510 Quantum Mechanical Basis of Molecular Spectra /27 : 3 



absorption of photons of the proper energy to raise the molecules to a 

 higher level is also of interest. Rotational spectra are discussed in sub- 

 section A, to follow. 



By contrast, differences in vibrational energy levels are large compared 

 to kT. At room temperature, most of the molecules will be in the 

 lowest vibrational state. When a photon is absorbed with energy 

 sufficient to increase the vibrational-energy level, there may be a change 

 in the rotational-energy level as well. Vibrational spectra are discussed 

 in subsection B. 



Spacings of electronic-energy levels are still larger. Thus, to increase 

 the electronic-energy level, the photons must be in the visible or ultra- 

 violet regions of the spectrum. At equilibrium, usually only the lowest 

 electronic state is occupied. (Some molecules have electronic eigen- 

 states whose energy levels are very close to the lowest one. Resonance 

 between these low-energy states gives such molecules added stability.) 

 Electronic spectra are described in the next section. 



A. Rotational Spectra 



The rotational changes involve the smallest energy differences of any 

 of the types of spectra considered in this chapter. The photons absorbed 

 and emitted by rotational changes correspond to comparatively long 

 wavelengths ranging from the "microwave" region where the wave- 

 length is of the order of 1 cm, to the "far infrared" where the wavelength 

 is of the order of 10 " 2 cm. If the molecule could be thought of as a 

 "classical" (Newtonian) rotor, with moment of inertia /, its angular 

 momentum P would be 



P 9 = I" (7) 



where a> is 2tt times the frequency of rotation. The kinetic energy E K 

 of the rotor is 



E K = ±Ia>* = (PJ)/(2/) (8) 



Quantum mechanics allows one to retain Equations 7 and 8, provided 

 that P and P are properly interpreted. Neither may be known pre- 

 cisely at any instant. However, their averages over long periods of time 

 are given by 



_ Jh 



P * = 277 



and 



where J is a positive integer or zero. These average values will be 



