfonts import TTFont
from reportlab.lib.pagesizes import A4
from reportlab.lib import colors
from reportlab.lib.styles import ParagraphStyle
from reportlab.lib.units import cm
from reportlab.lib.enums import TA_CENTER, TA_LEFT, TA_JUSTIFY
from reportlab.platypus import (
    SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle,
    HRFlowable, PageBreak
)

pdfmetrics.registerFont(TTFont('DS',  '/usr/share/fonts/google-droid-sans-fonts/DroidSans.ttf'))
pdfmetrics.registerFont(TTFont('DSB', '/usr/share/fonts/google-droid-sans-fonts/DroidSans-Bold.ttf'))

OUTPUT = "/tmp/workspace/atomic-structure/Atomic_Structure_Final.pdf"

doc = SimpleDocTemplate(
    OUTPUT, pagesize=A4,
    rightMargin=2.0*cm, leftMargin=2.0*cm,
    topMargin=2.2*cm,   bottomMargin=2.2*cm,
)
W = A4[0] - 4.0*cm

# ── colours (B&W only) ─────────────────────────────────────────────
BLACK    = colors.black
WHITE    = colors.white
LT_GREY  = colors.HexColor("#e0e0e0")
MID_GREY = colors.HexColor("#808080")
DK_GREY  = colors.HexColor("#303030")

# ── styles ─────────────────────────────────────────────────────────
def S(name, **kw): return ParagraphStyle(name, **kw)

sTitle   = S("sTitle",   fontName="DSB", fontSize=22, textColor=WHITE, alignment=TA_CENTER, spaceAfter=4, leading=30)
sSubtit  = S("sSubtit",  fontName="DS",  fontSize=11, textColor=WHITE, alignment=TA_CENTER, spaceAfter=2, leading=16)
sPart    = S("sPart",    fontName="DSB", fontSize=14, textColor=WHITE, alignment=TA_LEFT,   spaceAfter=4, spaceBefore=6, leftIndent=6, leading=20)
sSec     = S("sSec",     fontName="DSB", fontSize=13, textColor=BLACK, alignment=TA_LEFT,   spaceAfter=4, spaceBefore=8, leading=18)
sSub     = S("sSub",     fontName="DSB", fontSize=11.5, textColor=BLACK, alignment=TA_LEFT, spaceAfter=3, spaceBefore=5, leading=16)
sBody    = S("sBody",    fontName="DS",  fontSize=11, textColor=BLACK, alignment=TA_JUSTIFY, spaceAfter=4, leading=16)
sBullet  = S("sBullet",  fontName="DS",  fontSize=11, textColor=BLACK, alignment=TA_LEFT,   spaceAfter=3, leading=15, leftIndent=16)
sFormula = S("sFormula", fontName="DSB", fontSize=12.5, textColor=BLACK, alignment=TA_CENTER, spaceAfter=3, spaceBefore=3, leading=20)
sFormNote= S("sFormNote",fontName="DS",  fontSize=10.5, textColor=DK_GREY, alignment=TA_LEFT, spaceAfter=2, leading=15, leftIndent=4)
sTrap    = S("sTrap",    fontName="DSB", fontSize=11, textColor=BLACK, alignment=TA_LEFT,   spaceAfter=2, leading=15)
sNote    = S("sNote",    fontName="DS",  fontSize=11, textColor=BLACK, alignment=TA_LEFT,   spaceAfter=2, leading=15)
sTableH  = S("sTableH",  fontName="DSB", fontSize=10, textColor=WHITE, alignment=TA_CENTER, leading=13)
sTableC  = S("sTableC",  fontName="DS",  fontSize=10, textColor=BLACK, alignment=TA_CENTER, leading=13)
sTableL  = S("sTableL",  fontName="DS",  fontSize=10, textColor=BLACK, alignment=TA_LEFT,   leading=13)
sFooter  = S("sFooter",  fontName="DS",  fontSize=9,  textColor=MID_GREY, alignment=TA_CENTER, leading=12)

# ── helpers ────────────────────────────────────────────────────────
def sp(h=5):  return Spacer(1, h)
def thinhr(): return HRFlowable(width="100%", thickness=0.4, color=MID_GREY)
def thickhr():return HRFlowable(width="100%", thickness=1.0, color=BLACK)
def body(t):  return Paragraph(t, sBody)
def blt(t):   return Paragraph("&#8226;  " + t, sBullet)
def sec(t):   return Paragraph(t, sSec)
def sub_h(t): return Paragraph(t, sSub)

def part_header(t):
    tbl = Table([[Paragraph(t, sPart)]], colWidths=[W])
    tbl.setStyle(TableStyle([("BACKGROUND",(0,0),(-1,-1),BLACK),("ROWPADDING",(0,0),(-1,-1),8)]))
    return tbl

def formula_box(main, notes=None):
    elems = [Paragraph(main, sFormula)]
    if notes:
        elems.append(HRFlowable(width="100%", thickness=0.5, color=LT_GREY))
        for n in notes:
            elems.append(Paragraph(n, sFormNote))
    rows = [[e] for e in elems]
    inner = Table(rows, colWidths=[W-24])
    inner.setStyle(TableStyle([("BACKGROUND",(0,0),(-1,-1),WHITE),("ROWPADDING",(0,0),(-1,-1),5)]))
    outer = Table([[inner]], colWidths=[W])
    outer.setStyle(TableStyle([("BOX",(0,0),(-1,-1),2,BLACK),("ROWPADDING",(0,0),(-1,-1),6),("BACKGROUND",(0,0),(-1,-1),WHITE)]))
    return outer

def trap_box(t):
    tbl = Table([[Paragraph("&#9888;  NEET TRAP: " + t, sTrap)]], colWidths=[W])
    tbl.setStyle(TableStyle([("BOX",(0,0),(-1,-1),1.5,BLACK),("ROWPADDING",(0,0),(-1,-1),6),("BACKGROUND",(0,0),(-1,-1),LT_GREY)]))
    return tbl

def note_box(t):
    tbl = Table([[Paragraph("&#9733;  NOTE: " + t, sNote)]], colWidths=[W])
    tbl.setStyle(TableStyle([("BOX",(0,0),(-1,-1),1,BLACK),("ROWPADDING",(0,0),(-1,-1),6),("BACKGROUND",(0,0),(-1,-1),WHITE)]))
    return tbl

def make_table(headers, rows, col_widths=None, left_cols=None):
    if col_widths is None: col_widths = [W/len(headers)]*len(headers)
    left_cols = left_cols or []
    data = [[Paragraph(h, sTableH) for h in headers]]
    for row in rows:
        data.append([Paragraph(str(cell), sTableL if j in left_cols else sTableC) for j,cell in enumerate(row)])
    tbl = Table(data, colWidths=col_widths)
    cmds = [
        ("BACKGROUND",(0,0),(-1,0),BLACK),
        ("ROWPADDING",(0,0),(-1,-1),5),
        ("GRID",(0,0),(-1,-1),0.5,MID_GREY),
        ("VALIGN",(0,0),(-1,-1),"MIDDLE"),
        ("LINEBELOW",(0,0),(-1,0),1.0,BLACK),
    ]
    for i in range(1,len(data)):
        if i%2==0: cmds.append(("BACKGROUND",(0,i),(-1,i),colors.HexColor("#f4f4f4")))
    tbl.setStyle(TableStyle(cmds))
    return tbl

# ══════════════════════════════════════════════════════════════════
story = []

# COVER
cover_t = Table([[Paragraph("ATOMIC STRUCTURE", sTitle)]], colWidths=[W])
cover_t.setStyle(TableStyle([("BACKGROUND",(0,0),(-1,-1),BLACK),("ROWPADDING",(0,0),(-1,-1),20)]))
cover_s = Table([[Paragraph("Complete Chapter  |  All 41 Formulas  |  All Topics  |  Class 11 Chemistry  |  NEET / JEE", sSubtit)]], colWidths=[W])
cover_s.setStyle(TableStyle([("BACKGROUND",(0,0),(-1,-1),DK_GREY),("ROWPADDING",(0,0),(-1,-1),10)]))
story += [cover_t, cover_s, sp(12)]

# ══════════════════════════════════════════════════════════════════
# PART 1 — DISCOVERY OF SUB-ATOMIC PARTICLES
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 1 — DISCOVERY OF SUB-ATOMIC PARTICLES"), sp(8)]

story += [sec("1.1  Cathode Ray Experiment  (J.J. Thomson, 1897)")]
story += [body("High-voltage discharge tube with two metal electrodes (evacuated glass tube). "
               "Rays travel from cathode (&#8722;) to anode (+). These are <b>cathode rays</b>.")]
story += [sp(3), sub_h("Observations:")]
for b in [
    "Travel in straight lines; cast sharp shadows",
    "Deflect towards the positive plate  &#8594;  carry NEGATIVE charge",
    "Cause fluorescence on a ZnS screen",
    "Same e/m ratio regardless of cathode material or gas used  &#8594;  electrons are universal (same in all matter)",
    "Discovery: the <b>ELECTRON</b>",
]:  story.append(blt(b))
story += [sp(5),
    formula_box(
        "e / m<sub>e</sub>  =  1.758 &#215; 10<super>11</super>  C/kg",
        [
            "e = charge of electron = 1.602 &#215; 10<super>&#8722;19</super> C",
            "m<sub>e</sub> = mass of electron = 9.109 &#215; 10<super>&#8722;31</super> kg",
            "This ratio is CONSTANT for cathode rays in ALL gases.",
            "Canal rays (positive ions) have VARYING e/m  &#8212;  different gases give different ion masses.",
        ]
    ), sp(6)]

story += [sec("1.2  Millikan's Oil Drop Experiment  (1909)")]
story += [body("Balanced gravitational and electric forces on charged oil droplets to measure the exact charge on one electron."),
    formula_box(
        "e  =  1.602 &#215; 10<super>&#8722;19</super>  C",
        ["From known e and e/m ratio:   m<sub>e</sub> = 9.109 &#215; 10<super>&#8722;31</super> kg"]
    ), sp(6)]

story += [sec("1.3  Canal Ray Experiment  (Goldstein, 1886)")]
story += [body("Cathode with small holes. Rays appear <i>behind</i> the cathode and travel opposite to cathode rays. "
               "Discovery: <b>PROTON</b> (positively charged particle). "
               "The lightest positive ion from hydrogen gas is the proton (H<super>+</super>)."), sp(6)]

story += [sec("1.4  Discovery of Neutron  (Chadwick, 1932)")]
story += [body("Bombarded beryllium with alpha-particles &#8594; neutral radiation identified as <b>NEUTRONS</b>."),
    formula_box("Neutron charge = 0     |     m<sub>n</sub> = 1.675 &#215; 10<super>&#8722;27</super> kg"), sp(6)]

story += [sec("1.5  Sub-Atomic Particles — Summary")]
story.append(make_table(
    ["Particle","Symbol","Charge","Mass (kg)","Mass (amu)","Discoverer"],
    [
        ["Electron","e<super>&#8722;</super>","&#8722;1.602&#215;10<super>&#8722;19</super> C","9.109&#215;10<super>&#8722;31</super>","0.000549","Thomson (1897)"],
        ["Proton",  "p<super>+</super>",  "+1.602&#215;10<super>&#8722;19</super> C","1.673&#215;10<super>&#8722;27</super>","1.00728", "Goldstein/Rutherford"],
        ["Neutron", "n","0","1.675&#215;10<super>&#8722;27</super>","1.00867","Chadwick (1932)"],
    ],
    col_widths=[W*0.13,W*0.10,W*0.23,W*0.20,W*0.13,W*0.21], left_cols=[5]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 2 — ATOMIC MODELS
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 2 — ATOMIC MODELS"), sp(8)]

story += [sec("2.1  Thomson's Plum Pudding Model (1904)")]
for b in [
    "Atom = uniform positive sphere with electrons embedded like plums in a pudding",
    "Radius ~ 10<super>&#8722;10</super> m",
    "FAILED &#8212; could not explain Rutherford's alpha-scattering results",
]:  story.append(blt(b))
story.append(sp(6))

story += [sec("2.2  Rutherford's Nuclear Model (1911)")]
story += [sub_h("Alpha-Particle Scattering Observations:")]
for b in [
    "Most &#945;-particles passed straight through &#8594; atom is MOSTLY EMPTY SPACE",
    "Few deflected at small angles &#8594; small positive charge inside",
    "Very few (1 in 20,000) bounced back at 180&#176; &#8594; small, dense, positive NUCLEUS",
]:  story.append(blt(b))
story += [sp(4),
    formula_box(
        "Nuclear Radius:   r  =  r<sub>0</sub>  &#215;  A<super>1/3</super>",
        [
            "r<sub>0</sub> = nuclear radius constant = 1.2 &#215; 10<super>&#8722;15</super> m  =  1.2 fm",
            "A = mass number (total protons + neutrons)",
            "Nuclear density &#8776; 10<super>17</super> kg/m<super>3</super>  &#8212;  CONSTANT for ALL nuclei (independent of A and Z)",
            "1 cm<super>3</super> of nuclear matter weighs ~100 million tonnes!",
        ]
    ), sp(4)]
story += [sub_h("Limitations of Rutherford's Model:")]
for b in [
    "STABILITY: Accelerating electron should continuously radiate energy &#8594; spiral into nucleus &#8594; collapse in ~10<super>&#8722;8</super> s  (but atoms ARE stable!)",
    "LINE SPECTRA: A spiralling electron would emit a CONTINUOUS spectrum, NOT discrete line spectra",
]:  story.append(blt(b))
story.append(sp(6))

story += [sec("2.3  Nuclear Terminology")]
story.append(formula_box(
    "Mass Number:   A  =  Z  +  N",
    [
        "A = total nucleons (protons + neutrons)",
        "Z = atomic number = number of protons = electrons in neutral atom",
        "N = neutron number = A &#8722; Z",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["Term","Same","Different","Example"],
    [
        ["Isotopes","Z (same element)","A, N","<super>1</super>H,  <super>2</super>H (D),  <super>3</super>H (T)  &#8212; all Z=1"],
        ["Isobars","A","Z, N","<super>14</super><sub>6</sub>C  and  <super>14</super><sub>7</sub>N"],
        ["Isotones","N","Z, A","<super>3</super><sub>1</sub>H  and  <super>4</super><sub>2</sub>He  (both N=2)"],
        ["Isoelectronic","Total electrons","&#8212;","Na<super>+</super>, Mg<super>2+</super>, Ne, F<super>&#8722;</super>  (all 10 e<super>&#8722;</super>)"],
    ],
    col_widths=[W*0.18,W*0.22,W*0.18,W*0.42], left_cols=[0,1,2,3]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 3 — EM RADIATION
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 3 — ELECTROMAGNETIC RADIATION & PLANCK'S THEORY"), sp(8)]

