What are the units of absorbance?

Question

BlackTom AI · Accepted Answer

Absorbance is defined as A = -log10(I/I0), where I is transmitted intensity and I0 is incident intensity. Because I/I0 is a pure ratio of two identical physical quantities, the argument of the logarithm is dimensionless, so absorbance itself is dimensionless (has no units).

Relevant concepts:
- Logarithms require a dimensionless argument, so any quantity defined as a log of a ratio is unitless.
- Beer–Lambert law: A = ε · c · l. Here ε is the molar absorptivity (often reported in L·mol−1·cm−1), c is concentration (mol·L−1) and l is path length (cm). Multiplying their units shows the units cancel and A is unitless.

Step-by-step unit check using Beer–Lambert law:
1. Write A = ε · c · l.
2. Substitute units: [ε] = L·mol−1·cm−1 (or M−1·cm−1), [c] = mol·L−1, [l] = cm.
3. Multiply: (L·mol−1·cm−1) × (mol·L−1) × (cm) = (L/L) × (mol/mol) × (cm/cm) = 1 (dimensionless).
Thus A is unitless.

Why the correct choice is correct:
- "absorbance has no units" matches the mathematical definition and the unit analysis above. Instruments sometimes label results as "AU" (absorbance units) or "OD" (optical density), but these are not true physical units—they denote a dimensionless number.

Why the other options are incorrect:
- mg/100 mL is a concentration unit, not absorbance.
- Å (angstrom) and nm (nanometre) are units of length/wavelength; while wavelength is measured in nm or Å, absorbance itself is not a length.

Conclusion: Absorbance is dimensionless; the correct answer is "absorbance has no units," matching the provided answer.

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