The probability of this process occurring is more favorable when the vibrational levels of the two excited states overlap, since little or no energy must be gained or lost in the transition.
32.
James Franck recognized that changes in vibrational levels could be a consequence of the instantaneous nature of excitation to higher electronic energy levels and a new equilibrium position for the nuclear interaction potential.
33.
In the quantum mechanical picture, the vibrational levels and vibrational wavefunctions are those of quantum harmonic oscillators, or of more complex approximations to the potential energy of molecules, such as the Morse potential.
34.
Whereas the energy spacing between vibrational levels in the quantum harmonic oscillator is constant at h \ nu _ 0, the energy between adjacent levels decreases with increasing v in the Morse oscillator.
35.
Therefore, in the case of the heavier diatomic molecules such as chlorine or bromine, the quantum vibrational energy level spacings become finer, which allows more excitations into higher vibrational levels at lower temperatures.
36.
Above is the rotational spectrum at the ground state vibrational level of H 2 CO at 30 K . This spectrum was simulated using Pgopher and S-Reduction Rotational constants from Muller " et al ."
37.
Then for subsequently higher vibrational levels from 2 to 13 the number of maximum rotational levels decreasing going through the sequence 47, 44, 42, 39, 36, 33, 30, 27, 23, 19, 15, 11 and 6.
38.
In the electronic excited state molecules quickly relax to the lowest vibrational level of the lowest electronic excitation state ( Kasha's rule ), and from there can decay to the electronic ground state via photon emission.
39.
For the A 2 ??! X 2 ? + transition the lowest vibrational level transitions are the most prominent, however the A 2 ? energy level can have a vibration quantum state up to 13.
40.
Since electronic transitions are very fast compared with nuclear motions, vibrational levels are favored when they correspond to a minimal change in the nuclear coordinates, that is, when the transition is " vertical " on the energy level diagram.