story += [sec("3.1  Wave Theory of Light")]
for b in [
    "Light = electromagnetic wave  &#8212;  oscillating electric and magnetic fields perpendicular to each other and to the direction of travel",
    "All EM waves travel at c = 3 &#215; 10<super>8</super> m/s in vacuum (ALL frequencies, always)",
    "Do NOT require a medium to propagate",
]:  story.append(blt(b))
story.append(sp(5))
story.append(formula_box(
    "Wave Equation:   c  =  &#957;  &#215;  &#955;",
    [
        "c = speed of light = 3 &#215; 10<super>8</super> m/s  (universal constant)",
        "&#957; (nu) = frequency  in Hz (= s<super>&#8722;1</super>)",
        "&#955; (lambda) = wavelength  in metres",
        "&#957; and &#955; are INVERSELY proportional at constant c",
        "Unit conversions:  1 nm = 10<super>&#8722;9</super> m   |   1 &#8491; = 10<super>&#8722;10</super> m   |   1 pm = 10<super>&#8722;12</super> m",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Wave Number:   &#957;&#771;  =  1 / &#955;",
    [
        "Units: m<super>&#8722;1</super> or cm<super>&#8722;1</super>  (mainly cm<super>&#8722;1</super> in IR spectroscopy)",
        "CORRECT definition: &#957;&#771; = 1/&#955;     WRONG (common mistake): &#957;&#771; = &#957;/c",
    ]
))
story.append(sp(6))

story += [sec("3.2  Electromagnetic Spectrum")]
story.append(make_table(
    ["Region","Wavelength Range","Frequency Range","Notes"],
    [
        ["Gamma rays","&lt; 0.01 nm","&gt; 3&#215;10<super>19</super> Hz","Nuclear reactions"],
        ["X-rays","0.01 &#8211; 10 nm","3&#215;10<super>17</super> &#8211; 3&#215;10<super>19</super> Hz","Medical imaging"],
        ["UV","10 &#8211; 400 nm","7.5&#215;10<super>14</super> &#8211; 3&#215;10<super>17</super> Hz","Lyman series of H"],
        ["Visible","400 &#8211; 700 nm","4.3&#215;10<super>14</super> &#8211; 7.5&#215;10<super>14</super> Hz","Balmer series of H"],
        ["Infrared","700 nm &#8211; 1 mm","3&#215;10<super>11</super> &#8211; 4.3&#215;10<super>14</super> Hz","Paschen, Brackett series"],
        ["Microwaves","1 mm &#8211; 10 cm","3&#215;10<super>9</super> &#8211; 3&#215;10<super>11</super> Hz","Radar, cooking"],
        ["Radio waves","&gt; 10 cm","&lt; 3&#215;10<super>9</super> Hz","Broadcasting"],
    ],
    col_widths=[W*0.16,W*0.24,W*0.34,W*0.26], left_cols=[3]
))
story.append(sp(4))
story += [sub_h("Visible Light — VIBGYOR (increasing wavelength, decreasing energy):")]
story.append(make_table(
    ["Colour","Wavelength","Energy"],
    [["Violet","400 nm","3.10 eV"],["Indigo","425 nm","2.92 eV"],["Blue","450 nm","2.76 eV"],
     ["Green","520 nm","2.38 eV"],["Yellow","580 nm","2.14 eV"],["Orange","620 nm","2.00 eV"],["Red","700 nm","1.77 eV"]],
    col_widths=[W*0.33,W*0.33,W*0.34]
))
story.append(sp(6))

story += [sec("3.3  Planck's Quantum Theory (1900)")]
for b in [
    "Energy is NOT continuous &#8212; emitted/absorbed in discrete packets called QUANTA (photons)",
    "Energy of each quantum is directly proportional to its frequency",
]:  story.append(blt(b))
story.append(sp(4))
story.append(formula_box(
    "Energy of ONE Photon:   E  =  h&#957;  =  hc/&#955;  =  hc&#957;&#771;",
    [
        "h = Planck's constant = 6.626 &#215; 10<super>&#8722;34</super> J&#183;s",
        "&#957; = frequency (Hz)   |   &#955; = wavelength (m)   |   &#957;&#771; = wave number (m<super>&#8722;1</super>)",
        "E = energy of ONE photon  (in Joules or eV)   |   For n photons:  E<sub>total</sub> = n &#215; h&#957;",
        "Conversion:  1 eV = 1.602 &#215; 10<super>&#8722;19</super> J",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Energy-Wavelength Shortcut (fastest for NEET):   E(eV)  =  1240 / &#955;(nm)",
    [
        "&#955; MUST be in nanometres (nm).  Answer is in eV.",
        "For Angstroms:  E(eV) = 12400 / &#955;(&#8491;)      |      Derived from hc = 1240 eV&#183;nm",
        "Quick values:  400 nm &#8594; 3.1 eV   |   500 nm &#8594; 2.48 eV   |   700 nm &#8594; 1.77 eV",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Photon Momentum:   p  =  h/&#955;  =  E/c",
    ["Photon has ZERO rest mass but has energy E=h&#957; and momentum p=h/&#955;"]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 4 — ATOMIC SPECTRA
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 4 — ATOMIC SPECTRA & SPECTRAL SERIES"), sp(8)]

story += [sec("4.1  Line Spectrum of Hydrogen")]
story += [body("When hydrogen gas is excited (high voltage), it emits light of only certain wavelengths &#8212; "
               "a <b>LINE SPECTRUM</b> (not continuous). Each line = one specific electron transition.")]
story.append(sp(6))

story += [sec("4.2  Spectral Series of Hydrogen")]
story.append(make_table(
    ["Series","n<sub>1</sub> (lower)","n<sub>2</sub> (upper)","Region","First Line (&#955;)"],
    [
        ["Lyman",    "1","2, 3, 4...","UV","121.6 nm"],
        ["Balmer",   "2","3, 4, 5...","Visible + UV","656.3 nm  (H&#945;,  red)"],
        ["Paschen",  "3","4, 5, 6...","Near IR","1875 nm"],
        ["Brackett", "4","5, 6, 7...","IR","4051 nm"],
        ["Pfund",    "5","6, 7, 8...","Far IR","7459 nm"],
        ["Humphreys","6","7, 8, 9...","Far IR","&#8212;"],
    ],
    col_widths=[W*0.17,W*0.15,W*0.17,W*0.18,W*0.33]
))
story.append(sp(5))
story.append(formula_box(
    "Rydberg Equation:   1/&#955;  =  R<sub>H</sub>  &#215;  Z<super>2</super>  &#215;  ( 1/n<sub>1</sub><super>2</super>  &#8722;  1/n<sub>2</sub><super>2</super> )",
    [
        "R<sub>H</sub> = Rydberg constant = 1.097 &#215; 10<super>7</super> m<super>&#8722;1</super> = 109677 cm<super>&#8722;1</super>",
        "Z = atomic number  (Z=1 for H,  Z=2 for He<super>+</super>,  Z=3 for Li<super>2+</super>)",
        "n<sub>1</sub> = lower orbit  (determines the SERIES)   |   n<sub>2</sub> = upper orbit  (n<sub>2</sub> &gt; n<sub>1</sub>)",
        "First line of each series (longest &#955;):   n<sub>2</sub> = n<sub>1</sub> + 1",
        "Series limit (shortest &#955;):   n<sub>2</sub> = &#8734;   &#8594;   1/&#955; = R<sub>H</sub> &#215; Z<super>2</super> / n<sub>1</sub><super>2</super>",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Number of Spectral Lines  (n<sub>2</sub> &#8594; n<sub>1</sub>):   Lines  =  (n<sub>2</sub> &#8722; n<sub>1</sub>) (n<sub>2</sub> &#8722; n<sub>1</sub> + 1) / 2",
    [
        "Special case  &#8212;  electron falls to ground state (n<sub>1</sub> = 1):   Lines = n(n&#8722;1)/2",
        "Example 1:  n=5 &#8594; n=1:   5&#215;4/2 = <b>10 lines</b>",
        "Example 2:  n=5 &#8594; n=3:   (2)(3)/2 = <b>3 lines</b>",
        "Example 3:  n=4 &#8594; n=2:   (2)(3)/2 = <b>3 lines</b>",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 5 — BOHR'S MODEL
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 5 — BOHR'S ATOMIC MODEL (1913)"), sp(8)]

story += [sec("5.1  Postulates")]
for b in [
    "Electrons revolve in fixed circular orbits called STATIONARY STATES (no energy radiated while in orbit)",
    "Only orbits where angular momentum = whole-number multiple of h/2&#960; are allowed",
    "Energy absorbed or emitted ONLY when electron jumps between orbits",
    "Energy of emitted/absorbed photon = difference in orbital energies:   &#916;E = h&#957;",
]:  story.append(blt(b))
story.append(sp(8))

story += [sec("5.2  Bohr Model Formulas  (H and H-like ions: He<super>+</super>, Li<super>2+</super>, Be<super>3+</super>...)")]

story.append(sub_h("Formula 1 — Orbital Radius"))
story.append(formula_box(
    "r<sub>n</sub>  =  0.529  &#215;  n<super>2</super> / Z     &#8491;",
    [
        "r<sub>n</sub> = radius of n<super>th</super> orbit  (distance of electron from nucleus)",
        "0.529 &#8491; = a<sub>0</sub> = Bohr radius = radius of 1<super>st</super> orbit of H  (n=1, Z=1)",
        "n = principal quantum number = 1, 2, 3, 4...   |   Z = atomic number",
        "r<sub>n</sub> &#8733; n<super>2</super>  (quadruples when n doubles)   |   r<sub>n</sub> &#8733; 1/Z  (smaller for larger Z)",
        "Convert to metres: multiply by 10<super>&#8722;10</super>   (1 &#8491; = 10<super>&#8722;10</super> m)",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["n","H  (Z=1)","He<super>+</super>  (Z=2)","Li<super>2+</super>  (Z=3)"],
    [
        ["1","0.529 &#8491;","0.265 &#8491;","0.176 &#8491;"],
        ["2","2.116 &#8491;","1.058 &#8491;","0.705 &#8491;"],
        ["3","4.761 &#8491;","2.381 &#8491;","1.587 &#8491;"],
    ],
    col_widths=[W*0.15,W*0.28,W*0.28,W*0.29]
))
story.append(sp(6))

story.append(sub_h("Formula 2 — Orbital Velocity"))
story.append(formula_box(
    "v<sub>n</sub>  =  2.18 &#215; 10<super>6</super>  &#215;  Z / n     m/s",
    [
        "2.18 &#215; 10<super>6</super> m/s = velocity in 1<super>st</super> orbit of H  =  c/137  (much less than speed of light)",
        "v<sub>n</sub> &#8733; Z/n   |   Outer electrons move SLOWER  (hence easier to remove)",
        "H (n=1): 2.18&#215;10<super>6</super> m/s   |   H (n=2): 1.09&#215;10<super>6</super> m/s   |   H (n=3): 0.727&#215;10<super>6</super> m/s",
    ]
))
story.append(sp(6))

story.append(sub_h("Formula 3 — Total Energy"))
story.append(formula_box(
    "E<sub>n</sub>  =  &#8722;13.6  &#215;  Z<super>2</super> / n<super>2</super>     eV     =     &#8722;2.18&#215;10<super>&#8722;18</super>  &#215;  Z<super>2</super>/n<super>2</super>     J",
    [
        "E<sub>n</sub> = total energy of electron in n<super>th</super> orbit &#8212; ALWAYS NEGATIVE for a bound electron",
        "&#8722;13.6 eV = energy in 1<super>st</super> orbit of H  =  ionisation energy of H from ground state",
        "Negative sign indicates electron is BOUND to nucleus",
        "n=1 is most negative = most stable   |   At n=&#8734;:  E=0  (electron free = atom ionised)",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["n","Energy of H (Z=1)"],
    [
        ["1  (ground state)","&#8722;13.6 eV"],
        ["2","&#8722;3.4 eV"],
        ["3","&#8722;1.51 eV"],
        ["4","&#8722;0.85 eV"],
        ["5","&#8722;0.544 eV"],
        ["&#8734;  (ionised)","0 eV"],
    ],
    col_widths=[W*0.40,W*0.60]
))
story.append(sp(6))

story.append(sub_h("Formula 4 — Kinetic Energy, Potential Energy, Total Energy"))
story.append(formula_box(
    "KE  =  &#8722;E<sub>n</sub>  =  +13.6 Z<super>2</super>/n<super>2</super>  eV     (always POSITIVE)\n"
    "PE  =  2E<sub>n</sub>  =  &#8722;27.2 Z<super>2</super>/n<super>2</super>  eV     (always NEGATIVE)\n"
    "TE  =  KE + PE  =  E<sub>n</sub>",
    [
        "Three golden relationships:   KE = &#8722;TE     |     PE = 2 &#215; TE     |     PE = &#8722;2 &#215; KE",
        "Verification H (n=1):  KE=+13.6 eV,  PE=&#8722;27.2 eV,  TE=&#8722;13.6 eV     (13.6 &#8722; 27.2 = &#8722;13.6 &#10003;)",
    ]
))
story.append(sp(6))

story.append(sub_h("Formula 5 — Ionisation Energy"))
story.append(formula_box(
    "IE  =  0 &#8722; E<sub>n</sub>  =  +13.6  &#215;  Z<super>2</super> / n<super>2</super>     eV",
    [
        "IE = energy to remove electron from orbit n to infinity  (n &#8594; &#8734;)",
        "IE is ALWAYS positive   |   Decreases as n increases  (easier to remove from outer orbits)",
        "H (n=1): 13.6 eV = 1312 kJ/mol   |   He<super>+</super> (Z=2, n=1): 54.4 eV   |   Li<super>2+</super> (Z=3, n=1): 122.4 eV",
    ]
))
story.append(sp(6))

story.append(sub_h("Formula 6 — Energy of Emitted/Absorbed Photon"))
story.append(formula_box(
    "&#916;E  =  13.6  &#215;  Z<super>2</super>  &#215;  ( 1/n<sub>1</sub><super>2</super>  &#8722;  1/n<sub>2</sub><super>2</super> )     eV",
    [
        "n<sub>1</sub> = lower orbit  (electron LANDS here after emission)   n<sub>1</sub> &lt; n<sub>2</sub>",
        "n<sub>2</sub> = upper orbit  (electron STARTS here)   n<sub>2</sub> &gt; n<sub>1</sub>",
        "&#916;E is always POSITIVE",
        "EMISSION: electron falls n<sub>2</sub> &#8594; n<sub>1</sub>,  photon is released",
        "ABSORPTION: electron jumps n<sub>1</sub> &#8594; n<sub>2</sub>,  photon is absorbed",
    ]
))
story.append(sp(6))

story.append(sub_h("Formula 7 — Angular Momentum Quantisation (Bohr's Condition)"))
story.append(formula_box(
    "mv<sub>n</sub>r<sub>n</sub>  =  nh / 2&#960;  =  n&#295;",
    [
        "m = mass of electron (kg)   |   v = orbital velocity (m/s)   |   r<sub>n</sub> = orbital radius (m)",
        "n = principal quantum number  (1, 2, 3...)",
        "h = Planck's constant = 6.626&#215;10<super>&#8722;34</super> J&#183;s   |   &#295; = h/2&#960; = 1.055&#215;10<super>&#8722;34</super> J&#183;s",
    ]
))
story.append(sp(6))

