of the Ions formed in Gaseous Media. 

 A collision will take place if 



Mm ^., 



2 ilf + m 



where o- = fs' + -|s, the sum of the radii of the force spheres 

 of the ion and molecule. 



If R = 0, i.e. if the polarisation of the molecule due to the 

 ionic charge is negligible, the condition for a collision reduces 

 to h ^cr, as is otherwise obvious. 



The connection between the velocity U and the mean thermal 

 ionic velocity V can be deduced by the application of Maxwell's 

 law of distribution of velocities. We obtain 





Hence l-j^^^^ U' = ^MV' = ^mv'; thus Ij^^U' is the 

 2M + m ^ ^ 2M+m 



mean kinetic energy of the molecular motion. 



The effect of the polarisation due to the ionic charge is 

 therefore, as far as collisions are concerned, to replace a^ by 



2R. 



mv^ 

 Now the mean free path of an uncharged body of the same mass 



and dimensions as the ion is given by lirna^ \/ 1 + — > , where 



n denotes the number of molecules per c.c. Hence the actual 

 mean free path of the ion is L where 



L ^ = 7rn \/ 1 -^ (T-il -\ r 



V m ( mv^ 



Expression for the potential R due to the polarisation of the 

 molecule by the ionic charge. 



If the molecules of a gas are polarised by an electric field 

 of intensity X, the electric moment per c.c. is —j — X, where 

 K denotes the dielectric constant of the gas. 



The electric moment (a) of a molecule is therefore —, X. 



dX 

 The force on the molecule is /j, -y- , which is equal to 



— . -^7 . The potential is therefore given by 



1—2 



