XXIX. Energy required to Ionize a Molecule by Collision. 
By J. S. Townsend, Wykeham Professor of Physics, Oxford [Communicated by the Author.]. 

IN the theory of ionization o£ gases by collision, it has been 
shown that the quantity a, representing the number of 
molecules ionized by one electron in moving through a 
centimetre of the gas at a pressure of one millimetre, is given 

by an equation of the form [formula redacted] for the larger values 
of the force X. The agreement between the formula and the 
experimental results was much closer than might have been 
expected, considering the assumptions which were made in 
finding the formula. Thus, for example, at the lower values 
of X, it has been found that the velocity of agitation of the 
electrons exceeds the velocity acquired under the force. 

If the quantity a represents the number of collisions with 
molecules in which the velocity of the ion exceeds a certain 
value V f , the velocity Y f must be obtained on a different 
principle from that previously adopted, when the force X 
is small [citation redacted]. This may be illustrated by taking the values of 
[alpha] recently obtained by Wheatley [citation redacted] for air corresponding to 
small values of the ratio X/p. The velocity of agitation u, 
and the velocity in the direction of the electric force W, for 
these values of X/p, have also been determined§. 

For air at 1 millimetre pressure the values of a, w, W, and 
h are given in the following table, k being the factor by 
which the kinetic energy of the electrons exceeds that of the 
surrounding molecules. 


[table redacted]


The velocity of agitation of the molecules may be neglected 
in comparison with that of the electrons, and the mean free 
path I of an electron moving in air at 1 millimetre pressure 
may be taken as *032 centimetre. 





270 [header] 

When an electron travels a distance of 1 centimetre in the 
direction of the electric force, the total length of its trajectory 
is u/W approximately (since u is large compared with W), 
and the total number of collisions that it makes with molecules is [formula redacted]. 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', to the total number of 
collisions. 

Let [formula redacted] be the number of electrons moving with a 
velocity intermediate between V and [formula redacted]. The total 
length of the paths they traverse per second is [formula redacted], 
and the number of collisions in which the velocity of the 
electron is between V and [formula redacted] is [formula redacted] 

The number of collisions N' in which the velocity of the 
electron exceeds V is 


[formula redacted] 



If the velocities are distributed according to Maxwell's 
law 

[formula redacted]

and N' is proportional to 


[formula redacted]



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

[formula redacted]

The quantity b is [formula redacted] 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 
 
surrounding molecules by the factor k so that [formula redacted] 

where [formula redacted] is the kinetic energy of agitation of a molecule 

of the gas. Hence equating aWl/u to N'/N, the value of 
[formula redacted] is given by the following equation : — 

[formula redacted]


[header] 271 

The values of [formula redacted] for the different values of X are 
given in the following table, also the corresponding values of 
[formula redacted] :- 


[table redacted]


If V be the velocity acquired by an electron in travelling 
freely between two points differing in potential by P volts, 
it is easy to show that [formula redacted]. 
 

The values of P thus obtained are given in the last column 
of the above table, the determination corresponding to the 
lowest value of X being the most reliable. 

It thus appears that the energy required to produce 
ionization by collision in air is about 23e/300, e being the 
charge on the ion. This estimate of the energy is in agreement with that previously obtained by considering the larger 
values of [alpha]. 

It is remarkable that large alterations in the numbers 
given in the second column have very little effect on the 
values of P. It is only necessary, therefore, to know the 
values of [alpha], l, W, and u approximately, but the value of k 
must be known accurately, as an error in k would produce a 
proportional error in P.