story.append(sub_h("Formulas 8 & 9 — Time Period and Frequency of Revolution"))
story.append(formula_box(
    "T<sub>n</sub>  =  2&#960; r<sub>n</sub> / v<sub>n</sub>     &#8733;     n<super>3</super> / Z<super>2</super>     |     &#957;<sub>n</sub>  =  v<sub>n</sub> / (2&#960; r<sub>n</sub>)     &#8733;     Z<super>2</super> / n<super>3</super>",
    [
        "T<sub>n</sub> &#8733; n<super>3</super>  &#8212;  if n doubles, T becomes 2<super>3</super> = 8 times longer",
        "&#957;<sub>n</sub> &#8733; 1/n<super>3</super>  &#8212;  outer electrons orbit LESS frequently",
    ]
))
story.append(sp(3))
story.append(trap_box("If n doubles, time period increases by 2<super>3</super> = 8 times.  Frequency decreases 8 times."))
story.append(sp(6))

story += [sec("5.3  Limitations of Bohr's Model")]
for b in [
    "Works ONLY for hydrogen and H-like ions (one electron). Fails for multi-electron atoms.",
    "Cannot explain fine structure of spectral lines (Zeeman and Stark effects).",
    "Cannot explain relative intensities of spectral lines.",
    "Violates Heisenberg's Uncertainty Principle &#8212; definite orbits imply exact position AND momentum simultaneously.",
    "Does not explain chemical bonding or 3D shapes of molecules.",
]:  story.append(blt(b))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 6 — PHOTOELECTRIC EFFECT
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 6 — PHOTOELECTRIC EFFECT"), sp(8)]

story += [sec("6.1  Phenomenon and Why Wave Theory Fails")]
story += [body("When light of sufficient frequency falls on a metal surface, electrons are ejected  "
               "(called <b>photoelectrons</b>). Einstein explained this in 1905 using Planck's quantum theory  "
               "(Nobel Prize 1921).")]
story += [sp(3), sub_h("Observations that Wave Theory CANNOT explain:")]
for b in [
    "Emission is INSTANTANEOUS  (wave theory predicts a time delay for energy buildup)",
    "Below threshold frequency &#957;<sub>0</sub>:  NO emission regardless of how intense the light is",
    "Above &#957;<sub>0</sub>:  KE<sub>max</sub> depends on FREQUENCY, NOT intensity",
    "More intensity &#8594; MORE electrons emitted  (not faster electrons)",
]:  story.append(blt(b))
story.append(sp(5))

story.append(sub_h("Formula 10 — Einstein's Photoelectric Equation"))
story.append(formula_box(
    "h&#957;  =  &#966;  +  KE<sub>max</sub>",
    [
        "h&#957; = energy of incident photon (J or eV)",
        "&#966; (phi) = work function = minimum energy to eject ONE electron = h&#957;<sub>0</sub>  (J or eV)",
        "KE<sub>max</sub> = maximum KE of ejected photoelectron = (1/2) m<sub>e</sub> v<super>2</super><sub>max</sub>  (J or eV)",
        "If h&#957; &lt; &#966;:  NO emission at all (even at very high intensity)",
        "If h&#957; = &#966;:  Emission just starts,  KE<sub>max</sub> = 0",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 11 — Work Function"))
story.append(formula_box(
    "&#966;  =  h&#957;<sub>0</sub>",
    [
        "&#966; = work function &#8212; a fixed property of each metal surface",
        "&#957;<sub>0</sub> = threshold frequency &#8212; minimum frequency for photoelectric emission",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["Metal","&#966; (eV)","Threshold &#955;<sub>0</sub> (nm)","Responds to"],
    [
        ["Cs","2.0","620 nm","Visible light (red)"],
        ["K", "2.2","564 nm","Visible light (yellow)"],
        ["Na","2.3","539 nm","Visible light (green)"],
        ["Al","4.3","288 nm","UV only"],
        ["Zn","4.3","288 nm","UV only"],
        ["Pt","5.6","221 nm","UV only"],
    ],
    col_widths=[W*0.12,W*0.18,W*0.26,W*0.44], left_cols=[3]
))
story.append(sp(5))

story.append(sub_h("Formula 12 — Threshold Wavelength"))
story.append(formula_box(
    "&#955;<sub>0</sub>  =  hc / &#966;  =  c / &#957;<sub>0</sub>     &#8594;     &#955;<sub>0</sub>(nm)  =  1240 / &#966;(eV)",
    [
        "Light with &#955; &lt; &#955;<sub>0</sub>  (higher frequency)  &#8594;  emission OCCURS",
        "Light with &#955; &gt; &#955;<sub>0</sub>  (lower frequency)  &#8594;  NO emission  (regardless of intensity)",
        "Example:  &#966;=2.0 eV  &#8594;  &#955;<sub>0</sub>=620 nm (red)   |   &#966;=4.3 eV  &#8594;  &#955;<sub>0</sub>=288 nm (UV)",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 13 — Stopping Potential"))
story.append(formula_box(
    "eV<sub>0</sub>  =  KE<sub>max</sub>  =  h&#957;  &#8722;  &#966;",
    [
        "e = 1.602&#215;10<super>&#8722;19</super> C   |   V<sub>0</sub> = stopping potential  (minimum reverse voltage to stop ALL photoelectrons)  in Volts",
        "KE<sub>max</sub> in eV  numerically equals  V<sub>0</sub> in Volts  &#8212;  if KE<sub>max</sub>=2.5 eV then V<sub>0</sub>=2.5 V",
        "More INTENSITY:  photocurrent increases,  V<sub>0</sub> UNCHANGED",
        "Higher FREQUENCY:  V<sub>0</sub> increases,  photocurrent unchanged",
        "V<sub>0</sub> vs &#957; graph:  Slope = h/e = 4.136&#215;10<super>&#8722;15</super> V&#183;s   |   x-intercept = &#957;<sub>0</sub>   |   y-intercept = &#8722;&#966;/e",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 14 — Number of Photons per Unit Area per Second"))
story.append(formula_box(
    "n<sub>photons</sub>  =  I / h&#957;  =  I&#955; / hc",
    [
        "n<sub>photons</sub> = number of photons hitting unit area per second  (s<super>&#8722;1</super>&#183;m<super>&#8722;2</super>)",
        "I = intensity = energy per unit area per second  (W/m<super>2</super>)",
        "More intensity = MORE photons = MORE electrons ejected = LARGER photocurrent",
        "Each photon gives its energy to ONE electron &#8212; so KE<sub>max</sub> is unaffected by intensity",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 7 — de BROGLIE
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 7 — DUAL NATURE OF MATTER  (de Broglie, 1924)"), sp(8)]

story += [sec("7.1  Background")]
for b in [
    "Louis de Broglie (1924): If light (wave) can behave as particles (photons), matter (particles) should also show wave properties",
    "Wave-particle duality: all matter has both wave and particle properties",
    "Only observable for MICROSCOPIC particles (electrons, protons) &#8212; not for macroscopic objects",
    "Experimental proof: Davisson-Germer experiment (1927) &#8212; electron diffraction by nickel crystal confirmed electron wave nature",
]:  story.append(blt(b))
story.append(sp(5))

story.append(sub_h("Formula 15 — de Broglie Wavelength (General)"))
story.append(formula_box(
    "&#955;  =  h / mv  =  h / p",
    [
        "&#955; = de Broglie (matter) wavelength (m)",
        "h = Planck's constant = 6.626&#215;10<super>&#8722;34</super> J&#183;s",
        "m = mass of particle (kg)   |   v = velocity (m/s)   |   p = mv = momentum (kg&#183;m/s)",
        "Cricket ball (0.1 kg, 30 m/s):   &#955; ~ 2&#215;10<super>&#8722;34</super> m  &#8212;  unmeasurably tiny",
        "Electron (9.1&#215;10<super>&#8722;31</super> kg, 10<super>6</super> m/s):   &#955; ~ 0.7 nm  &#8212;  detectable by X-ray diffraction!",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 16 — de Broglie Wavelength from Kinetic Energy"))
story.append(formula_box(
    "&#955;  =  h / &#8730;(2m &#183; KE)",
    [
        "Derived from &#955; = h/mv and KE = (1/2)mv<super>2</super>   &#8594;   mv = &#8730;(2m&#183;KE)",
        "KE MUST be in Joules.  Convert:  KE(J) = KE(eV) &#215; 1.602&#215;10<super>&#8722;19</super>",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 17 — de Broglie Wavelength for Accelerated Electron"))
story.append(formula_box(
    "&#955;  =  12.27 / &#8730;V     &#8491;       (electrons only)",
    [
        "12.27 = constant for ELECTRONS only = h/&#8730;(2&#183;m<sub>e</sub>&#183;e)  in &#8491;&#183;V<super>1/2</super> units",
        "V = accelerating potential difference in VOLTS   |   Answer in ANGSTROMS",
        "For PROTON:   &#955; = 0.286/&#8730;V  &#8491;",
        "V=100 V &#8594; &#955;=1.227 &#8491;   |   V=1000 V &#8594; &#955;=0.388 &#8491;   |   V=10000 V &#8594; &#955;=0.123 &#8491;",
        "Used in electron microscopy  (&#955; much smaller than visible light &#8594; far higher resolution)",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 18 — de Broglie and Bohr Connection"))
story.append(formula_box(
    "2&#960; r<sub>n</sub>  =  n&#955;   (circumference = whole-number multiples of the de Broglie wavelength)",
    [
        "Bohr's quantisation (mvr = nh/2&#960;) is equivalent to the electron's de Broglie wave fitting exactly into the orbit.",
        "This gives a wave-mechanical basis to Bohr's model.",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 8 — HEISENBERG
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 8 — HEISENBERG'S UNCERTAINTY PRINCIPLE (1927)"), sp(8)]

story += [sec("8.1  Statement")]
story += [body("It is IMPOSSIBLE to simultaneously determine the exact position AND exact momentum (or velocity) "
               "of a microscopic particle. This is a fundamental law of nature &#8212; NOT due to measurement error.")]
story.append(sp(5))

story.append(sub_h("Formula 19 — Heisenberg's Uncertainty Principle"))
story.append(formula_box(
    "&#916;x  &#183;  &#916;p  &#8805;  h / 4&#960;         or         &#916;x  &#183;  m&#916;v  &#8805;  h / 4&#960;",
    [
        "&#916;x = uncertainty in position (m)   |   &#916;p = uncertainty in momentum (kg&#183;m/s)",
        "&#916;v = uncertainty in velocity (m/s)",
        "h/4&#960; = 5.27&#215;10<super>&#8722;35</super> J&#183;s  (minimum allowed product  &#8212;  cannot be smaller than this)",
        "Equivalent form:   &#916;x &#183; &#916;p  &#8805;  &#295;/2       where  &#295; = h/2&#960; = 1.055&#215;10<super>&#8722;34</super> J&#183;s",
        "Energy-time version:   &#916;E &#183; &#916;t  &#8805;  h/4&#960;",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 20 — Minimum Uncertainty in Velocity"))
story.append(formula_box(
    "&#916;v<sub>min</sub>  =  h / (4&#960;  &#215;  m  &#215;  &#916;x)",
    [
        "If &#916;x = 0 (exact position known):   &#916;p = &#8734;  (momentum completely unknown)",
        "If &#916;p = 0 (exact momentum known):   &#916;x = &#8734;  (position completely unknown)",
        "Applies to ALL microscopic particles &#8212; not due to experimental limitations",
    ]
))
story.append(sp(4))
story.append(trap_box("Heisenberg's UP INVALIDATES Bohr's model &#8212; definite circular orbits would require exact position AND exact velocity simultaneously, which is FORBIDDEN by the Uncertainty Principle."))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 9 — QUANTUM NUMBERS
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 9 — QUANTUM MECHANICAL MODEL & QUANTUM NUMBERS"), sp(8)]

story += [sec("9.1  Orbital vs Orbit")]
story.append(make_table(
    ["Feature","Orbit (Bohr)","Orbital (Quantum Mechanics)"],
    [
        ["Definition","Definite circular path","Region of space where probability of finding electron is 90% or more"],
        ["Heisenberg","VIOLATES HUP","Consistent with HUP"],
        ["Dimensions","2D circle","3D region of space"],
        ["Position","Exact position known","Only probability density known"],
    ],
    col_widths=[W*0.18,W*0.28,W*0.54], left_cols=[0,1,2]
))
story.append(sp(8))

story += [sec("9.2  The Four Quantum Numbers")]
story += [body("Every electron in an atom is described by a UNIQUE set of 4 quantum numbers. "
               "No two electrons can have the same set of all 4  (Pauli's Exclusion Principle).")]
story.append(sp(5))

story.append(sub_h("(a) Principal Quantum Number  (n)"))
story.append(formula_box(
    "n  =  1,  2,  3,  4,  5,  6,  7  ...",
    [
        "Determines ENERGY and SIZE of the orbital",
        "Higher n = larger orbital = higher energy = farther from nucleus",
        "Shell names:  n=1 &#8594; K     n=2 &#8594; L     n=3 &#8594; M     n=4 &#8594; N",
    ]
))
story.append(sp(5))

story.append(sub_h("(b) Azimuthal Quantum Number  (l)  —  Subsidiary / Angular Momentum QN"))
story.append(formula_box(
    "l  =  0,  1,  2,  ...,  (n&#8722;1)",
    [
        "Determines SHAPE of orbital and SUBSHELL",
        "l=0 &#8594; s (sphere)   |   l=1 &#8594; p (dumbbell)   |   l=2 &#8594; d (double dumbbell)   |   l=3 &#8594; f (complex)",
        "For n=1: l=0 only (1s)   |   n=2: l=0,1 (2s, 2p)   |   n=3: l=0,1,2 (3s, 3p, 3d)",
    ]
))
story.append(sp(5))

story.append(sub_h("(c) Magnetic Quantum Number  (m<sub>l</sub>)"))
story.append(formula_box(
    "m<sub>l</sub>  =  &#8722;l,  &#8722;(l&#8722;1),  ...,  0,  ...,  (l&#8722;1),  +l     &#8594;     Total values = 2l+1",
    [
        "Determines ORIENTATION of orbital in space",
        "s (l=0):  m<sub>l</sub>=0  (1 orbital)   |   p (l=1):  m<sub>l</sub>=&#8722;1,0,+1  (3 orbitals: p<sub>x</sub>, p<sub>y</sub>, p<sub>z</sub>)",
        "d (l=2):  m<sub>l</sub>=&#8722;2,&#8722;1,0,+1,+2  (5 orbitals)   |   f (l=3):  7 orbitals",
    ]
))
story.append(sp(5))

story.append(sub_h("(d) Spin Quantum Number  (m<sub>s</sub>)"))
story.append(formula_box(
    "m<sub>s</sub>  =  +1/2  (spin up &#8593;)     or     &#8722;1/2  (spin down &#8595;)     [only two possible values]",
    [
        "Every electron has spin &#8212; an intrinsic property",
        "Pauli's principle: two electrons in the same orbital MUST have opposite m<sub>s</sub> values",
    ]
))
story.append(sp(8))

