ENERGY EXCHANGE IN PHOTOREACTIONS 49 



energy will lie on plane V of Fig. l-17a, shown in the vertical cross section, 

 Fig. l-17e. The entire collision path can be projected on a vertical plane 

 parallel to the abscissa of Fig. 1-I7a, as shown in Fig. 1-17/. The latter 

 figure is similar to the collision trajectories previously employed for 

 quenching by atoms, and, like that case, the rate constant may be 

 expressed by absolute theory thus: 



('iTrmwY ^T'pkT /rr 



1 



f,-Eo/RT 



\ Q—hv,%/kT 



~ 'h / 2irmJcT Y' ('IrmxykTY ^^'^^y^^^ 1 ^ ' ^ 



\ /i2 / \ ^2 ) h-i ' 1 _ e->^^xr/kT 



The term t contains, in addition to the crossing probability 2p(l — p), 

 a factor to exclude those points of III at which crossing will not satisfy 

 the quantum restrictions for the particular vibrational state on the lower 

 slope. Only those coUisional configurations on line III which have just 

 the relative momenta to produce allowed components of vibratory motion 

 in the HgA'-l' direction will be successful in quantum transfers. Cross- 

 ing with energy just E'q, the minimum value, as shown in Fig. l-17e, 

 would be successful if there existed a vibrational energy level at 1 on the 

 lower surface. If, instead, the level lies at 2, for which the original elec- 

 tronic energy is excessive by the amount Et, the collision path would have 

 to be angled toward line II in such a way that the energy discrepancy 

 Et is diverted into translation. Similarly, if the vibrational level in the 

 lower state lies at 3 in Fig. l-17e, so that the electronic energy is inade- 

 quate, the extra energy E[ must be obtained from an external degree of 

 freedom in order to satisfy the requirements of the lower state. The 

 extra energy must come from increased violence of collision and so will 

 appear as an additional increment in the collision energy E^. Thus, if 

 there are no other complications, the probability of excitation of vibration 

 would be expected to fall off roughly as e~^"'^^. 



On the other hand, in the case where the quanta of the quenching 

 oscillator fall more and more in magnitude below the electronic quanta 

 that are to be quenched, the successful trajectories must cross line III 

 nearer the axis along the right-to-left valley bottom (see Fig. l-17a). 

 This reduces the resultant vibrational motion across the valley. Such a 

 crossing will involve an increase in the collision energy roughly propor- 

 tional to the energy excess Ei, since the potential energy of line III will 

 tend to rise as the valley axis is approached (Fig. 1-11 d). Again, failure 

 to match energies because of vibrational quanta being too small should 

 cause an exponential drop in rate constant with energy discrepancy. 

 Thus, all other things being equal, the rate constant for energy transfer 

 when plotted against vibrational frequency should produce a sharply 



