28 Prof. W. 0. M. Lewis on an Unsolved Prohlem in the 



vacuo, v the frequency of the radiation causing the chemical 

 change, and n the refractive index, which, for gaseous 

 systems, we shall take as unity. 



If there are N molecules of AB present in the system 

 considered, the total amount of energy of frequency v 

 absorbed per second is then 



8ttV 2 /^ 3 



Further, since hv is the quantity required to decompose a 

 single molecule, it follows that the number of molecules 

 decomposed per second in the system is 



o o 9 * 



-7T — - . e~ hvkT x N. 

 6mo° 



This is simply the rate of the unimolecular reaction, which 

 is ordinarily expressed : 



dT$/dt = koN, 



where k is the unimolecular velocity constant. 

 It follows therefore that 



8 1 9 t 



omc 



On substituting numerical values for the constants in this 

 expression we find : 



/r = 2-465xl0- 22 xKX^- 7 ^ T . . . . (1) 



We have now to compare this result with experiment. 

 The reaction considered is the unimolecular decomposition of 

 phosphine gas, which has been recently investigated by 

 Trautz and Bhandarkar (Zeitscli. anorg. Chem. cvi. p. 95, 

 1919) over a considerable range of temperature. From the 

 observed velocity constants at different temperatures in the 

 region 940° to 953° absolute, it is found that the critical 

 increment E per grammolecule lies somewhere between 

 70,000 and 80,000 calories. We shall not be making any 

 serious error if we take the mean value to be 75,000 cals. 

 W r e then have : 



N /u/ = 75000, 

 where N = 6 : l x 10 23 . It follows that 



*; = 8xl0 14 (or\ = 375 / z / u). 



