Explain why the separation between vibrational levels is somewhat smaller in an

Question

Explain why the separation between vibrational levels is somewhat smaller in an excited electronic state than in the ground electronic state (see Figure 12-9). Explain the same effect for rotational states

4 -Etc. Next higher electronic state 2 10 8 One electronic 4 Etc Vibrational evels E Rotational levels Er" 0 Figure 12-9 Illustrating the molecular energy versus internuclear separation curves for twa electronic states. Each electronic state has its own set of vibrational levels, and each vibrational level has its own set of rotational levels

Explanation / Answer

The energy difference between rotational states are much smaller than that of vibrational states, and the energy difference between vibrational states is much smaller than that of electronic states. That means that many vibrational states belong to the same electronic state, and that many rotational states belong to the same vibrational states. As the vibrational or rotational energy increases, the difference between adjacent levels decreases, until the levels are no longer discrete, but approach the classic limit. The intensity of the transition is decided by the Franck-Condon principle: the more the wave function of the initial and final states overlap, the higher the probability of that transition (and therefore the higher its intensity).

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