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# Absorptivity

If the absorptivity varies over the frequency spread of the beam, the more strongly absorbed frequencies will be depleted, and the absorptivity will therefore decrease with sample path length. Chemical and physical interactions in the sample may modify the nature of the absorbing species, causing the absorptivity to vary with concentration. Thus it is necessary to check each sample to determine whether Beer's law is obeyed before attempting a quantitative analysis.

## Definition

The absorptivity is defined as the fraction of the energy incident on a body that is absorbed by the body. The incident radiation depends on the radiative conditions at the source of the incident energy. The spectral distribution of the incident radiation is independent of the temperature or physical nature of the absorbing surface unless radiation emitted from the surface is partially reflected back to the surface. Compared with emissivity, the absorptivity has additional complexities because directional and spectral characteristics of the incident radiation must be included. It is desirable to have relations between emissivity and absorptivity so that measured values of one will allow the other to be calculated.

## Formula

Absorbance A is directly proportional to the path length l and the concentration of the absorbing species c. That is
A ∝ cl
A = acl
where a is a proportionality constant called the absorptivity. When the concentration is expressed in moles/litre and the path length in centimeters, the absorptivity is called the molar absorptivity or molar extinction coefficient ε.

Thus, A = εcl
or
$\log$ $\frac{I_{0}}{I}$ = $\varepsilon\ cl$