940 Dr. R. D. Kleeman on Disintegration of an Ion 



integration this equation gives u 2 = ce~ 7cx , where c is an 

 arbitrary constant. When x = the chance of a cluster 

 getting disintegrated through a single collision with a neutral 

 molecule is unity, hence c==N, where N denotes the number 

 of collisions the cluster undergoes in passing over 1 cm., or 

 c = N p, where N denotes the number o£ collisions at 

 standard pressure. Since — x.dn 2 is the sum of the paths 

 whose lengths are between x and x-Vdx, the sum of all the 

 paths in one cm. is 



-£*.**= J ( 



Nto?- fa =l, 



which gives & = N = N /?. The value of n 2 is then given by 



n 2 = N pe x , putting <t=y^ the value of the path at the 



end of which an ion cluster is disintegrated. The number of 

 chances an ion cluster would have of disintegrating in passing 

 over one cm., due to the bombardment by neutral molecules 

 and the action of the electric field, is approximately equal to 

 the sum of the chances of each considered separately, or equal 

 to Wj + %2. The mean free path L of disintegration of the 

 cluster is the reciprocal of this expression, or 



L = Z , ■ = l W^v - - • ( 5 ) 



n x -\-n 2 



N p + 



%rp- 

 x 



We have seen that it passes through a maximum as the 

 electric field is increased. Strictly, it is the average free 

 path about which all the different paths are grouped according 

 to some law of distribution resembling that applying to the 

 ordinary mean free paths of a molecule. This arises from 

 the fact that the ordinary free path of a molesule is not 

 constant, and that the molecules at any instant in a gas have 

 different velocities. The formula was obtained on the 

 supposition that the velocity of a cluster is proportional to 

 the electric field. This is, however, not likely to hold in 

 most cases, as we have seen. 



The period of life t d of an ion cluster under the action of 

 an electric field is given by 



X Q Yp 



x 



L e 



It remains constant with increase of electric field till the 



