Velocity of Unimolecular Reactions. 463 



that the relaxation is hindered by all the valency electrons. 

 It seems probable, however, that in the gaseous state where 

 we are concerned with the movement of one electron in 

 a single molecule isolated from the others, the time of 

 relaxation will, as in the case of solid silver and copper, be 

 exactly equal to the period of vibration of the electron. 



As a very close approximation we may therefore write 

 K=i/, or the rate of a monomolecular reaction 



dn ** 



= -- = v . e *t. 

 dt 



For the decomposition of phosphine according to Lewis 



hv 



v = 8.10 u and 0~at~=4'37.1O~ 18 ; hence the velocity constant 



dn __^L 



~ — v.e at — 3-5. 10~ 3 , while the observed value is 1O2.10 -3 . 



It may be noted that the natural vibration frequency of 

 phosphorus v violet = 14*9 . 10 14 , indicating that the mechanism 

 of decomposition operates through an electron whose time 

 period has not been sensibly affected by the presence of the 

 hydrogen atoms. 



The general expression for the velocity coefficient of a 

 monomolecular reaction is thus in accordance with the 

 observation of Dushman and Langmuir (who have recently 

 computed the reaction velocity constants of a great number 

 of physical and chemical reactions from this law), and is 

 thus an indirect confirmation of the radiation hypothesis. 



This, however, leads to the somewhat singular conclusion 

 that one " light wave "contains one quantum of energy Jiv, 

 for the molecule acquires this amount of energy in a time 

 period 1/v which on the wave theory of light is identical 

 with the time for light to make one undulation. 



Assuming that the premises of the radiation theory of 

 chemical action are correct, light appears to be corpuscular 

 in nature, the energy varying inversely as the size of the 

 corpuscular quantum. Sir J. J. Thomson's Faraday-tube 

 hypothesis would lead to similar conclusions. 



On the corpuscular assumptions, as W. 0, M. Lewis has 

 pointed out, it should be possible to calculate the velocity 

 coefficient on the ba<is of a bimolecular reaction between 

 phosphine molecules and quanta. The velocity coefficient is 

 then equal to 



dn .—= - , ir.,8v 



— = 77 a\ v 7 «i 2 + "'2 



iv 



where \ = ~ the quantum diameter, a the effective diameter 