story += [sec("9.3  Angular Momentum Formulas")]
story.append(sub_h("Formula 21 — Orbital Angular Momentum"))
story.append(formula_box(
    "L  =  &#8730;[l(l+1)]  &#183;  &#295;",
    [
        "L = magnitude of orbital angular momentum (J&#183;s)",
        "l = azimuthal quantum number   |   &#295; = h/2&#960; = 1.055&#215;10<super>&#8722;34</super> J&#183;s",
        "s (l=0): L=0   |   p (l=1): L=&#8730;2 &#183; &#295;   |   d (l=2): L=&#8730;6 &#183; &#295;   |   f (l=3): L=2&#8730;3 &#183; &#295;",
    ]
))
story.append(trap_box("Bohr's model gave L=n&#295;  (WRONG). Correct quantum mechanics: L=&#8730;[l(l+1)]&#183;&#295;. s orbitals have ZERO orbital angular momentum &#8212; NOT &#295;."))
story.append(sp(5))

story.append(sub_h("Formula 22 — z-Component of Angular Momentum"))
story.append(formula_box(
    "L<sub>z</sub>  =  m<sub>l</sub>  &#183;  &#295;",
    [
        "L<sub>z</sub> = projection of angular momentum on the z-axis",
        "p (l=1):  L<sub>z</sub>=&#8722;&#295;, 0, +&#295;  (3 orientations)",
        "d (l=2):  L<sub>z</sub>=&#8722;2&#295;, &#8722;&#295;, 0, +&#295;, +2&#295;  (5 orientations)",
        "A magnetic field splits these orientations  &#8594;  Zeeman effect",
    ]
))
story.append(sp(5))

story.append(sub_h("Formula 23 — Spin Angular Momentum"))
story.append(formula_box(
    "S  =  &#8730;[s(s+1)]  &#183;  &#295;  =  (&#8730;3/2)  &#183;  &#295;     [same for ALL electrons]",
    [
        "s = spin quantum number = 1/2 always (intrinsic property, cannot change)",
        "The MAGNITUDE of spin is fixed for all electrons; only DIRECTION (m<sub>s</sub> = &#177;1/2) can vary",
    ]
))
story.append(sp(8))

story += [sec("9.4  Shell / Subshell Count Formulas")]
story.append(formula_box(
    "Orbitals in n<super>th</super> shell  =  n<super>2</super>                Max electrons in n<super>th</super> shell  =  2n<super>2</super>\n"
    "Orbitals in a subshell  =  2l+1          Max electrons in a subshell  =  2(2l+1)",
    [
        "n=1: 1 orbital, 2 e<super>&#8722;</super>   |   n=2: 4 orbitals, 8 e<super>&#8722;</super>   |   n=3: 9 orbitals, 18 e<super>&#8722;</super>   |   n=4: 16 orbitals, 32 e<super>&#8722;</super>",
        "s: 1 orbital, 2 e<super>&#8722;</super>   |   p: 3 orbitals, 6 e<super>&#8722;</super>   |   d: 5 orbitals, 10 e<super>&#8722;</super>   |   f: 7 orbitals, 14 e<super>&#8722;</super>",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 10 — SHAPES OF ORBITALS
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 10 — SHAPES OF ORBITALS"), sp(8)]
story.append(make_table(
    ["Orbital","Shape","Angular Nodes","Nodal Planes","Starts at n"],
    [
        ["s (l=0)","Sphere","0","None (spherical symmetry)","n=1"],
        ["p (l=1)","Dumbbell  (2 lobes)","1","p<sub>x</sub>: yz-plane   p<sub>y</sub>: xz-plane   p<sub>z</sub>: xy-plane","n=2"],
        ["d (l=2)","Double dumbbell/clover (4 lobes); d<sub>z</sub><super>2</super> has donut+dumbbell","2","Two nodal planes per orbital","n=3"],
        ["f (l=3)","Complex multi-lobed","3","Three nodal regions","n=4"],
    ],
    col_widths=[W*0.12,W*0.31,W*0.14,W*0.29,W*0.14], left_cols=[1,3]
))
story.append(sp(4))
for b in [
    "1s: 1 sphere.  2s: 2 concentric spheres (1 radial node inside).  3s: 3 concentric spheres.",
    "Three p orbitals (p<sub>x</sub>, p<sub>y</sub>, p<sub>z</sub>) are identical in shape but oriented along different axes &#8212; DEGENERATE (same energy in the absence of a field).",
    "Five d orbitals: d<sub>xy</sub>, d<sub>xz</sub>, d<sub>yz</sub>, d<sub>x&#178;&#8722;y&#178;</sub> (clover-leaf) and d<sub>z&#178;</sub> (doughnut + dumbbell along z-axis).",
]:  story.append(blt(b))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 11 — NODES
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 11 — NODES"), sp(8)]
story.append(formula_box(
    "Radial nodes  =  n &#8722; l &#8722; 1\n"
    "Angular nodes  =  l\n"
    "Total nodes  =  n &#8722; 1",
    [
        "Radial nodes = spherical surfaces INSIDE the orbital where electron density = 0",
        "Angular nodes = flat planes (or cones) through the NUCLEUS where electron probability = 0",
        "Proof:  (n&#8722;l&#8722;1) + l  =  n&#8722;1     &#10003;  (always true for any orbital)",
    ]
))
story.append(sp(5))
story.append(make_table(
    ["Orbital","n","l","Radial  (n&#8722;l&#8722;1)","Angular  (l)","Total  (n&#8722;1)"],
    [
        ["1s","1","0","0","0","0"],
        ["2s","2","0","1","0","1"],
        ["2p","2","1","0","1","1"],
        ["3s","3","0","2","0","2"],
        ["3p","3","1","1","1","2"],
        ["3d","3","2","0  &#9888;","2","2"],
        ["4s","4","0","3","0","3"],
        ["4p","4","1","2","1","3"],
        ["4d","4","2","1","2","3"],
        ["4f","4","3","0","3","3"],
    ],
    col_widths=[W*0.12,W*0.08,W*0.08,W*0.24,W*0.22,W*0.26]
))
story.append(sp(3))
story.append(trap_box("3d has ZERO radial nodes  (students often say 1 &#8212; that is WRONG)."))
story.append(trap_box("2s and 2p BOTH have 1 total node but DIFFERENT types:  2s has 1 RADIAL node (spherical shell),  2p has 1 ANGULAR node (flat plane through nucleus)."))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 12 — ELECTRONIC CONFIGURATION
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 12 — ELECTRONIC CONFIGURATION"), sp(8)]

story += [sec("12.1  Three Fundamental Rules")]
story.append(sub_h("Rule 1 — Aufbau Principle"))
story += [body("Fill orbitals in INCREASING order of energy (n+l rule). "
               "If two orbitals have the same (n+l), fill the one with LOWER n first.")]
story.append(sp(3))
story.append(formula_box(
    "Filling order:  1s &#8594; 2s &#8594; 2p &#8594; 3s &#8594; 3p &#8594; 4s &#8594; 3d &#8594; 4p &#8594; 5s &#8594; 4d &#8594; 5p &#8594; 6s &#8594; 4f &#8594; 5d &#8594; 6p",
    [
        "4s (n+l=4) is filled BEFORE 3d (n+l=5)",
        "4f (n+l=7) is filled BEFORE 5d (n+l=7, but 5d has higher n  &#8594;  filled later)",
    ]
))
story.append(sp(5))

story.append(sub_h("Rule 2 — Pauli's Exclusion Principle"))
story += [body("No two electrons in the same atom can have the SAME SET of all four quantum numbers. "
               "Maximum 2 electrons per orbital with OPPOSITE spins (one &#8593;, one &#8595;).")]
story.append(sp(5))

story.append(sub_h("Rule 3 — Hund's Rule of Maximum Multiplicity"))
story += [body("In degenerate orbitals (same energy), electrons fill SINGLY first (one per orbital) "
               "with PARALLEL spins before any pairing occurs.")]
story.append(sp(3))
story.append(note_box("Nitrogen (Z=7):  1s<super>2</super> 2s<super>2</super> 2p<super>3</super>   &#8594;   2p orbitals:  &#8593; | &#8593; | &#8593;   (singly occupied  &#8212;  CORRECT)     NOT:  &#8593;&#8595; | &#8593; | _  (pairing before all singly occupied  &#8212;  WRONG)"))
story.append(sp(8))

story += [sec("12.2  Electronic Configurations  (Z = 1 to 30)")]
story.append(make_table(
    ["Z","Element","Configuration","Unpaired e<super>&#8722;</super>"],
    [
        ["1","H","1s<super>1</super>","1"],
        ["2","He","1s<super>2</super>","0"],
        ["3","Li","[He] 2s<super>1</super>","1"],
        ["4","Be","[He] 2s<super>2</super>","0"],
        ["5","B","[He] 2s<super>2</super> 2p<super>1</super>","1"],
        ["6","C","[He] 2s<super>2</super> 2p<super>2</super>","2"],
        ["7","N","[He] 2s<super>2</super> 2p<super>3</super>","3"],
        ["8","O","[He] 2s<super>2</super> 2p<super>4</super>","2"],
        ["9","F","[He] 2s<super>2</super> 2p<super>5</super>","1"],
        ["10","Ne","[He] 2s<super>2</super> 2p<super>6</super>","0"],
        ["11","Na","[Ne] 3s<super>1</super>","1"],
        ["12","Mg","[Ne] 3s<super>2</super>","0"],
        ["13","Al","[Ne] 3s<super>2</super> 3p<super>1</super>","1"],
        ["14","Si","[Ne] 3s<super>2</super> 3p<super>2</super>","2"],
        ["15","P","[Ne] 3s<super>2</super> 3p<super>3</super>","3"],
        ["16","S","[Ne] 3s<super>2</super> 3p<super>4</super>","2"],
        ["17","Cl","[Ne] 3s<super>2</super> 3p<super>5</super>","1"],
        ["18","Ar","[Ne] 3s<super>2</super> 3p<super>6</super>","0"],
        ["19","K","[Ar] 4s<super>1</super>","1"],
        ["20","Ca","[Ar] 4s<super>2</super>","0"],
        ["21","Sc","[Ar] 3d<super>1</super> 4s<super>2</super>","1"],
        ["22","Ti","[Ar] 3d<super>2</super> 4s<super>2</super>","2"],
        ["23","V","[Ar] 3d<super>3</super> 4s<super>2</super>","3"],
        ["24  &#9888;","Cr  (EXCEPTION)","[Ar] 3d<super>5</super> 4s<super>1</super>   (NOT 3d<super>4</super> 4s<super>2</super>)","6"],
        ["25","Mn","[Ar] 3d<super>5</super> 4s<super>2</super>","5"],
        ["26","Fe","[Ar] 3d<super>6</super> 4s<super>2</super>","4"],
        ["27","Co","[Ar] 3d<super>7</super> 4s<super>2</super>","3"],
        ["28","Ni","[Ar] 3d<super>8</super> 4s<super>2</super>","2"],
        ["29  &#9888;","Cu  (EXCEPTION)","[Ar] 3d<super>10</super> 4s<super>1</super>   (NOT 3d<super>9</super> 4s<super>2</super>)","1"],
        ["30","Zn","[Ar] 3d<super>10</super> 4s<super>2</super>","0"],
    ],
    col_widths=[W*0.13,W*0.18,W*0.53,W*0.16], left_cols=[2]
))
story.append(sp(4))
story.append(note_box(
    "Reason for Cr and Cu exceptions:  Half-filled (d<super>5</super>) and fully-filled (d<super>10</super>) "
    "subshells have extra stability due to  (1) Symmetrical distribution of electrons,  "
    "(2) Maximum exchange energy."
))
story.append(sp(8))

story += [sec("12.3  Magnetic Properties")]
story.append(sub_h("Formula 31 — Spin Multiplicity"))
story.append(formula_box(
    "Spin multiplicity  =  2S + 1         where  S  =  (number of unpaired electrons) / 2",
    [
        "Multiplicity = 1 (singlet):  all electrons paired  &#8594;  DIAMAGNETIC (repelled by magnetic field)",
        "Multiplicity &gt; 1:  unpaired electrons  &#8594;  PARAMAGNETIC (attracted by magnetic field)",
        "Higher multiplicity = more unpaired electrons = stronger paramagnetism",
    ]
))
story.append(sp(4))
story.append(make_table(
    ["Unpaired e<super>&#8722;</super>","S","Multiplicity","Type","Example"],
    [
        ["0","0","1  (singlet)","Diamagnetic","He, Ne, Zn, Be, Mg"],
        ["1","1/2","2  (doublet)","Paramagnetic","H, F, Na, Cu<super>2+</super>"],
        ["2","1","3  (triplet)","Paramagnetic","C, O, Ni<super>2+</super>"],
        ["3","3/2","4  (quartet)","Paramagnetic","N, Co<super>2+</super>, Cr<super>3+</super>"],
        ["4","2","5  (quintet)","Paramagnetic","Fe<super>2+</super>, Cr<super>2+</super>"],
        ["5","5/2","6  (sextet)","Paramagnetic","Mn<super>2+</super>, Fe<super>3+</super>"],
    ],
    col_widths=[W*0.14,W*0.10,W*0.22,W*0.18,W*0.36], left_cols=[4]
))
story.append(sp(5))

