30 Prof. W. 0. M. Lewis on an Unsolved Problem in the 



the velocity of light, since molecular speed may be neglected 

 in comparison. The rate of! the reaction is then given by 



d^ 1 /dt = 7raia 2 c NiN 2 , 



or the unimolecular velocity constant is given by 



/: = 7rcr 1 cr 2 6'N 2 . 



We have now to evaluate N 2 , the number of quanta per 

 (C.c, N 2 being a constant throughout the reaction, as long, 

 in tact, as the temperature is maintained constant. 



Obviously the number of quanta of frequency v in one c.c. 

 is obtained by dividing the radiation density u v dv by the 

 quantity h v. That is, 



/.■ = 7to- 1 o- 2 c . ^- . e-W kT . dv. 

 cr 



Setting a l = 2x 10~ 8 cm., and o" 3 = 2 X 10~ 13 cm., we have 



£ = 3'4xl0- 40 . v 2 . e - hv J kT .dv. ... (2) 



The term dv corresponds to the width of the band at the 

 frequency v. Certain estimates of the limiting value of d\ 

 to which a physical significance can be attributed, are given 

 by Schuster ('Theory of Optics/ 2nd ed. p. 346), from 

 which it appears that the limiting value of dX is approximately 

 10 ~ 12 cm. In the case of phosphine, where \ itself occurs 



at approximately 375 /x/x, it follows that dv = — v — — is of 



the order 10 7 . If we give an excessively large value to d\ 

 hy setting it equal to 100^, we find dv to be of the order 

 10 11 . Even employing this large value, it is evident that 

 equation (2) will give rise to a far smaller value for k than 

 does equation (1). The discrepancy between the observed 

 and calculated velocity constant is therefore still greater on 

 the discontinuous view of absorption than it is on the 

 continuous view. 



We are forced back therefore, I think, to the c >ntinuous 

 view of absorption as being the more hopeful of the two in 

 spite of the great discrepancy which still exists. The problem 

 which awaits solution is to account for the discrepancy 

 factor, which, rather remarkably, seems to be about the same 

 quantity for different gaseous reactions, and further, is 

 apparently independent of temperature. The mean value of 

 this factor is approx. 4 x 10 7 , this being the quantity by 

 which the right-hand expression in equation (1) must be 

 multiplied in order to arrive at a result in agreement with 

 experiment. The discovery of the cause of this discrepancy 

 would be a very great advance in chemical kinetics. It 

 looks as though some modification of Planck's expression for 



