bei48482_FM

288 Chapter Eight

This diagram also shows the fine structure in the vibrational levels caused by the

simultaneous excitation of rotational levels.

Vibrational Spectra

The selection rule for transitions between vibrational states is

Selection rule   1 (8.18)

in the harmonic-oscillator approximation. This rule is easy to understand. An oscillat-

ing dipole whose frequency is  0 can absorb or emit only electromagnetic radiation of

the same frequency and all quanta of frequency  0 have the energy h 0. The oscillat-

ing dipole accordingly can only absorb Eh 0 at a time, in which case its energy

increases from ( ^12 )h 0 to ( ^12 1)h 0. It can also emit only Eh 0 at a

time, in which case its energy decreases from ( ^12 )h 0 to ( ^12 1)h 0. Hence

the selection rule  1.

Example 8.3

When CO is dissolved in liquid carbon tetrachloride, infrared radiation of frequency 6.42 

1013 Hz is absorbed. Carbon tetrachloride by itself is transparent at this frequency, so the

absorption must be due to the CO. (a) What is the force constant of the bond in the CO molecule?

(b) What is the spacing between its vibrational energy levels?

Vibrational energy levels

Rotational energy levels

U

R

Figure 8.20The potential energy of a diatomic molecule as a function of interatomic distance, show-

ing vibrational and rotational energy levels.

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