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The Beer-Lambert law is the relationship between the attenuation of light through a substance and the properties of that substance.

Beer-Lambert law is used in chemistry to measure the concentration of chemical solutions, analyze oxidation, and measure polymer degradation. This law fails at high concentrations due to electrostatic interactions between molecules in proximity. The Beer-Lambert law is mathematically presented as $\text{A=}\raisebox{1ex}{$c$}\!\left/ \!\raisebox{-1ex}{$\mathrm{Î\mu }$}\right.$, where A is absorbance, is molar absorptivity, l is the length of the path of light, and c is concentration.

Molar absorptivity ($\mathbf{Î\mu }$)is defined as a constant that is characteristic of the compound at a particular wavelength.It is the absorbance observed for a 1.00 M solution in a cell with a 1.00 cm path length. The abbreviation comes from the fact that molar absorptivity was formerly called the extinction coefficient.

For example, the molar absorptivity of methyl vinyl ketone dissolved in hexane is 14,000 M^-1 cm^-1at 219 nm.

It is given that the solution of a compound in hexane shows an absorbance (A) of 0.40 at 252 nm in a cell with a 1 cm light path. It is also mentioned that the concentration of the compound at 252 nm is $4.0×{10}^{−5}\text{ â¶Ä‰}\mathrm{M}$.

By applying the Beer-Lambert law, where A = c l$\mathrm{Î\mu }$, the molar absorptivity ($\mathrm{Î\mu }$) of compound in hexane can be calculated as shown below.

$\mathrm{Î\mu }=\frac{\mathrm{A}}{\mathrm{l}\text{ }\mathrm{c}}$

$\begin{array}{l}\mathrm{Î\mu }=\frac{0.40}{4.0×{10}^{−5}}\\ \mathrm{Î\mu }\text{ â¶Ä‰}=\text{ â¶Ä‰}10,000\text{ â¶Ä‰}{\mathrm{M}}^{−1}\text{ }{\mathrm{cm}}^{−1}\end{array}$

Hence,the molar absorptivity ($\mathrm{Î\mu }$)of a compound in hexane at 252 nm is 10,000 M^-1cm^-1.