The intensities of transitions theoretical aspects

We can solve these two simultaneous equations for the two unknowns (the molar concentrations of A and B) and find 

There may be a wavelength, X°, called the isosbestic wavelength, at which the molar extinction coefficients of the two species are equal we write this common value as °. The total absorbance of the mixture at the isosbestic wavelength is 

Even if A and B are interconverted in a reaction of the form A B or its reverse, then because their total concentration remains constant, so does A°. As a result, one or more isosbestic points, which are invariant points in the absorption spectrum, may be observed (Fig. 12.10). It is very unlikely that three or more species would have the same molar extinction coefficients at a single wavelength. Therefore, the observation of an isosbestic point, or at least not more than one such point, is compelling evidence that a solution consists of only two solutes in equilibrium with each other with no intermediates. 

The intensity of a spectroscopic transition depends on a variety of factors, including the form of the wavefunctions of the initial and final states of the molecule and the population of the initial energy levels. 

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