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# Molar absorptivity

The molar extinction coefficient, also known as molar absorptivity, is a measurement of how strongly a chemical species absorbs light at a given wavelength. It is an intrinsic property of the species; the actual absorbance, A, of a sample is dependent on the pathlength l and the concentration c of the species via the Beer-Lambert law, $A=epsilon c l$. The units of ε are usually in M-1cm-1 or L mol-1cm-1. As 1 liter corresponds to 1000 cm3, sometimes a value 1000 times larger is given in cm2 mol-1, especially in old literature.

The molar extinction coefficient and mass extinction coefficient (defined below) should not be confused with the different definition of "extinction coefficient" used more commonly in physics, namely the imaginary part of the complex index of refraction (which is unitless). In fact, they have a straightforward but nontrivial relationship; see Mathematical descriptions of opacity.

In biochemistry, the extinction coefficient of a protein at 280 nm depends almost exclusively on the number of aromatic residues, particularly tryptophan, and can be predicted from the sequence of amino acids. If the extinction coefficient is known, it can be used to determine the concentration of a protein in solution.

Another measure of the extinction coefficient is E 1% which gives the mass extinction coefficient. E1% is the absorbance of a 1% solution by mass and has the units g-1L cm-1.

When there is more than one absorbing species in a solution, the overall absorbance is the sum of the absorbances for each individual species (X, Y etc.):

$A = \left(varepsilon_\left\{mathrm X\right\} c_\left\{mathrm X\right\} + varepsilon_\left\{mathrm Y\right\} c_\left\{mathrm\left\{Y\right\}\right\} + cdots\right)l$,

The composition of a mixture of N components can be found by measuring the absorbance at N wavelengths (the values of ε for each compound at these wavelengths must also be known). The wavelengths chosen are usually the wavelengths of maximum absorption (absorbance maxima) for the individual components. None of the wavelengths must be an isosbestic point for a pair of species. For N components with concentrations $c_i$ and wavelengths $lambda_i$, absorbances $A\left(lambda_i\right)$ are obtained:

$A\left(lambda_i\right) = lsum_\left\{j=1\right\}^N varepsilon_j\left(lambda_i\right) c_j$.

This set of simultaneous equations can be solved to find concentrations of each absorbing species.

The molar extinction coefficient $varepsilon$ is directly related to the Absorption cross section $sigma$ via:

$sigma = 2303 frac\left\{varepsilon\right\}\left\{N\right\} = 3.82 times 10^\left\{-21\right\} varepsilon$.
In units of cm2

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