story.append(sub_h("Formula 32 — Magnetic Moment"))
story.append(formula_box(
    "&#956;  =  &#8730;[n(n+2)]     BM   (Bohr Magneton)",
    [
        "n = number of unpaired electrons   |   1 BM (Bohr Magneton) = 9.274&#215;10<super>&#8722;24</super> J/T",
        "1 unpaired: &#956; = &#8730;3 &#8776; 1.73 BM  (Cu<super>2+</super>, Ti<super>3+</super>)   |   2 unpaired: &#956; = &#8730;8 &#8776; 2.83 BM  (Ni<super>2+</super>)",
        "3 unpaired: &#956; = &#8730;15 &#8776; 3.87 BM  (Co<super>2+</super>, Cr<super>3+</super>)   |   4 unpaired: &#956; = &#8730;24 &#8776; 4.90 BM  (Fe<super>2+</super>)",
        "5 unpaired: &#956; = &#8730;35 &#8776; 5.92 BM  (Mn<super>2+</super>, Fe<super>3+</super>)",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 13 — CONSTANTS
# ══════════════════════════════════════════════════════════════════
story.append(PageBreak())
story += [part_header("PART 13 — COMPLETE CONSTANTS REFERENCE"), sp(8)]
story.append(make_table(
    ["Symbol","Name","Value","Unit"],
    [
        ["h","Planck's constant","6.626 &#215; 10<super>&#8722;34</super>","J&#183;s"],
        ["&#295;","Reduced Planck  (h/2&#960;)","1.055 &#215; 10<super>&#8722;34</super>","J&#183;s"],
        ["c","Speed of light","3 &#215; 10<super>8</super>","m/s"],
        ["e","Elementary charge","1.602 &#215; 10<super>&#8722;19</super>","C"],
        ["m<sub>e</sub>","Mass of electron","9.109 &#215; 10<super>&#8722;31</super>","kg"],
        ["m<sub>p</sub>","Mass of proton","1.673 &#215; 10<super>&#8722;27</super>","kg"],
        ["m<sub>n</sub>","Mass of neutron","1.675 &#215; 10<super>&#8722;27</super>","kg"],
        ["a<sub>0</sub>","Bohr radius  (1<super>st</super> orbit of H)","0.529 &#8491; = 5.29&#215;10<super>&#8722;11</super> m","m"],
        ["R<sub>H</sub>","Rydberg constant","1.097&#215;10<super>7</super> m<super>&#8722;1</super>  =  109677 cm<super>&#8722;1</super>","m<super>&#8722;1</super>"],
        ["r<sub>0</sub>","Nuclear radius constant","1.2 &#215; 10<super>&#8722;15</super> m  =  1.2 fm","m"],
        ["1 eV","In Joules","1.602 &#215; 10<super>&#8722;19</super>","J"],
        ["1 amu","In kg","1.66 &#215; 10<super>&#8722;27</super>","kg"],
        ["1 &#8491;","In metres","10<super>&#8722;10</super>","m"],
        ["1 nm","In metres","10<super>&#8722;9</super>","m"],
        ["1 pm","In metres","10<super>&#8722;12</super>","m"],
        ["1 fm","In metres","10<super>&#8722;15</super>","m"],
    ],
    col_widths=[W*0.14,W*0.40,W*0.32,W*0.14], left_cols=[1]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# MASTER FORMULA SHEET
# ══════════════════════════════════════════════════════════════════
story.append(PageBreak())
story += [part_header("MASTER FORMULA SHEET — ALL 41 FORMULAS AT A GLANCE"), sp(8)]
story.append(make_table(
    ["#","Formula Name","Expression"],
    [
        ["1","Orbital radius","r<sub>n</sub> = 0.529 &#215; n<super>2</super>/Z   &#8491;"],
        ["2","Orbital velocity","v<sub>n</sub> = 2.18&#215;10<super>6</super> &#215; Z/n   m/s"],
        ["3","Total energy","E<sub>n</sub> = &#8722;13.6 &#215; Z<super>2</super>/n<super>2</super>   eV"],
        ["4","Kinetic energy","KE = &#8722;E<sub>n</sub> = +13.6 Z<super>2</super>/n<super>2</super>   eV"],
        ["5","Potential energy","PE = 2E<sub>n</sub> = &#8722;27.2 Z<super>2</super>/n<super>2</super>   eV"],
        ["6","Ionisation energy","IE = +13.6 &#215; Z<super>2</super>/n<super>2</super>   eV"],
        ["7","Photon energy (transition)","&#916;E = 13.6 Z<super>2</super> (1/n<sub>1</sub><super>2</super> &#8722; 1/n<sub>2</sub><super>2</super>)   eV"],
        ["8","Rydberg equation","1/&#955; = R<sub>H</sub> Z<super>2</super> (1/n<sub>1</sub><super>2</super> &#8722; 1/n<sub>2</sub><super>2</super>)"],
        ["9","Angular momentum (Bohr)","mv<sub>n</sub>r<sub>n</sub> = nh/2&#960; = n&#295;"],
        ["10","Time period","T<sub>n</sub> &#8733; n<super>3</super>/Z<super>2</super>"],
        ["11","Revolution frequency","&#957;<sub>n</sub> &#8733; Z<super>2</super>/n<super>3</super>"],
        ["12","Spectral lines count","(n<sub>2</sub>&#8722;n<sub>1</sub>)(n<sub>2</sub>&#8722;n<sub>1</sub>+1)/2"],
        ["13","Wave equation","c = &#957;&#955;"],
        ["14","Wave number","&#957;&#771; = 1/&#955;   (m<super>&#8722;1</super> or cm<super>&#8722;1</super>)"],
        ["15","Photon energy","E = h&#957; = hc/&#955; = hc&#957;&#771;"],
        ["16","Energy shortcut","E(eV) = 1240/&#955;(nm)"],
        ["17","Photon momentum","p = h/&#955; = E/c"],
        ["18","Photoelectric equation","h&#957; = &#966; + KE<sub>max</sub>"],
        ["19","Work function","&#966; = h&#957;<sub>0</sub>"],
        ["20","Threshold wavelength","&#955;<sub>0</sub>(nm) = 1240/&#966;(eV)"],
        ["21","Stopping potential","eV<sub>0</sub> = KE<sub>max</sub> = h&#957; &#8722; &#966;"],
        ["22","Photon count (intensity)","n = I/h&#957; = I&#955;/hc"],
        ["23","de Broglie  (general)","&#955; = h/mv = h/p"],
        ["24","de Broglie  (from KE)","&#955; = h/&#8730;(2m&#183;KE)"],
        ["25","de Broglie  (electron, V)","&#955; = 12.27/&#8730;V   &#8491;"],
        ["26","Heisenberg's UP","&#916;x&#183;&#916;p &#8805; h/4&#960;"],
        ["27","Min velocity uncertainty","&#916;v<sub>min</sub> = h/(4&#960;&#183;m&#183;&#916;x)"],
        ["28","Orbital angular momentum","L = &#8730;[l(l+1)]&#183;&#295;"],
        ["29","L z-component","L<sub>z</sub> = m<sub>l</sub>&#183;&#295;"],
        ["30","Spin angular momentum","S = (&#8730;3/2)&#183;&#295;   [all electrons]"],
        ["31","Orbitals per shell","n<super>2</super>"],
        ["32","Max e<super>&#8722;</super> per shell","2n<super>2</super>"],
        ["33","Orbitals per subshell","2l+1"],
        ["34","Max e<super>&#8722;</super> per subshell","2(2l+1)"],
        ["35","Radial nodes","n &#8722; l &#8722; 1"],
        ["36","Angular nodes","l"],
        ["37","Total nodes","n &#8722; 1"],
        ["38","Spin multiplicity","2S+1   where S=(unpaired e<super>&#8722;</super>)/2"],
        ["39","Magnetic moment","&#956; = &#8730;[n(n+2)]   BM"],
        ["40","Nuclear radius","r = r<sub>0</sub> &#215; A<super>1/3</super>"],
        ["41","e/m ratio  (electron)","1.758 &#215; 10<super>11</super>   C/kg"],
    ],
    col_widths=[W*0.06,W*0.36,W*0.58], left_cols=[1,2]
))
story.append(sp(8))

story.append(thinhr())
story.append(sp(4))
story.append(Paragraph(
    "Atomic Structure  |  Class 11 Chemistry  |  Complete Chapter  |  All 41 Formulas  |  NEET / JEE",
    sFooter
))

doc.build(story)
print("PDF created:", OUTPUT)

"""
Motion in a Plane — Complete Chapter PDF
Class 11 Physics | NEET / JEE
Black & White, DroidSans Unicode font, ReportLab HTML markup,
NO placeholder squares, large fonts, print-optimised.
"""
from reportlab.pdfbase import pdfmetrics
from reportlab.pdfbase.ttfonts import TTFont
from reportlab.lib.pagesizes import A4
from reportlab.lib import colors
from reportlab.lib.styles import ParagraphStyle
from reportlab.lib.units import cm
from reportlab.lib.enums import TA_CENTER, TA_LEFT, TA_JUSTIFY
from reportlab.platypus import (
    SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle,
    HRFlowable, PageBreak
)

pdfmetrics.registerFont(TTFont('DS',  '/usr/share/fonts/google-droid-sans-fonts/DroidSans.ttf'))
pdfmetrics.registerFont(TTFont('DSB', '/usr/share/fonts/google-droid-sans-fonts/DroidSans-Bold.ttf'))

OUTPUT = "/tmp/workspace/motion-in-plane/Motion_in_a_Plane_Complete.pdf"

doc = SimpleDocTemplate(
    OUTPUT, pagesize=A4,
    rightMargin=2.0*cm, leftMargin=2.0*cm,
    topMargin=2.2*cm,   bottomMargin=2.2*cm,
)
W = A4[0] - 4.0*cm

# ── colours ────────────────────────────────────────────────────────
BLACK    = colors.black
WHITE    = colors.white
LT_GREY  = colors.HexColor("#e0e0e0")
MID_GREY = colors.HexColor("#808080")
DK_GREY  = colors.HexColor("#303030")

# ── styles ─────────────────────────────────────────────────────────
def S(name, **kw): return ParagraphStyle(name, **kw)

sTitle   = S("sTitle",   fontName="DSB", fontSize=22, textColor=WHITE, alignment=TA_CENTER, spaceAfter=4, leading=30)
sSubtit  = S("sSubtit",  fontName="DS",  fontSize=11, textColor=WHITE, alignment=TA_CENTER, spaceAfter=2, leading=16)
sPart    = S("sPart",    fontName="DSB", fontSize=14, textColor=WHITE, alignment=TA_LEFT,   spaceAfter=4, spaceBefore=6, leftIndent=6, leading=20)
sSec     = S("sSec",     fontName="DSB", fontSize=13, textColor=BLACK, alignment=TA_LEFT,   spaceAfter=4, spaceBefore=8, leading=18)
sSub     = S("sSub",     fontName="DSB", fontSize=11.5, textColor=BLACK, alignment=TA_LEFT, spaceAfter=3, spaceBefore=5, leading=16)
sBody    = S("sBody",    fontName="DS",  fontSize=11, textColor=BLACK, alignment=TA_JUSTIFY, spaceAfter=4, leading=16)
sBullet  = S("sBullet",  fontName="DS",  fontSize=11, textColor=BLACK, alignment=TA_LEFT,   spaceAfter=3, leading=15, leftIndent=16)
sFormula = S("sFormula", fontName="DSB", fontSize=12.5, textColor=BLACK, alignment=TA_CENTER, spaceAfter=3, spaceBefore=3, leading=20)
sFormNote= S("sFormNote",fontName="DS",  fontSize=10.5, textColor=DK_GREY, alignment=TA_LEFT, spaceAfter=2, leading=15, leftIndent=4)
sTrap    = S("sTrap",    fontName="DSB", fontSize=11, textColor=BLACK, alignment=TA_LEFT,   spaceAfter=2, leading=15)
sNote    = S("sNote",    fontName="DS",  fontSize=11, textColor=BLACK, alignment=TA_LEFT,   spaceAfter=2, leading=15)
sTableH  = S("sTableH",  fontName="DSB", fontSize=10, textColor=WHITE, alignment=TA_CENTER, leading=13)
sTableC  = S("sTableC",  fontName="DS",  fontSize=10, textColor=BLACK, alignment=TA_CENTER, leading=13)
sTableL  = S("sTableL",  fontName="DS",  fontSize=10, textColor=BLACK, alignment=TA_LEFT,   leading=13)
sFooter  = S("sFooter",  fontName="DS",  fontSize=9,  textColor=MID_GREY, alignment=TA_CENTER, leading=12)

# ── helpers ────────────────────────────────────────────────────────
def sp(h=5):  return Spacer(1, h)
def thinhr(): return HRFlowable(width="100%", thickness=0.4, color=MID_GREY)
def body(t):  return Paragraph(t, sBody)
def blt(t):   return Paragraph("•  " + t, sBullet)
def sec(t):   return Paragraph(t, sSec)
def sub_h(t): return Paragraph(t, sSub)

def part_header(t):
    tbl = Table([[Paragraph(t, sPart)]], colWidths=[W])
    tbl.setStyle(TableStyle([("BACKGROUND",(0,0),(-1,-1),BLACK),("ROWPADDING",(0,0),(-1,-1),8)]))
    return tbl

def formula_box(main, notes=None):
    elems = [Paragraph(main, sFormula)]
    if notes:
        elems.append(HRFlowable(width="100%", thickness=0.5, color=LT_GREY))
        for n in notes:
            elems.append(Paragraph(n, sFormNote))
    rows = [[e] for e in elems]
    inner = Table(rows, colWidths=[W-24])
    inner.setStyle(TableStyle([("BACKGROUND",(0,0),(-1,-1),WHITE),("ROWPADDING",(0,0),(-1,-1),5)]))
    outer = Table([[inner]], colWidths=[W])
    outer.setStyle(TableStyle([("BOX",(0,0),(-1,-1),2,BLACK),("ROWPADDING",(0,0),(-1,-1),6),("BACKGROUND",(0,0),(-1,-1),WHITE)]))
    return outer

def trap_box(t):
    tbl = Table([[Paragraph("⚠  TRAP: " + t, sTrap)]], colWidths=[W])
    tbl.setStyle(TableStyle([("BOX",(0,0),(-1,-1),1.5,BLACK),("ROWPADDING",(0,0),(-1,-1),6),("BACKGROUND",(0,0),(-1,-1),LT_GREY)]))
    return tbl

def note_box(t):
    tbl = Table([[Paragraph("★  NOTE: " + t, sNote)]], colWidths=[W])
    tbl.setStyle(TableStyle([("BOX",(0,0),(-1,-1),1,BLACK),("ROWPADDING",(0,0),(-1,-1),6),("BACKGROUND",(0,0),(-1,-1),WHITE)]))
    return tbl

def make_table(headers, rows, col_widths=None, left_cols=None):
    if col_widths is None: col_widths = [W/len(headers)]*len(headers)
    left_cols = left_cols or []
    data = [[Paragraph(h, sTableH) for h in headers]]
    for row in rows:
        data.append([Paragraph(str(cell), sTableL if j in left_cols else sTableC) for j,cell in enumerate(row)])
    tbl = Table(data, colWidths=col_widths)
    cmds = [
        ("BACKGROUND",(0,0),(-1,0),BLACK),
        ("ROWPADDING",(0,0),(-1,-1),5),
        ("GRID",(0,0),(-1,-1),0.5,MID_GREY),
        ("VALIGN",(0,0),(-1,-1),"MIDDLE"),
        ("LINEBELOW",(0,0),(-1,0),1.0,BLACK),
    ]
    for i in range(1,len(data)):
        if i%2==0: cmds.append(("BACKGROUND",(0,i),(-1,i),colors.HexColor("#f4f4f4")))
    tbl.setStyle(TableStyle(cmds))
    return tbl

# ══════════════════════════════════════════════════════════════════
story = []

# ── COVER ─────────────────────────────────────────────────────────
cover_t = Table([[Paragraph("MOTION IN A PLANE", sTitle)]], colWidths=[W])
cover_t.setStyle(TableStyle([("BACKGROUND",(0,0),(-1,-1),BLACK),("ROWPADDING",(0,0),(-1,-1),20)]))
cover_s = Table([[Paragraph(
    "Complete Chapter  |  All Formulas  |  All Topics  |  Class 11 Physics  |  NEET / JEE",
    sSubtit)]], colWidths=[W])
cover_s.setStyle(TableStyle([("BACKGROUND",(0,0),(-1,-1),DK_GREY),("ROWPADDING",(0,0),(-1,-1),10)]))
story += [cover_t, cover_s, sp(12)]

