Molar absorptivity (ε) in Beer–Lambert law: what does ε quantify for a given species at a specified wavelength?

Introduction / Context:
Molar absorptivity, ε (units L mol^-1 cm^-1), is the proportionality constant that links absorbance to concentration and path length in Beer–Lambert law. It captures how strongly a species absorbs light at a particular wavelength.

Given Data / Assumptions:

• Beer–Lambert law: A = ε * l * c.
• Fixed wavelength and defined measurement conditions.
• Linearity holds in the concentration range used.

Concept / Approach:
Rearranging A = εlc gives ε = A / (l * c). Thus, ε quantifies absorbance per unit concentration per unit path length. In words, it reflects the intrinsic absorbing power of the analyte.

Step-by-Step Solution:
Start with A = εlc.Solve for ε: ε = A / (l * c).Interpretation: for l = 1 cm, ε equals absorbance per molar concentration.Hence, option describing “per unit concentration (at defined l)” is most accurate among the choices.

Verification / Alternative check:
Spectrophotometer calibration uses ε to convert measured A into concentration via c = A / (εl) for standard 1 cm cuvettes.

Why Other Options Are Wrong:
Per unit length only (a) omits concentration. Option c incorrectly mixes reflection with absorption. Option e is transmittance ratio, not ε. Therefore, b best describes ε.

Common Pitfalls:
Confusing ε with absorbance or with instrument-specific sensitivity; ε is an analyte-and-wavelength property.

Final Answer:
Amount of light absorbed per unit concentration (at a defined path length).