BERNARD L. STREHLER 253 



high, so this factor may not become important until frequencies are 

 reached that are well above vo- 



Let us place one mole of the substance in state C in a vessel at 

 temperature T whose walls are perfect reflectors of radiation, so that 

 all the radiation emitted by the reaction is trapped inside the vessel. 

 Eventually a steady state ought to be reached in which the rates of 

 transitions from the states C* to state D are balanced by absorption 

 of quanta by molecules in state D which return them to state C*. The 

 density of radiation present in this steady state leads to a thermo- 

 dynamically defined upper limit to the luminosity that is attainable 

 from the conversion of C to D through the intermediates C*. 



Transitions from state C* to state D can occur in two ways: in the 

 first place, there is a probability, Aidt, that a molecule in state Ci* 

 will in the absence of radiation undergo a transition to state D in a 

 small time interval dt. Secondly, if radiation is present, the probability 

 of a transition is increased by an amount p,B,(if where p, is the energy 

 per unit volume of radiation whose frequency lies in the range 

 between n and n + 1 cycles per second. The fundamental quantum 

 theory of electromagnetic radiation ( Mott and Sneddon, 1948 ) shows 

 that A,/B, = S-Trhvi^/c^, where c is the velocity of light. Furthermore, 

 the probability of a reverse transition, D -^ Q*, occurring in time 

 interval dt is equal to piBidt. (Since state D is assumed to have less 

 energy than states C,*, there can be no transitions from D -^ d* in 

 the absence of radiation. ) Writing the concentrations of C;* and D as 

 (Ci*) and (D), we see that when the steady state is reached, 



(p.B, + A,)(C,*) = p,B,(D) (1) 



Since the states Cj* are assumed to be populated from C by thennal 

 activation, we may make use of the equihbrium constant, 



Ki* = (C.*)/(C) = exp(-hui*/kT) (2) 



From (1) and (2) and the value of Ai/Bi we find for the steady state 

 radiation density 



^' ^ (D) (3) 



(C)' ^ 



where a = Stt/i/c^. Note that no steady state is possible if (D)/(C) ^ 

 exp(— hvi/kT). Let us compare this result with the ordinary thermal 



