ENERGY EXCHANGE IN PHOTOREACTIONS 27 



in which Cp is the total specific heat and C'p is that for the external 

 degrees of freedom only. Now, if v is the vibrational frequency of the 

 molecules, 



coo = kio(l - e-""/*^), (1-16) 



in which kio is the rate constant for the deexcitation from the upper 

 vibrational state to the lowest state and is related to the reverse con- 

 stant koi by the principle of detailed balancing thus: 



koi = klof-'""''=^ (1-17) 



the rate constant in terms of experimental quantities is 



"■» = "- (i§f^!)7-""'- ('-!«' 



The reciprocal of kio divided by the half -period of oscillation gives directly 

 the number of colUsions required to transfer a single vibrational quantum. 

 The rate constants are, of course, the sums of all successful collision tra- 

 jectories regardless of original vibrational phase (classical sense), relative 

 translational motion, and number of participating gateways. From the 

 numbers of collisions calculated in this way, which are listed in Table 1-1, 

 it can be seen that the exchange of energy between vibrational and trans- 

 lational degrees of freedom is a very poor process, especially if one of the 

 partners is chemically inert or the bond involved is strong. The gas N2, 

 which is quite unreactive and has a very high bond energy of the order of 

 200 kcal/mole, requires more collisions than does O2 with a bond energy 

 of 117 kcal. The gas O2, in turn, requires many more colhsions than CI2, 

 which has a bond strength of 58 kcal/mole. Hydrogen is very efficient 

 in energy transfer. It has a decided affinity for many substances, and 

 its small size favors close approach and high translational velocities 

 (Eyring, 1935; Hirschf elder et al, 1936). 



3-4. COLLISIONS OF POLYATOMIC MOLECULES 



When polyatomic molecules undergo collision, further complexity is 

 introduced into any exact calculation by the fact that any atom will 

 participate in many normal modes of vibration, all of which may have 

 to be treated in the calculation. The essential process is still the inter- 

 action of two atoms, one in each molecule. The problem has therefore 

 been treated as the collision of atoms with additional factors for the 

 coupling to various degrees of freedom of these atoms. Two semiclassi- 

 cal treatments employing simple repulsive potential functions are due to 

 Jackson and Mott (1932) and to Zener (1931). Zener's treatment is 

 particularly simple and provides a model for promising developments 

 currently in progress. He used the potential function 



Ce---^^ (1-19) 