# ══════════════════════════════════════════════════════════════════
# PART 1 — SCALARS AND VECTORS
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 1 — SCALARS AND VECTORS"), sp(8)]

story += [sec("1.1  Scalar Quantities")]
story += [body("Quantities that have only <b>magnitude</b> (no direction). Obey ordinary arithmetic.")]
story += [blt("Examples: mass, speed, distance, time, temperature, energy, work, power, charge, density")]
story.append(sp(4))

story += [sec("1.2  Vector Quantities")]
story += [body("Quantities that have both <b>magnitude AND direction</b>. Obey vector algebra (not ordinary arithmetic).")]
story += [blt("Examples: displacement, velocity, acceleration, force, momentum, torque, electric field")]
story.append(sp(4))

story += [sec("1.3  Representation of Vectors")]
for b in [
    "A vector is represented by a bold letter or letter with arrow: <b>A</b> or A&#8407;",
    "Magnitude of A&#8407; is written as |A&#8407;| or simply A  (always positive or zero)",
    "Graphically: an arrow where length = magnitude and arrowhead = direction",
    "A negative vector &#8722;A&#8407; has same magnitude but exactly opposite direction",
    "Equal vectors: same magnitude AND same direction  (can have different positions in space)",
]:  story.append(blt(b))
story.append(sp(6))

story += [sec("1.4  Types of Vectors")]
story.append(make_table(
    ["Type","Definition","Example"],
    [
        ["Zero (Null) vector","Magnitude = 0, direction undefined","Velocity of a stationary object"],
        ["Unit vector","Magnitude = 1, used to indicate direction only","i&#770;, j&#770;, k&#770;  (along x, y, z axes)"],
        ["Equal vectors","Same magnitude and same direction","Parallel arrows of equal length"],
        ["Negative vector","Same magnitude, opposite direction","&#8722;A&#8407;"],
        ["Collinear vectors","Lie along same or parallel lines","Can be parallel or anti-parallel"],
        ["Coplanar vectors","Lie in the same plane","Any two vectors are always coplanar"],
        ["Position vector","Vector from origin O to point P","r&#8407; = xi&#770; + yj&#770; + zk&#770;"],
        ["Displacement vector","Change in position vector","&#916;r&#8407; = r&#8407;<sub>2</sub> &#8722; r&#8407;<sub>1</sub>"],
    ],
    col_widths=[W*0.22,W*0.44,W*0.34], left_cols=[0,1,2]
))
story.append(sp(8))

# ══════════════════════════════════════════════════════════════════
# PART 2 — VECTOR ALGEBRA
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 2 — VECTOR ALGEBRA"), sp(8)]

story += [sec("2.1  Addition of Vectors")]
story += [sub_h("Triangle Law of Vector Addition")]
story += [body("If two vectors A&#8407; and B&#8407; are represented by two sides of a triangle taken in order, "
               "then the third side (closing side) taken in reverse order represents the resultant R&#8407; = A&#8407; + B&#8407;.")]
story += [sp(3), sub_h("Parallelogram Law of Vector Addition")]
story += [body("If two vectors A&#8407; and B&#8407; are represented by two adjacent sides of a parallelogram, "
               "then the diagonal of the parallelogram from the same point represents the resultant R&#8407;.")]
story.append(sp(4))
story.append(formula_box(
    "Magnitude of Resultant:   R  =  &#8730;(A<super>2</super> + B<super>2</super> + 2AB cos&#952;)",
    [
        "A = magnitude of vector A&#8407;   |   B = magnitude of vector B&#8407;",
        "&#952; (theta) = angle between A&#8407; and B&#8407;  (angle between their positive directions)",
        "R = magnitude of resultant R&#8407; = A&#8407; + B&#8407;",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Direction of Resultant:   tan&#945;  =  B sin&#952; / (A + B cos&#952;)",
    [
        "&#945; (alpha) = angle that resultant R&#8407; makes with vector A&#8407;",
        "B sin&#952; = component of B&#8407; perpendicular to A&#8407;",
        "A + B cos&#952; = component of B&#8407; along A&#8407; added to A",
    ]
))
story.append(sp(4))

story += [sub_h("Special Cases:")]
story.append(make_table(
    ["Angle &#952; between A&#8407; and B&#8407;","Resultant Magnitude","Direction"],
    [
        ["&#952; = 0&#176;  (parallel, same direction)","R = A + B  (maximum)","Along A&#8407; and B&#8407;"],
        ["&#952; = 180&#176;  (anti-parallel)","R = |A &#8722; B|  (minimum)","Along larger vector"],
        ["&#952; = 90&#176;  (perpendicular)","R = &#8730;(A<super>2</super> + B<super>2</super>)","tan&#945; = B/A"],
        ["A = B, &#952; = 60&#176;","R = A = B","&#945; = 30&#176;"],
        ["A = B, &#952; = 120&#176;","R = A = B","&#945; = 60&#176;"],
        ["A = B, any &#952;","R = 2A cos(&#952;/2)","&#945; = &#952;/2"],
    ],
    col_widths=[W*0.38,W*0.34,W*0.28], left_cols=[0,1,2]
))
story.append(sp(6))

story += [sec("2.2  Subtraction of Vectors")]
story.append(formula_box(
    "A&#8407; &#8722; B&#8407;  =  A&#8407; + (&#8722;B&#8407;)",
    [
        "Subtraction = adding the negative of the second vector",
        "|A&#8407; &#8722; B&#8407;| = &#8730;(A<super>2</super> + B<super>2</super> &#8722; 2AB cos&#952;)      (same formula with &#952; replaced by 180&#176; &#8722; &#952;)",
        "Direction: tan&#946; = B sin&#952; / (A &#8722; B cos&#952;)    where &#946; is angle with A&#8407;",
    ]
))
story.append(sp(6))

story += [sec("2.3  Multiplication of a Vector by a Scalar")]
story.append(formula_box(
    "k A&#8407;  =  vector of magnitude |k|A  in direction of A&#8407;  (if k &gt; 0)  or  &#8722;A&#8407;  (if k &lt; 0)",
    [
        "k = any real number (scalar)   |   A&#8407; = vector",
        "Direction is reversed if k is negative",
        "Unit vector:   A&#770; = A&#8407; / |A&#8407;| = A&#8407; / A      (divide vector by its magnitude)",
    ]
))
story.append(sp(6))

story += [sec("2.4  Resolution of Vectors — Components")]
story += [body("Any vector in a plane can be resolved into two perpendicular components along the x and y axes.")]
story.append(sp(3))
story.append(formula_box(
    "A<sub>x</sub>  =  A cos&#952;          A<sub>y</sub>  =  A sin&#952;",
    [
        "A<sub>x</sub> = x-component of A&#8407; = projection along x-axis",
        "A<sub>y</sub> = y-component of A&#8407; = projection along y-axis",
        "&#952; = angle A&#8407; makes with the positive x-axis  (measured anticlockwise)",
        "A&#8407; = A<sub>x</sub>i&#770; + A<sub>y</sub>j&#770;",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Magnitude:   A  =  &#8730;(A<sub>x</sub><super>2</super> + A<sub>y</sub><super>2</super>)          Direction:   tan&#952;  =  A<sub>y</sub> / A<sub>x</sub>",
    [
        "These two formulas reconstruct the original vector from its components",
        "For 3D:  A = &#8730;(A<sub>x</sub><super>2</super> + A<sub>y</sub><super>2</super> + A<sub>z</sub><super>2</super>)",
    ]
))
story.append(sp(6))

story += [sec("2.5  Unit Vectors")]
story.append(formula_box(
    "i&#770;,  j&#770;,  k&#770;  are unit vectors along x, y, z axes respectively",
    [
        "|i&#770;| = |j&#770;| = |k&#770;| = 1   (magnitude = 1 each)",
        "i&#770; &#183; i&#770; = j&#770; &#183; j&#770; = k&#770; &#183; k&#770; = 1     |     i&#770; &#183; j&#770; = j&#770; &#183; k&#770; = k&#770; &#183; i&#770; = 0",
        "i&#770; &#215; j&#770; = k&#770;     |     j&#770; &#215; k&#770; = i&#770;     |     k&#770; &#215; i&#770; = j&#770;",
        "Any vector:  A&#8407; = A<sub>x</sub>i&#770; + A<sub>y</sub>j&#770; + A<sub>z</sub>k&#770;",
    ]
))
story.append(sp(6))

story += [sec("2.6  Addition of Vectors by Components")]
story.append(formula_box(
    "R&#8407;  =  A&#8407; + B&#8407;  =  (A<sub>x</sub>+B<sub>x</sub>)i&#770; + (A<sub>y</sub>+B<sub>y</sub>)j&#770;",
    [
        "R<sub>x</sub> = A<sub>x</sub> + B<sub>x</sub>     |     R<sub>y</sub> = A<sub>y</sub> + B<sub>y</sub>",
        "R = &#8730;(R<sub>x</sub><super>2</super> + R<sub>y</sub><super>2</super>)     |     &#952; = tan<super>&#8722;1</super>(R<sub>y</sub>/R<sub>x</sub>)",
        "This method works for ANY number of vectors &#8212; just add all x-components and all y-components separately",
    ]
))
story.append(sp(8))

story += [sec("2.7  Dot Product (Scalar Product)")]
story.append(formula_box(
    "A&#8407; &#183; B&#8407;  =  AB cos&#952;  =  A<sub>x</sub>B<sub>x</sub> + A<sub>y</sub>B<sub>y</sub> + A<sub>z</sub>B<sub>z</sub>",
    [
        "Result is a SCALAR  (no direction)",
        "&#952; = angle between A&#8407; and B&#8407;  (0&#176; &#8804; &#952; &#8804; 180&#176;)",
        "A&#8407; &#183; B&#8407; = 0 when &#952;=90&#176;  (vectors are perpendicular)   |   Maximum when &#952;=0&#176;:  A&#8407; &#183; B&#8407; = AB",
        "Commutative:  A&#8407; &#183; B&#8407; = B&#8407; &#183; A&#8407;",
        "i&#770; &#183; i&#770; = j&#770; &#183; j&#770; = k&#770; &#183; k&#770; = 1     |     i&#770; &#183; j&#770; = j&#770; &#183; k&#770; = k&#770; &#183; i&#770; = 0",
        "Work done: W = F&#8407; &#183; s&#8407; = Fs cos&#952;",
    ]
))
story.append(sp(6))

story += [sec("2.8  Cross Product (Vector Product)")]
story.append(formula_box(
    "|A&#8407; &#215; B&#8407;|  =  AB sin&#952;          Direction: Right-Hand Rule",
    [
        "Result is a VECTOR  (perpendicular to the plane containing A&#8407; and B&#8407;)",
        "&#952; = angle between A&#8407; and B&#8407;",
        "|A&#8407; &#215; B&#8407;| = 0 when &#952;=0&#176; or 180&#176;  (parallel or anti-parallel vectors)",
        "Maximum when &#952;=90&#176;:  |A&#8407; &#215; B&#8407;| = AB",
        "Anti-commutative:  A&#8407; &#215; B&#8407; = &#8722;(B&#8407; &#215; A&#8407;)",
        "i&#770; &#215; j&#770; = k&#770;     |     j&#770; &#215; k&#770; = i&#770;     |     k&#770; &#215; i&#770; = j&#770;",
        "i&#770; &#215; i&#770; = j&#770; &#215; j&#770; = k&#770; &#215; k&#770; = 0&#8407;",
        "Torque: &#964;&#8407; = r&#8407; &#215; F&#8407;   |   Angular momentum: L&#8407; = r&#8407; &#215; p&#8407;",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "A&#8407; &#215; B&#8407;  =  (A<sub>y</sub>B<sub>z</sub>&#8722;A<sub>z</sub>B<sub>y</sub>)i&#770; + (A<sub>z</sub>B<sub>x</sub>&#8722;A<sub>x</sub>B<sub>z</sub>)j&#770; + (A<sub>x</sub>B<sub>y</sub>&#8722;A<sub>y</sub>B<sub>x</sub>)k&#770;",
    ["Component form of cross product  (evaluated using determinant of 3&#215;3 matrix)"]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 3 — MOTION IN A PLANE (GENERAL)
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 3 — MOTION IN A PLANE — GENERAL EQUATIONS"), sp(8)]

story += [sec("3.1  Position Vector and Displacement")]
story.append(formula_box(
    "r&#8407;  =  xi&#770; + yj&#770;          &#916;r&#8407;  =  r&#8407;<sub>2</sub> &#8722; r&#8407;<sub>1</sub>  =  &#916;xi&#770; + &#916;yj&#770;",
    [
        "r&#8407; = position vector at any instant",
        "&#916;r&#8407; = displacement vector  (always a straight line from initial to final position)",
        "Distance (scalar) = actual path length &#8805; |&#916;r&#8407;|  (displacement magnitude)",
    ]
))
story.append(sp(6))

story += [sec("3.2  Velocity in a Plane")]
story.append(formula_box(
    "Average velocity:   v&#8407;<sub>avg</sub>  =  &#916;r&#8407; / &#916;t  =  &#916;x/&#916;t  i&#770; + &#916;y/&#916;t  j&#770;",
    [
        "Direction of average velocity = direction of displacement &#916;r&#8407;",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Instantaneous velocity:   v&#8407;  =  dr&#8407;/dt  =  dx/dt  i&#770; + dy/dt  j&#770;  =  v<sub>x</sub>i&#770; + v<sub>y</sub>j&#770;",
    [
        "v<sub>x</sub> = dx/dt  (x-component of velocity)",
        "v<sub>y</sub> = dy/dt  (y-component of velocity)",
        "Speed:   v = |v&#8407;| = &#8730;(v<sub>x</sub><super>2</super> + v<sub>y</sub><super>2</super>)",
        "Direction:   tan&#952; = v<sub>y</sub> / v<sub>x</sub>",
        "Instantaneous velocity is always TANGENT to the path at that point",
    ]
))
story.append(sp(6))

story += [sec("3.3  Acceleration in a Plane")]
story.append(formula_box(
    "Average acceleration:   a&#8407;<sub>avg</sub>  =  &#916;v&#8407; / &#916;t  =  &#916;v<sub>x</sub>/&#916;t  i&#770; + &#916;v<sub>y</sub>/&#916;t  j&#770;",
))
story.append(sp(4))
story.append(formula_box(
    "Instantaneous acceleration:   a&#8407;  =  dv&#8407;/dt  =  dv<sub>x</sub>/dt  i&#770; + dv<sub>y</sub>/dt  j&#770;  =  a<sub>x</sub>i&#770; + a<sub>y</sub>j&#770;",
    [
        "a<sub>x</sub> = dv<sub>x</sub>/dt   |   a<sub>y</sub> = dv<sub>y</sub>/dt",
        "|a&#8407;| = &#8730;(a<sub>x</sub><super>2</super> + a<sub>y</sub><super>2</super>)",
        "Key: in 2D motion, x and y components are INDEPENDENT of each other",
    ]
))
story.append(sp(6))

story += [sec("3.4  Equations of Motion in a Plane (Uniform Acceleration)")]
story += [body("When acceleration is constant (uniform), each component obeys the same equations as 1D motion:")]
story.append(sp(3))
story.append(formula_box(
    "v<sub>x</sub> = u<sub>x</sub> + a<sub>x</sub>t          v<sub>y</sub> = u<sub>y</sub> + a<sub>y</sub>t\n"
    "x = u<sub>x</sub>t + (1/2)a<sub>x</sub>t<super>2</super>          y = u<sub>y</sub>t + (1/2)a<sub>y</sub>t<super>2</super>\n"
    "v<sub>x</sub><super>2</super> = u<sub>x</sub><super>2</super> + 2a<sub>x</sub>x          v<sub>y</sub><super>2</super> = u<sub>y</sub><super>2</super> + 2a<sub>y</sub>y",
    [
        "u<sub>x</sub>, u<sub>y</sub> = initial velocity components  (at t=0)",
        "a<sub>x</sub>, a<sub>y</sub> = acceleration components  (constant)",
        "x, y = displacement components in time t",
        "v<sub>x</sub>, v<sub>y</sub> = velocity components at time t",
        "The two directions are completely INDEPENDENT &#8212; solve each axis separately",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 4 — PROJECTILE MOTION
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 4 — PROJECTILE MOTION"), sp(8)]

