PHYSICAL PRINCIPLES OF CHEMICAL REACTIONS 209 



3-2. ELEMENTARY PROCESSES 

 INVOLVING EXCITED DIATOMIC MOLECULES 



3-2a. Energy of Electronic Configuration, Vibration, Rotation, and Trans- 

 lation. An isolated diatomic molecule can, like an atom, exist only in 

 one of a certain number of well-defined "quantum" states, each of which 

 is characterized by a set of values of those properties of the molecule which 

 are well defined. In contrast to the atomic case, however, this character- 

 ization includes not only specification of the electronic state of the mol- 

 ecule, but also of its vibrational state and rotational state. A molecule 

 may also have translational energy, as in the atomic case, and again this 

 energy may have any arbitrary magnitude, but one can properly ignore 

 it in consideration of the energies of the various molecular states. 



The electronic state of a molecule reflects the structure of the electrons 

 of the constituent atoms, although, again, the positions of the electrons 

 are not well-defined properties. It is specified by a conventional sym- 

 bolism similar to, but necessarily more complex than that used for atoms 

 (cf. Fig. 3-3). The excitation energies for electronic states are again of 

 order of magnitude of several ev, so that the emission or absorption 

 spectra arising from transitions between two such states again lie in the 

 optical region. 



A diatomic molecule in. any given electronic state may still be in one of 

 a large number of vibrational states, each corresponding to a different 

 amount o^ energy of vibration of the two atoms with respect to one 

 another. (By "vibrational energy" — also called oscillational energy — is 

 meant, of course, the total energy of vibration. For a molecule in a given 

 vibrational state the potential energy and kinetic energy of the two 

 atoms with respect to each other changes mth time, but the sum is 

 constant.) The vibration of a stable molecule in a low vibrational state 

 is ordinarily quite analogous to a simple harmonic oscillator. A vibra- 

 tional state is much more easily characterized than is an electronic state; 

 indeed, one parameter v, which is termed the vibrational quantum num- 

 ber and must be a positive integer or zero, is usually sufficient. Thus, 

 according to quantum theory, the vibrational energy of a diatomic mol- 

 ecule is given (approximately) by 



E^b = hv,,h{v + ^i) 



It is obvious that the possible vibrational energy levels, corresponding to 

 different values of v, namely, 0, 1,2, 3, 4, etc., are (approximately) equally 

 spaced. The spacing is determined by the fundamental frequency f„i6 

 and depends not only on the nature but also on the particular electronic 

 state of the vibrating molecule. For higher vibrational levels it decreases, 

 often approaching zero at the dissociation limit. The energy hv^ib for a 

 diatomic molecule is ordinarily of order of magnitude 0.1 ev; for H2, a very 



