Beer’s Law

Absorbance is the more common unit for expressing the attenuation of radiation because it is a linear function of the analyte’s concentration. When monochromatic electromagnetic radiation passes through an infinitesimally thin layer of sample of thickness dx, it experiences a decrease in its power of dP, as shown here.

Figure10.22

The fractional decrease in power is proportional to the sample’s thickness and the analyte’s concentration, C; thus

–dP/P = αCdx

where α is a proportionality constant. Integrating this equation over the total pathlength, b, that the radiation traverses through the sample leads to Beer’s law

A = –logT = –log(PT/Po) = εbC

where ε is the sample’s molar absorptivity, which has units of cm–1 M–1.

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