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Beer and Lambert s law

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Beer-Lambert law absorbance light path length concentration

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"Beer-Lambert" AND pulse oximetry

Beer-Lambert law

Statement: For monochromatic light, absorbance is directly proportional to both the concentration of the absorbing species and the length of the light path through the solution.
Equation:
A = −log T = log (P₀/P) = abc
  • A = absorbance (no units)
  • a = absorptivity (L g⁻¹ cm⁻¹ when c is in g/L)
  • b = path length, usually 1 cm
  • c = concentration of the absorbing species
When c is in mol/L, the equation becomes A = εbc. Here ε is the molar absorptivity (L mol⁻¹ cm⁻¹). It is a constant for a given compound at a given wavelength, solvent, temperature and pH.
  • Henry's Clinical Diagnosis and Management by Laboratory Methods, Ch. 4
  • Tietz Textbook of Laboratory Medicine, 7th Ed., Ch. 16
Transmittance and absorbance: They are inversely and logarithmically related: A = 2 − log %T.
  • Example from Henry's: a solution with 10% T has A = 2 − 1 = 1.
  • Absorbance increases linearly with concentration. Transmittance falls exponentially.
Worked example (Tietz):
  • Pure bilirubin has ε = 60,700 cm⁻¹M⁻¹ at 453 nm. Its molecular weight is 584.
  • A 5 mg/L solution has c = 0.005/584 mol/L.
  • With a 1 cm path: A = 60,700 × 1 × (0.005/584) = 0.520.
Practical uses:
  • Calibration and quantitation: A plot of A against c is a straight line through zero with slope ab. Unknown concentrations are read from it.
  • Reagent sensitivity: A higher ε gives a more sensitive assay. For iron, s-tripyridyltriazine (ε about 22,600) gives roughly twice the absorbance of 1,10-phenanthroline (ε about 11,000) at the same concentration.
  • Pulse oximetry and co-oximetry: Each hemoglobin species absorbs light in proportion to its concentration. One wavelength is needed per species measured. - Mulholland and Greenfield's Surgery, Monitors of Oxygenation
  • Anesthetic gas analysers: Infrared absorption by a gas is proportional to its concentration. - Morgan and Mikhail's Clinical Anesthesiology, 7e
  • Laser-tissue interaction: Laser energy falls off exponentially as it is absorbed in tissue. - Campbell-Walsh Urology, Light-Tissue Interaction
Limitations (deviations from linearity): Per Henry's, absorbance values above about 2.0 are unreliable.
  • Polychromatic light: The law assumes monochromatic light. A wide instrument bandpass causes deviation.
  • High concentration or absorbance: The curve bends toward the concentration axis. This is a negative deviation, and the relative concentration error grows.
  • Refractive index changes: These occur at high absorbance.
  • Chemical or physical equilibrium shifts of the absorber: Changes in pH, ionic strength or temperature can cause these.
  • Other interactions of light with matter: Examples are stray light and scattering.
Mnemonic: A = ε·l·c, so absorbance goes up with concentration and with path length.
I ran a quick PubMed check for recent systematic reviews on this topic. It returned nothing relevant, only unrelated pacing papers. The law itself is long established, so I don't expect any update.

Roman me

Maine "Roman me" ka matlab Roman script (Hindi/Urdu) mein samjhana liya hai. Neeche wahi explanation hai.

Beer-Lambert law (Roman Hindi/Urdu mein)

Law kya kehta hai: Jab ek hi wavelength ki roshni (monochromatic light) kisi solution se guzarti hai, to solution ki absorbance do cheezon ke seedhe barabar badhti hai:
  1. Solution mein light absorb karne wali cheez ki concentration (c)
  2. Roshni ka path length (b), yaani roshni solution mein kitna safar karti hai
Formula:
A = −log T = log (P₀/P) = abc
  • A = absorbance (iski koi unit nahi)
  • a = absorptivity
  • b = path length, aam taur par 1 cm
  • c = concentration
Agar c mol/L mein ho, to formula A = εbc ban jata hai. Yahan ε molar absorptivity hai (unit L mol⁻¹ cm⁻¹). Ye ek compound ke liye ek wavelength, solvent, temperature aur pH par constant hota hai.
Transmittance aur absorbance ka rishta:
  • A = 2 − log %T
  • Misal: agar %T = 10 ho, to A = 2 − 1 = 1.
  • Absorbance concentration ke saath seedhi line mein badhti hai. Transmittance exponential tareeqe se ghat-ti hai.
Solved example (Tietz se):
  • Bilirubin ka ε = 60,700 at 453 nm, aur molecular weight = 584.
  • 5 mg/L solution ka c = 0.005/584 mol/L.
  • Path length 1 cm lene par: A = 60,700 × 1 × (0.005/584) = 0.520
Istemal kahan hota hai:
  • Lab mein concentration nikalna: A aur c ka graph origin se guzarti seedhi line hota hai, jiski slope ab hoti hai. Isse unknown sample ki concentration padh li jati hai.
  • Reagent ki sensitivity: ε jitna zyada, assay utna sensitive. Iron ke liye s-tripyridyltriazine (ε lagbhag 22,600) ka absorbance 1,10-phenanthroline (ε lagbhag 11,000) se taqriban double aata hai.
  • Pulse oximetry aur co-oximetry: Har hemoglobin species apni concentration ke hisab se roshni absorb karti hai.
  • Anesthesia gas analyser: Infrared absorption se gas ki concentration naapi jati hai.
  • Laser aur tissue: Tissue mein laser energy exponential tareeqe se kam hoti hai.
Limitations (jahan law fail hota hai):
  • Absorbance 2.0 se zyada ho to result ghalat aa sakte hain.
  • Roshni bilkul monochromatic na ho (instrument ka bandpass chaura ho).
  • Concentration bahut zyada ho, to graph concentration axis ki taraf mud jata hai.
  • Solution ka pH, ionic strength ya temperature badal jaye.
  • Refractive index mein tabdeeli, stray light ya scattering ho.
Yaad rakhne ka tareeqa: A = ε × l × c. Concentration ya path length badhao, to absorbance bhi badhegi.
Sources: Henry's Clinical Diagnosis and Management by Laboratory Methods, Ch. 4, aur Tietz Textbook of Laboratory Medicine, 7th Ed., Ch. 16.
Agar aap ka matlab kuch aur tha, jaise sirf short notes ya MCQs, to bata dein.
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