ENERGY EXCHANGE IN PHOTOREACTIONS 23 



cessful, the apparent entropy will, of course, be large and negative. A 

 wide gateway means that a number of variations in the position and 

 velocity of the collision paths in the region of the gateway are allowed, 

 and hence less negative entropies of collision will be found. The height 

 of the gateway determines the heat of collision. 



For the time being we forgo more elaborate discussion. The matter 

 for emphasis is that simple collision theory is inadequate for energy trans- 

 fer, just as it is inadequate for rates of reaction. In the new theory, 

 gateways take the place of the saddle points of absolute-reaction theory, 

 and collision processes are interpreted in terms of rate constants that are 

 further expressible as functions of two parameters: one, the entropy of 

 collision, which is not associated with temperature, and the other, the 

 heat of collision, which is. 



It has been the usual convention to calculate effective cross sections 

 for the comparison of various energy-transfer processes. These are 

 defined on the basis that every collision results in transfer. For instance, 

 if one knows that the fluorescence of N excited molecules of a total Nf of 

 type 1 is destroyed per cubic centimeter per second by quenching col- 

 lisions with type 2 molecules (N2 per cubic centimeter), A^ is taken equal 

 to Z, the collision number, given by kinetic theory as 



Z = 2N*N2a' 



27rkr(mi + 7n2) 



m 1W2 



(1-13) 



where m is the particle mass. The collision cross section a^ is determined 

 by this condition. Since the collision number is also the specific rate 

 constant for quenching, the relation between the rate constant k and a- is 

 also expressed by Eq. (1-13). 



3-2. ENERGY TRANSFER INVOLVING ROTATIONAL DEGREES 



OF FREEDOM 



As depicted in Fig. 1-10, we may discuss gateways of maximum restric- 

 tion for any collision path. One or a few of these gateways are probably 

 of primary importance in any particular collision process. Furthermore 

 there is no reason that the relative importance of different gateways can- 

 not change with temperature, just as different saddle points can vary in 

 importance for reactions in different temperature regions. The data on 

 the thermal dependence of energy-transfer processes are insufficient for a 

 general picture to be formed, but we do know quite generally that 

 increased temperature causes increased efficiency in transfer. The 

 amount of change for a given temperature increment varies consider- 

 ably. It is smallest for processes involving only translational and rota- 

 tional energy, since the heats of collision are small. Translational proc- 

 esses are essentially trivial, though the determination of an effective 

 interaction potential in any case is difficult. Rotational processes, as 



