ENERGY EXCHANGE IN PHOTOREACTIONS 



1-3. BLACK-BODY RADIATION 



At ordinary temperatures, induced emission is small compared with 

 spontaneous emission. Black-body radiation has an appreciable inten- 

 sity only in the far infrared at ordinary temperatures. In each second 

 there will be a small fraction Aege-^^'^'^ of molecules emitting. Taking 

 Aeg = 10^ and E = 35,200 (corresponding to red light of 6000 A), we 

 obtain 3 X 10~'^ for the fraction of molecules emitting per second. By 

 the principle of detailed balancing, this is likewi.se the fraction of mole- 

 cules activated per second by black-body radiation. The rate for this 



kT 

 same excitation by collision is -r ^-(e+eo)/rt^ or faster than black-body 



excitation by a factor of 6 X 10^ providing the added activation energy 

 Eo is zero. 



The principle of detailed balancing (or microscopic reversibility) 

 requires at equilibrium that the number of reactions in the forward 

 direction on any reaction path equal the number in the backward direc- 

 tion. Thus quenching and excitation by collision balance according to 

 the equation 



kegNtNe = kgeNtNg, (1-5) 



in which keg is the rate constant for quenching of radiation from state e, 

 kge is the rate constant for excitation from g to e, Nt is the number of 

 molecules acting as quenchers and exciters by thermal collision, A^'e is the 

 number of excited molecules, and Ng is the number of molecules in the 

 ground state. Similarly 



p(v)Bge = p(p)Beg + Aeg, [p{p)Beg « Aeg] (1-6) 



in which p{v) is the intensity of black-body radiation of frequency p. 

 The fraction of molecules quenched in a simple case is 



O = y^J (1-7) 



and can be determined from experiment. For levels where Q approaches 

 zero, clearly the radiation hypothesis of activation (i.e., black-body acti- 

 vation outruns coUisional activation; Kassel, 1932, p. 313) is not at all a 

 dead issue, since here emission outruns quenching, and it follows that for 

 the reverse process activation by black-body radiation will correspond- 

 ingly outrun activation by collision. 



1-4. POTENTIAL-ENERGY DIAGRAMS 



The two-dimensional potential-energy diagrams thus far employed are 

 strictly applicable only to diatomic molecules. Little loss in generahty 

 is incurred if the curves are used to represent cross sections through the 

 many-dimensional surfaces of polyatomic molecules. In these cases the 



