270 Energy required to Ionize a Molecule by Collision. 



When an electron travels a distance of 1 centimetre in the 

 direction of the electric force, the total length of its trajectory 

 is ujW approximately (since u is large compared with W), 

 and the total number of collisions that it makes with mole- 

 cules is u/Wl. The number that are ionized is a, so that 

 aWlju is the ratio of the number of collisions in which the 

 velocity of the electron exceeds V x , to the total number of 

 collisions. 



Let (f>(Y)dY be the number of electrons moving with a 

 velocity intermediate between V and Y + dY. The total 

 length of the paths they traverse per second is <j>(Y)YdY, 

 and the number of collisions in which the velocity of the 

 electron is between V and Y + dY is [cj>(Y)YdY]/L 



The number of collisions N' in which the velocity of the 

 electron exceeds V is 



U> v > 



YdY. 



If the velocities are distributed according to Maxwell's 

 law 



V2 



and N' is proportional io 





V2 



6 b Y 3 dY. 



The ratio N'/N, where N is the total number of collisions pei 

 second, is 



V'2 





2c 2 

 The quantity h is ~ where e is the mean velocity of 



agitation. In the case of electrons moving in an electric 



field the kinetic energy of agitation exceeds that of the 



2kc 2 

 surrounding molecules by the factor k so that 6~ -'^-} 



where — ^— is the kinetic energy of agitation of a molecule 



of the gas. Hence equating aWl/u to N'/N, the value of 

 Y'^jt'o 2 is given by the following equation : — 



3V'2 



ocWl 



Wl ^/ , 3V' 2 \ 



