Absorption by Trace Gases

MOLECULAR BASIS FOR DIFFERING RELATIONSHIPS BETWEEN INFRARED ABSORPTION AND CONCENTRATION 

The reason for the different dependencies of absorption on the concentration can be seen starting with the Beer-Lambert Law. If L° is the radiance of frequency v incident on an absorber with absorption coefficient a present at concentration N and the effective path length is /, the transmitted radiance Lv is given by 

Since absorption lines have a finite width and since measurements of absorption in practice are carried out over a small but finite range of frequencies, the absorbed radiance over some interval Av is the parameter of interest  

The incident radiation L° usually does not change significantly over one line so that L v can be taken as a constant. The remainder of Eq. (D) is defined as the equivalent line width, W, 

FIGURE 14-8 (a) Meaning of equivalent width, W (b) Doppler and Lorentzian line-shapes for equivalent half-widths (c) transmission curves for an absorption line for a weak and strong absorber, respectively (adapted from Lenoble, 1993). 

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