What are the units of absorbance?

Question

BlackTom AI · Accepted Answer

Absorbance is defined by A = -log10(T) = log10(I0/I), where T = I/I0 (transmittance), so...

1) Relevant knowledge points and concepts
- Transmittance T is the ratio of transmitted light intensity I to incident intensity I0; it is dimensionless because it’s a ratio of two like quantities.
- Absorbance A is the base-10 logarithm of a dimensionless ratio: A = log10(I0/I). Logarithms require dimensionless arguments, so their result is dimensionless.
- Beer–Lambert law: A = ε c l. Here A is dimensionless, so the molar absorptivity ε carries units that cancel concentration (c) and path length (l) units.

2) Step-by-step reasoning
- Start with I0 and I having the same physical units (e.g., W·m^-2 or photon counts). Form the ratio I/I0 → dimensionless.
- Compute A = -log10(I/I0) → logarithm of dimensionless number → A is dimensionless (no units).

3) Calculations / intermediate steps (example)
- Example: I0 = 100 units, I = 10 units → T = I/I0 = 10/100 = 0.1 (dimensionless).
- A = -log10(0.1) = 1. No units attached.

4) Why the correct answer is correct
- Because absorbance is the logarithm of a dimensionless intensity ratio, it carries no physical units. When using A = ε c l, ε’s units are chosen so ε·c·l is unitless (for c in mol·L^-1 and l in cm, ε typically has units L·mol^-1·cm^-1 or M^-1·cm^-1).

5) Why the other options are incorrect
- a. nm (nanometres) is a unit of wavelength, not absorbance. 
- c. mg/100 mL is a concentration or mass/volume unit, not dimensionless. 
- d. mM (millimolar) is a concentration unit; absorbance itself is not expressed in molarity.

6) Conclusion
- Therefore absorbance has no units. This matches the provided correct answer: b. absorbance has no units.

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