27 : 3/ Quantum Mechanical Basis of Molecular Spectra 509 



electron has an average angular momentum about an external axis due 

 to its motion in the field of the atom. For historical reasons, the latter 

 is called an orbital angular momentum. The vector sum of the intrinsic 

 and orbital angular momenta is called the total angular momentum. 

 Because these momenta are all averages, it is not surprising that the 

 average projection of these momenta on any prechosen axis is also 

 quantized, that is, it can have only a discrete set of eigenvalues. 



In applying quantum mechanics, it is important to distinguish that 

 which is small and hence described by quantum mechanics from that 

 which is large and adequately interpreted by classical physics. In 

 general, angular momenta may be compared to Planck's constant, h; 

 distances may be compared to the radius of a hydrogen atom ; energies — 

 to the lowest possible for the given system; and masses — to atomic 

 masses. From the point of view of quantum mechanics, a virus particle, 

 too small to observe with the light microscope, is still a macroscopic 

 object. In fact, for some considerations of quantum mechanics, even 

 a protein molecule is a macroscopic object. 



Quantum mechanics of proteins and nucleic acids becomes significant 

 only when one discusses the nature of the bonds between atoms and the 

 absorption spectra characteristic of that particular species of molecules. 

 In the following sections, it will be shown that modern quantum 

 mechanics is useful for a qualitative understanding of molecular spectra. 



3. Molecular Spectra — Rotational and 

 Vibrational Bands 



As described in the last section, a photon will be absorbed only if its 

 energy is just sufficient to raise the molecule to another eigenstate. 

 Molecules excited by thermal or other means may fall to a lower energy 

 eigenstate by emitting a photon. In addition to the necessary energy 

 values, there are certain selection rules, correctly predicted by quantum 

 mechanics, which give the energy-level changes most likely to produce 

 absorption or emission spectra. The energy changes can be related to 

 wavelengths through the use of Equation 2. 



Molecular spectra result from changes in energy levels within mole- 

 cules. Three types of molecular energy can be readily distinguished ; 

 rotational, vibrational, and electronic. The spacings of rotational- 

 energy levels are small compared to the average thermal energy k T at 

 room temperature. (For T a 300°K, kT = 4 x 10" 14 ergs.) At equi- 

 librium, at this temperature, a group of molecules will be distributed 

 among various rotational levels. In a collision between two molecules, 

 either or both may jump from one energy level to another. Spectral 