story += [sec("4.1  Introduction and Assumptions")]
story += [body("A projectile is any object thrown/projected with an initial velocity and then moving under the "
               "influence of gravity alone  (no air resistance).")]
story += [sp(3), sub_h("Assumptions:")]
for b in [
    "No air resistance",
    "g is constant throughout the motion (= 9.8 m/s&#178; &#8773; 10 m/s&#178; downward)",
    "Earth is flat (valid for short ranges)",
    "Motion is in a vertical plane",
]:  story.append(blt(b))
story += [sp(3), sub_h("Key Principle: x and y motions are COMPLETELY INDEPENDENT")]
for b in [
    "Horizontal (x): uniform velocity  (no acceleration, since g acts only vertically)",
    "Vertical (y): uniformly accelerated motion under g  (free fall)",
]:  story.append(blt(b))
story.append(sp(6))

story += [sec("4.2  Setting Up the Equations")]
story += [body("A projectile is launched from the origin with initial speed u at angle &#952; to the horizontal.")]
story.append(sp(3))
story.append(formula_box(
    "Initial velocity components:   u<sub>x</sub> = u cos&#952;          u<sub>y</sub> = u sin&#952;",
    [
        "u = initial speed of projection",
        "&#952; = angle of projection with horizontal  (0&#176; &lt; &#952; &lt; 90&#176;)",
        "Acceleration:  a<sub>x</sub> = 0  (horizontal)   |   a<sub>y</sub> = &#8722;g  (vertical, downward)",
    ]
))
story.append(sp(6))

story += [sec("4.3  Equations of Projectile Motion at Time t")]
story.append(formula_box(
    "Horizontal:   x  =  u cos&#952; &#183; t          (uniform velocity in x)",
    [
        "No acceleration in x &#8594; horizontal velocity remains u cos&#952; throughout",
        "v<sub>x</sub> = u cos&#952; = constant  (at ALL times)",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Vertical:   y  =  u sin&#952; &#183; t  &#8722;  (1/2)gt<super>2</super>",
    [
        "v<sub>y</sub> = u sin&#952; &#8722; gt   (vertical velocity decreases, becomes zero at peak, then negative)",
        "v<sub>y</sub><super>2</super> = (u sin&#952;)<super>2</super> &#8722; 2gy",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Velocity at time t:   v  =  &#8730;(v<sub>x</sub><super>2</super> + v<sub>y</sub><super>2</super>)          Direction:   tan&#946; = v<sub>y</sub>/v<sub>x</sub>",
    [
        "&#946; = angle velocity makes with horizontal at time t",
        "Speed changes continuously (magnitude of velocity changes), direction also changes",
    ]
))
story.append(sp(6))

story += [sec("4.4  Equation of Trajectory (Path Shape)")]
story.append(formula_box(
    "y  =  x tan&#952;  &#8722;  gx<super>2</super> / (2u<super>2</super>cos<super>2</super>&#952;)",
    [
        "Derived by eliminating t from x = u cos&#952; &#183; t  and  y = u sin&#952; &#183; t &#8722; (1/2)gt&#178;",
        "This is an equation of a PARABOLA  (y = ax &#8722; bx&#178;  form  &#8594;  downward parabola)",
        "Projectile always follows a PARABOLIC path  (under uniform gravity, no air resistance)",
    ]
))
story.append(sp(6))

story += [sec("4.5  Time of Flight  (T)")]
story.append(formula_box(
    "T  =  2u sin&#952; / g",
    [
        "T = total time from launch to landing  (when y = 0 again)",
        "Derived by setting y = 0:   0 = u sin&#952; &#183; t &#8722; (1/2)gt&#178;   &#8594;   t = 0 (launch) or t = 2u sin&#952;/g",
        "Time of ascent = Time of descent = T/2 = u sin&#952;/g",
        "T depends only on vertical component  (u sin&#952;) and g",
        "For &#952; = 90&#176; (vertical throw):  T = 2u/g  (maximum)",
    ]
))
story.append(sp(6))

story += [sec("4.6  Maximum Height  (H)")]
story.append(formula_box(
    "H  =  u<super>2</super> sin<super>2</super>&#952; / (2g)",
    [
        "H = maximum height reached above the launch point",
        "At maximum height: v<sub>y</sub> = 0  (vertical velocity becomes zero at peak)",
        "Derived from:  v<sub>y</sub><super>2</super> = u<sub>y</sub><super>2</super> &#8722; 2gH  with v<sub>y</sub>=0   &#8594;   H = u<sub>y</sub><super>2</super>/2g = (u sin&#952;)<super>2</super>/2g",
        "At maximum height: horizontal velocity = u cos&#952; (unchanged), vertical velocity = 0",
        "Speed at max height = u cos&#952;  (minimum speed during flight)",
    ]
))
story.append(sp(6))

story += [sec("4.7  Horizontal Range  (R)")]
story.append(formula_box(
    "R  =  u<super>2</super> sin 2&#952; / g",
    [
        "R = horizontal distance from launch to landing  (when projectile returns to same height)",
        "Derived from:  R = u cos&#952; &#215; T = u cos&#952; &#215; (2u sin&#952;/g) = u&#178; &#215; 2sin&#952;cos&#952;/g = u&#178;sin2&#952;/g",
        "Maximum range (R<sub>max</sub>) when sin2&#952; = 1 &#8594; 2&#952; = 90&#176; &#8594; <b>&#952; = 45&#176;</b>",
        "R<sub>max</sub> = u<super>2</super>/g   (at &#952; = 45&#176;)",
        "Complementary angles give equal range:  R(&#952;) = R(90&#176;&#8722;&#952;)   e.g. 30&#176; and 60&#176; give the same R",
    ]
))
story.append(sp(4))
story.append(trap_box("Range is the same for complementary angles (e.g. 30&#176; and 60&#176;), but the TIME OF FLIGHT and MAXIMUM HEIGHT are different."))
story.append(sp(6))

story += [sec("4.8  Projectile from a Height / Horizontal Projection")]
story += [body("A body projected horizontally from height h with speed u:")]
story.append(sp(3))
story.append(formula_box(
    "x = ut          y = (1/2)gt<super>2</super>          (taking downward as positive y)",
    [
        "u<sub>x</sub> = u  (horizontal),   u<sub>y</sub> = 0  (no initial vertical velocity)",
        "Time to hit ground:  t = &#8730;(2h/g)",
        "Horizontal range:  x = u &#215; &#8730;(2h/g)",
        "Vertical velocity at ground:  v<sub>y</sub> = gt = &#8730;(2gh)",
        "Speed at ground:  v = &#8730;(u<super>2</super> + 2gh)",
        "Angle with horizontal at ground:  tan&#946; = v<sub>y</sub>/u = &#8730;(2gh)/u",
    ]
))
story.append(sp(6))

story += [sec("4.9  Projectile Motion Summary Table")]
story.append(make_table(
    ["Quantity","Formula","When it applies"],
    [
        ["Horizontal velocity",     "v<sub>x</sub> = u cos&#952;",                "ALL times  (constant)"],
        ["Vertical velocity",       "v<sub>y</sub> = u sin&#952; &#8722; gt",      "At time t"],
        ["x-displacement",          "x = u cos&#952; &#183; t",                   "At time t"],
        ["y-displacement",          "y = u sin&#952; &#183; t &#8722; (1/2)gt&#178;", "At time t"],
        ["Trajectory (path)",       "y = x tan&#952; &#8722; gx&#178;/(2u&#178;cos&#178;&#952;)", "Shape of path"],
        ["Time of flight",          "T = 2u sin&#952;/g",                         "Total time of flight"],
        ["Time to max height",      "t<sub>H</sub> = u sin&#952;/g",              "Time to reach peak"],
        ["Maximum height",          "H = u&#178;sin&#178;&#952;/2g",              "Height at peak"],
        ["Horizontal range",        "R = u&#178;sin2&#952;/g",                    "Horizontal distance"],
        ["Max range",               "R<sub>max</sub> = u&#178;/g  at &#952;=45&#176;","Maximum possible range"],
        ["Speed at max height",     "v = u cos&#952;",                            "At the peak"],
    ],
    col_widths=[W*0.25,W*0.42,W*0.33], left_cols=[0,1,2]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 5 — UNIFORM CIRCULAR MOTION
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 5 — UNIFORM CIRCULAR MOTION  (UCM)"), sp(8)]

story += [sec("5.1  Definition and Key Characteristics")]
story += [body("A body moves in a circle of fixed radius r with <b>constant speed</b>. "
               "Although speed is constant, velocity changes continuously (direction changes) &#8594; "
               "there IS acceleration.")]
story += [sp(3)]
for b in [
    "Speed = constant   |   Velocity = changing  (direction changes continuously)",
    "Acceleration = constant magnitude, but direction changes continuously",
    "Acceleration is always directed towards the CENTRE of the circle  (centripetal)",
    "No net tangential force  (tangential acceleration = 0)",
]:  story.append(blt(b))
story.append(sp(6))

story += [sec("5.2  Angular Quantities")]
story.append(formula_box(
    "Angular displacement:   &#952;  =  s / r   radians",
    [
        "s = arc length  (distance along the circular path)",
        "r = radius of circle",
        "1 revolution = 2&#960; radians = 360&#176;",
        "Relationship:  s = r&#952;",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Angular velocity:   &#969;  =  &#916;&#952; / &#916;t  =  d&#952;/dt     rad/s",
    [
        "&#969; (omega) = angular velocity = angle swept per unit time",
        "For uniform circular motion: &#969; = constant",
        "Relationship with time period:  &#969; = 2&#960;/T = 2&#960;&#957;",
        "T = time period (time for one complete revolution)",
        "&#957; (nu) = frequency (revolutions per second)",
    ]
))
story.append(sp(4))
story.append(formula_box(
    "Relationship between linear and angular quantities:   v  =  r&#969;",
    [
        "v = linear speed of the particle",
        "r = radius of circular path",
        "&#969; = angular velocity",
        "Also:  s = r&#952;   |   a<sub>t</sub> = r&#945;  (for non-uniform circular motion)",
    ]
))
story.append(sp(6))

story += [sec("5.3  Centripetal Acceleration")]
story.append(formula_box(
    "a<sub>c</sub>  =  v<super>2</super>/r  =  &#969;<super>2</super>r  =  v&#969;",
    [
        "a<sub>c</sub> = centripetal acceleration  (always directed toward the CENTRE)",
        "v = speed of particle   |   r = radius of circle   |   &#969; = angular velocity",
        "Derived from: direction of velocity changes by d&#952; in time dt  &#8594;  |dv&#8407;| = v&#183;d&#952;  &#8594;  a = v&#183;d&#952;/dt = v&#969; = v&#178;/r",
        "Magnitude is constant in UCM  (v and r are constant)",
        "Direction rotates with the particle  (always inward, radially toward centre)",
    ]
))
story.append(sp(4))
story.append(trap_box("Centripetal acceleration does NOT change the speed &#8212; it only changes the DIRECTION of velocity. Speed remains constant in UCM."))
story.append(sp(6))

story += [sec("5.4  Centripetal Force")]
story.append(formula_box(
    "F<sub>c</sub>  =  ma<sub>c</sub>  =  mv<super>2</super>/r  =  m&#969;<super>2</super>r",
    [
        "F<sub>c</sub> = centripetal force  (always directed toward the CENTRE)",
        "m = mass of particle   |   v = speed   |   r = radius   |   &#969; = angular velocity",
        "This is NOT a new kind of force &#8212; it is the NET inward force provided by existing forces",
        "Examples of what provides centripetal force:",
        "  &#8594; Tension in string for circular motion of a ball on string",
        "  &#8594; Gravity for satellite orbiting Earth",
        "  &#8594; Normal force (banked roads) and friction (flat roads) for vehicles",
        "  &#8594; Coulomb force for electron orbiting nucleus  (Bohr model)",
    ]
))
story.append(sp(4))
story.append(note_box("Centrifugal force is a PSEUDO force (fictitious force) that appears only in the rotating (non-inertial) reference frame. It is NOT a real force and does NOT exist in the ground (inertial) frame."))
story.append(sp(6))

story += [sec("5.5  Time Period and Frequency")]
story.append(formula_box(
    "T  =  2&#960;r / v  =  2&#960; / &#969;          &#957;  =  1/T  =  &#969; / 2&#960;",
    [
        "T = time period = time for one complete revolution  (seconds)",
        "&#957; = frequency = number of revolutions per second  (Hz or s<super>&#8722;1</super>)",
        "&#969; = 2&#960;&#957; = 2&#960;/T   (angular frequency in rad/s)",
        "Angular velocity and time period are inversely related:  &#969;T = 2&#960;",
    ]
))
story.append(sp(6))

story += [sec("5.6  Complete Formula Summary for UCM")]
story.append(make_table(
    ["Quantity","Symbol","Formula","SI Unit"],
    [
        ["Arc length",          "s",             "s = r&#952;",                         "m"],
        ["Angular velocity",    "&#969;",         "&#969; = 2&#960;/T = 2&#960;&#957; = v/r",  "rad/s"],
        ["Linear speed",        "v",             "v = r&#969; = 2&#960;r/T",            "m/s"],
        ["Time period",         "T",             "T = 2&#960;/&#969; = 2&#960;r/v",     "s"],
        ["Frequency",           "&#957;",         "&#957; = 1/T = &#969;/2&#960;",       "Hz"],
        ["Centripetal acc.",    "a<sub>c</sub>",  "a<sub>c</sub> = v&#178;/r = &#969;&#178;r",  "m/s&#178;"],
        ["Centripetal force",   "F<sub>c</sub>",  "F<sub>c</sub> = mv&#178;/r = m&#969;&#178;r","N"],
    ],
    col_widths=[W*0.25,W*0.14,W*0.38,W*0.23]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 6 — RELATIVE VELOCITY IN 2D
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 6 — RELATIVE VELOCITY IN TWO DIMENSIONS"), sp(8)]

story += [sec("6.1  Concept")]
story += [body("The velocity of object A as observed from object B  (which is itself moving)  is the "
               "<b>relative velocity of A with respect to B</b>.")]
story.append(sp(5))
story.append(formula_box(
    "v&#8407;<sub>AB</sub>  =  v&#8407;<sub>A</sub>  &#8722;  v&#8407;<sub>B</sub>",
    [
        "v&#8407;<sub>AB</sub> = velocity of A relative to B  (as seen from B)",
        "v&#8407;<sub>BA</sub> = velocity of B relative to A = &#8722;v&#8407;<sub>AB</sub>",
        "v&#8407;<sub>A</sub> = absolute velocity of A  (relative to ground)",
        "v&#8407;<sub>B</sub> = absolute velocity of B  (relative to ground)",
        "Magnitude:  |v&#8407;<sub>AB</sub>| = &#8730;(v<sub>A</sub><super>2</super> + v<sub>B</sub><super>2</super> &#8722; 2v<sub>A</sub>v<sub>B</sub>cos&#952;)",
        "where &#952; = angle between v&#8407;<sub>A</sub> and v&#8407;<sub>B</sub>",
    ]
))
story.append(sp(6))

