# 9.1: The Magnitude of Molar Absorptivities

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

Molar absorptivities,$${\epsilon}$$, have units of liters/(mole cm) and range in value from 0 to 105.  The relationship between $${\epsilon}$$ and the capture cross-section for a photon - chemical species interaction and the probability for an energy-absorbing transition was shown by Braude (J. Am Chem Soc, 379 (1950) to be

$${\epsilon}$$ = 8.7 x 1019 PA

where P is the transition probability and A is the section target area in units of cm2.  Typical organic molecules have been shown to have cross-sectional areas on the order of 10-15 cm2 and transition probabilities range from 0  to 1.

Absorption bands with $${\epsilon}$$ ranging from 104 to 105 are considered strong absorbers while absorption bands with $${\epsilon}$$ less than or equal to 103 are considered weak absorbers and are likely the results of quantum mechanically forbidden transitions with P < 0.01.

9.1: The Magnitude of Molar Absorptivities is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.