Photons quantized vibrational energy levels

The multiplicity of excitations possible are shown more clearly in Figure 9.16, in which the Morse curves have been omitted for clarity. Initially, the electron resides in a (quantized) vibrational energy level on the ground-state Morse curve. This is the case for electrons on the far left of Figure 9.16, where the initial vibrational level is v" = 0. When the electron is photo-excited, it is excited vertically (because of the Franck-Condon principle) and enters one of the vibrational levels in the first excited state. The only vibrational level it cannot enter is the one with the same vibrational quantum number, so the electron cannot photo-excite from v" = 0 to v = 0, but must go to v = 1 or, if the energy of the photon is sufficient, to v = 1, v = 2, or an even higher vibrational state. 

We have now looked at the way photons are absorbed. Photons of UV and visible light cause electrons to promote between orbitals. Infrared photons have less energy, and are incapable of exciting electrons between orbitals, but they do allow excitation between quantized vibrational levels. The absorption of microwaves, which are less energetic still, effects the excitation between quantized rotational levels. 

We have already seen how, on the microscopic level, the vibrational energies of bonds are quantized in a similar manner to the way the energies required for electronic excitation are quantized. For this reason, irradiation with an infrared light from the sun or a lamp results in a photon absorption, and the bonds vibrate, which we experience as the sensation of heat. 

Where AE is the difference in energy between two quantized states, h is the Planck s constant and v is the frequency of the light. Then the molecule "absorbs" AE when it is excited from Pito E2 and "emits" AE when it reverts form 2 to The infrared absorption spectra originate in photons in the infrared region that are absorbed by transitions between two vibrational levels of the molecule in the electronic ground state. 

A simple theoretical expression for kg, similar to Eq. (19.2), cannot be obtained here because, first, quantization of the ground-state vibrational levels must be taken into account and, second, quasistationary states in the upper potential well supported by the centrifugal barrier might be involved [442]. Nevertheless, since here the energy of the emitted photons is of the order of the molecular dissociation energy, it may be expected that Pr will not be much lower than 10" with the di2 Pe) value typical for allowed transitions. As follows even from Eq. (19.4) the temperature dependence in this case is weak and may be negative. The negative temperature dependence of kj. here is due to the existence of quasistationary states in the upper potential weU. 

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