story += [sec("6.2  Important Cases")]
story.append(make_table(
    ["Case","Condition","Relative velocity magnitude"],
    [
        ["Same direction","&#952; = 0&#176;","v<sub>AB</sub> = |v<sub>A</sub> &#8722; v<sub>B</sub>|   (difference)"],
        ["Opposite directions","&#952; = 180&#176;","v<sub>AB</sub> = v<sub>A</sub> + v<sub>B</sub>   (sum)"],
        ["Perpendicular","&#952; = 90&#176;","v<sub>AB</sub> = &#8730;(v<sub>A</sub><super>2</super> + v<sub>B</sub><super>2</super>)"],
    ],
    col_widths=[W*0.26,W*0.26,W*0.48], left_cols=[0,2]
))
story.append(sp(6))

story += [sec("6.3  River-Boat Problems")]
story += [body("A boat crosses a river of width d. River flows with speed v<sub>r</sub>. "
               "Boat speed in still water = v<sub>b</sub>. Boat steers at angle &#952; to the direction perpendicular to the river bank.")]
story.append(sp(3))
story.append(formula_box(
    "Resultant velocity:   v<sub>res</sub>  =  &#8730;(v<sub>b</sub><super>2</super> + v<sub>r</sub><super>2</super>)      when &#952; = 90&#176; to bank",
    [
        "Time to cross river  (when boat aims perpendicular to bank):  t = d / v<sub>b</sub>",
        "Drift downstream:  x = v<sub>r</sub> &#215; t = v<sub>r</sub>d / v<sub>b</sub>",
        "To go STRAIGHT across (zero drift):  boat must aim upstream at angle &#945; where sin&#945; = v<sub>r</sub>/v<sub>b</sub>   (only possible if v<sub>b</sub> &gt; v<sub>r</sub>)",
        "Minimum time to cross: aim perpendicular to bank  &#8594;  t<sub>min</sub> = d/v<sub>b</sub>",
        "Minimum drift: aim at angle &#945; = sin<super>&#8722;1</super>(v<sub>r</sub>/v<sub>b</sub>) upstream",
    ]
))
story.append(sp(6))

story += [sec("6.4  Rain Problems")]
story += [body("A person walks with velocity v&#8407;<sub>p</sub>. Rain falls with velocity v&#8407;<sub>r</sub>. "
               "To avoid getting wet, the person should hold the umbrella in the direction of "
               "relative velocity of rain with respect to the person.")]
story.append(sp(3))
story.append(formula_box(
    "v&#8407;<sub>rain w.r.t. person</sub>  =  v&#8407;<sub>rain</sub>  &#8722;  v&#8407;<sub>person</sub>",
    [
        "Umbrella should be tilted in the direction of  v&#8407;<sub>rain</sub> &#8722; v&#8407;<sub>person</sub>",
        "If rain falls vertically at speed v<sub>r</sub> and person walks at speed v<sub>p</sub>:",
        "  Angle of umbrella from vertical = tan<super>&#8722;1</super>(v<sub>p</sub>/v<sub>r</sub>)",
    ]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 7 — NON-UNIFORM CIRCULAR MOTION
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 7 — NON-UNIFORM CIRCULAR MOTION"), sp(8)]

story += [sec("7.1  Definition")]
story += [body("Circular motion where the <b>speed changes</b> with time. Both tangential acceleration "
               "(changing speed) and centripetal acceleration (changing direction) are present.")]
story.append(sp(5))

story += [sec("7.2  Tangential Acceleration")]
story.append(formula_box(
    "a<sub>t</sub>  =  dv/dt  =  r&#945;",
    [
        "a<sub>t</sub> = tangential acceleration = rate of change of speed  (scalar: can be + or &#8722;)",
        "&#945; (alpha) = angular acceleration = d&#969;/dt  (in rad/s&#178;)",
        "Direction: tangent to the circle  (same or opposite to velocity)",
    ]
))
story.append(sp(5))

story += [sec("7.3  Total Acceleration")]
story.append(formula_box(
    "a<sub>total</sub>  =  &#8730;(a<sub>c</sub><super>2</super> + a<sub>t</sub><super>2</super>)",
    [
        "a<sub>c</sub> = centripetal acceleration = v&#178;/r  (directed inward, toward centre)",
        "a<sub>t</sub> = tangential acceleration  (directed along tangent)",
        "a<sub>c</sub> and a<sub>t</sub> are perpendicular to each other",
        "Angle of total acceleration with radius:  tan&#966; = a<sub>t</sub>/a<sub>c</sub>",
    ]
))
story.append(sp(5))

story += [sec("7.4  Angular Equations of Motion (Analogous to Linear)")]
story.append(make_table(
    ["Linear  (1D)","Angular  (circular)","Condition"],
    [
        ["v = u + at",           "&#969; = &#969;<sub>0</sub> + &#945;t",                  "Uniform angular acceleration"],
        ["s = ut + (1/2)at&#178;","&#952; = &#969;<sub>0</sub>t + (1/2)&#945;t&#178;",      "Uniform angular acceleration"],
        ["v&#178; = u&#178; + 2as","&#969;&#178; = &#969;<sub>0</sub>&#178; + 2&#945;&#952;","Uniform angular acceleration"],
    ],
    col_widths=[W*0.34,W*0.42,W*0.24], left_cols=[0,1,2]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 8 — IMPORTANT DERIVED RESULTS & SPECIAL CASES
# ══════════════════════════════════════════════════════════════════
story += [part_header("PART 8 — IMPORTANT RESULTS & SPECIAL CASES"), sp(8)]

story += [sec("8.1  Projectile on Inclined Plane")]
story += [body("Projectile launched at angle &#945; to an incline of angle &#946; to horizontal:")]
story.append(formula_box(
    "Range on incline:   R  =  2u<super>2</super>sin(&#945;&#8722;&#946;)cos&#945; / g cos<super>2</super>&#946;",
    [
        "Maximum range on incline when &#945; = 45&#176; + &#946;/2",
        "For projectile thrown down the incline, &#946; is negative",
    ]
))
story.append(sp(6))

story += [sec("8.2  Velocity at Any Point on Projectile Path")]
story.append(formula_box(
    "v  =  &#8730;(u<super>2</super> &#8722; 2gy)          at height y above launch",
    [
        "Derived from energy conservation  (or from v&#178; = u&#178; &#8722; 2gy  in vertical direction + v<sub>x</sub>=u cos&#952; constant)",
        "At y=0 (launch and landing): v = u  (same speed at same height)",
        "At maximum height (y=H): v = u cos&#952;  (minimum speed)",
    ]
))
story.append(sp(6))

story += [sec("8.3  Angle Between Velocity and Acceleration in Projectile")]
story.append(formula_box(
    "cos&#966;  =  &#8722;v<sub>y</sub> / v  =  &#8722;(u sin&#952; &#8722; gt) / v",
    [
        "At launch: &#966; = 90&#176; &#8722; &#952;  (angle between v and g)",
        "At maximum height: &#966; = 90&#176;  (velocity horizontal, g vertical  &#8594;  perpendicular)",
        "At landing: velocity makes angle &#952; below horizontal",
    ]
))
story.append(sp(6))

story += [sec("8.4  Key NEET/JEE Results to Memorise")]
story.append(make_table(
    ["Result","Expression","Condition"],
    [
        ["Same range for complementary angles",  "R(&#952;) = R(90&#176;&#8722;&#952;)",        "Same u, same launch height"],
        ["Max range",                            "R<sub>max</sub> = u&#178;/g",                "&#952; = 45&#176;"],
        ["Relation H and R",                     "R = 4H/tan&#952;",                           "Same u, same &#952;"],
        ["Max height at &#952;=90&#176;",         "H<sub>max</sub> = u&#178;/2g",               "Vertical throw"],
        ["Speed at top = u cos&#952;",           "v<sub>top</sub> = u cos&#952;",              "At max height"],
        ["Velocity at landing",                  "Same speed as launch = u",                   "Same height as launch"],
        ["Total time &#8733; sin&#952;",          "T &#8733; sin&#952;",                        "For fixed u"],
        ["Max height &#8733; sin&#178;&#952;",   "H &#8733; sin&#178;&#952;",                  "For fixed u"],
        ["Range &#8733; sin 2&#952;",            "R &#8733; sin 2&#952;",                       "For fixed u"],
        ["Centripetal acc. &#8733; 1/r",         "a<sub>c</sub> = v&#178;/r  &#8733; 1/r",     "Fixed speed v"],
    ],
    col_widths=[W*0.35,W*0.32,W*0.33], left_cols=[0,1,2]
))
story.append(sp(10))

# ══════════════════════════════════════════════════════════════════
# PART 9 — COMPLETE FORMULA SHEET
# ══════════════════════════════════════════════════════════════════
story.append(PageBreak())
story += [part_header("MASTER FORMULA SHEET — MOTION IN A PLANE"), sp(8)]
story.append(make_table(
    ["#","Topic","Formula"],
    [
        # VECTORS
        ["1","Resultant (Parallelogram law)","R = &#8730;(A&#178; + B&#178; + 2AB cos&#952;)"],
        ["2","Direction of resultant","tan&#945; = B sin&#952; / (A + B cos&#952;)"],
        ["3","Subtraction magnitude","|A&#8407;&#8722;B&#8407;| = &#8730;(A&#178; + B&#178; &#8722; 2AB cos&#952;)"],
        ["4","x-component","A<sub>x</sub> = A cos&#952;"],
        ["5","y-component","A<sub>y</sub> = A sin&#952;"],
        ["6","Magnitude from components","A = &#8730;(A<sub>x</sub>&#178; + A<sub>y</sub>&#178;)"],
        ["7","Unit vector","A&#770; = A&#8407;/|A&#8407;|"],
        ["8","Dot (scalar) product","A&#8407;&#183;B&#8407; = AB cos&#952; = A<sub>x</sub>B<sub>x</sub>+A<sub>y</sub>B<sub>y</sub>+A<sub>z</sub>B<sub>z</sub>"],
        ["9","Cross (vector) product","|A&#8407;&#215;B&#8407;| = AB sin&#952;"],
        # GENERAL 2D MOTION
        ["10","Displacement","&#916;r&#8407; = r&#8407;<sub>2</sub> &#8722; r&#8407;<sub>1</sub>"],
        ["11","Velocity","v&#8407; = dr&#8407;/dt = v<sub>x</sub>i&#770; + v<sub>y</sub>j&#770;"],
        ["12","Speed","v = &#8730;(v<sub>x</sub>&#178;+v<sub>y</sub>&#178;)"],
        ["13","Acceleration","a&#8407; = dv&#8407;/dt = a<sub>x</sub>i&#770; + a<sub>y</sub>j&#770;"],
        # PROJECTILE
        ["14","Initial components","u<sub>x</sub>=u cos&#952;   |   u<sub>y</sub>=u sin&#952;"],
        ["15","x at time t","x = u cos&#952; &#183; t"],
        ["16","y at time t","y = u sin&#952; &#183; t &#8722; (1/2)gt&#178;"],
        ["17","v<sub>x</sub> at time t","v<sub>x</sub> = u cos&#952; = constant"],
        ["18","v<sub>y</sub> at time t","v<sub>y</sub> = u sin&#952; &#8722; gt"],
        ["19","Speed at time t","v = &#8730;(v<sub>x</sub>&#178;+v<sub>y</sub>&#178;)"],
        ["20","Trajectory (parabola)","y = x tan&#952; &#8722; gx&#178;/(2u&#178;cos&#178;&#952;)"],
        ["21","Time of flight","T = 2u sin&#952;/g"],
        ["22","Maximum height","H = u&#178;sin&#178;&#952;/(2g)"],
        ["23","Horizontal range","R = u&#178;sin2&#952;/g"],
        ["24","Maximum range","R<sub>max</sub> = u&#178;/g   at  &#952;=45&#176;"],
        ["25","Speed at max height","v<sub>top</sub> = u cos&#952;"],
        ["26","Horizontal projection: time to ground","t = &#8730;(2h/g)"],
        ["27","Horizontal projection: range","x = u&#8730;(2h/g)"],
        ["28","Horizontal projection: speed at ground","v = &#8730;(u&#178;+2gh)"],
        # CIRCULAR
        ["29","Arc length","s = r&#952;"],
        ["30","Angular velocity","&#969; = d&#952;/dt = v/r = 2&#960;/T = 2&#960;&#957;"],
        ["31","Linear speed","v = r&#969;"],
        ["32","Time period","T = 2&#960;/&#969; = 2&#960;r/v"],
        ["33","Frequency","&#957; = 1/T = &#969;/2&#960;"],
        ["34","Centripetal acceleration","a<sub>c</sub> = v&#178;/r = &#969;&#178;r"],
        ["35","Centripetal force","F<sub>c</sub> = mv&#178;/r = m&#969;&#178;r"],
        # RELATIVE VELOCITY
        ["36","Relative velocity","v&#8407;<sub>AB</sub> = v&#8407;<sub>A</sub> &#8722; v&#8407;<sub>B</sub>"],
        ["37","Relative velocity magnitude","v<sub>AB</sub> = &#8730;(v<sub>A</sub>&#178;+v<sub>B</sub>&#178;&#8722;2v<sub>A</sub>v<sub>B</sub>cos&#952;)"],
        # NON-UNIFORM CIRCULAR
        ["38","Tangential acceleration","a<sub>t</sub> = dv/dt = r&#945;"],
        ["39","Total acceleration","a = &#8730;(a<sub>c</sub>&#178;+a<sub>t</sub>&#178;)"],
        ["40","Angular equations (3 eqs)","&#969;=&#969;<sub>0</sub>+&#945;t   |   &#952;=&#969;<sub>0</sub>t+(1/2)&#945;t&#178;   |   &#969;&#178;=&#969;<sub>0</sub>&#178;+2&#945;&#952;"],
    ],
    col_widths=[W*0.06,W*0.34,W*0.60], left_cols=[1,2]
))
story.append(sp(8))

# ── CONSTANTS USED ────────────────────────────────────────────────
story += [part_header("CONSTANTS & STANDARD VALUES"), sp(8)]
story.append(make_table(
    ["Symbol","Name","Standard Value","Unit"],
    [
        ["g","Acceleration due to gravity","9.8 m/s&#178;  (use 10 m/s&#178; in NEET)","m/s&#178;"],
        ["&#960;","Pi","3.14159...","dimensionless"],
        ["1 rev","In radians","2&#960; rad  =  6.283 rad","rad"],
        ["1&#176;","In radians","&#960;/180  &#8773;  0.01745 rad","rad"],
        ["1 rad","In degrees","180&#176;/&#960;  &#8773;  57.3&#176;","degrees"],
    ],
    col_widths=[W*0.12,W*0.36,W*0.38,W*0.14], left_cols=[1,2]
))
story.append(sp(8))

story.append(thinhr())
story.append(sp(4))
story.append(Paragraph(
    "Motion in a Plane  |  Class 11 Physics  |  Complete Chapter  |  All 40 Formulas  |  NEET / JEE",
    sFooter
))

doc.build(story)
print("PDF created:", OUTPUT)