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Unformatted text preview: Chem 120A Spectroscopy: the absorption of radiation by molecules 05/01/06 Spring 2006 Lecture 39 READING: Engel (QCS): Ch. 15.4-15.5 McQuarrie and Simon: Sections 13-7 and 13-11 Absorption As discussed in Lectures 37-38, the characteristic absorption properties of a molecule are related to two quantities in the long wavelength limit according to Fermis golden rule, which gives the transition rate W g e : the conservation of the unperturbed energy and the quantity e ~ g which is called the transition dipole moment. The conservation of the unperturbed energy indicates that the energy, h , of absorbed radiation must be equal to the difference in energy between the excited state e and the ground state g in order for the absorption to occur (Fig. 1). Because, as we have seen, the allowed states of a molecule are quantized, the conservation of energy tells us that the absorption can only occur at very specific frequencies. This implies that the an absorption spectrum of the vibrational-electronic (vibronic) transitions of a molecule should look like a series of very sharp peaks, or sticks, as a function of frequency. The intensity of the absorption and therefore the height of the peak is proportional to the square of the transition dipole moment | e ~ g | 2 . We have, however, neglected the fact that we always measure spectra of molecules in some environment where they are moving with some kinetic energy proportional to k B T , and can undergo collisions with other molecules. The effect of this motion and collisions is that the peaks in the vibronic spectrum actually have some definite width. The other characteristic of the system that we have neglectedspectrum actually have some definite width....
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