170 Prof. Thomson, The rate of recombination 



The rate of recombination and the size of gaseous ions. By 

 J. J. Thomson, M.A., Cavendish Professor of Experimental 

 Physics. 



[Bead 1 May 1905.] 



If two oppositely charged ions start from rest, the attraction 

 between them will cause them to run together, they will form a 

 permanently connected system and cease to act as ions. If, 

 however, the two ions instead of starting from rest start with 

 high velocities, then though they will approach each other, their 

 momentum will cause them to separate again ; they will not form 

 a single system, but will continue to act as ions. Now, if the 

 charged ions possess on the average the same kinetic energy as 

 is possessed by the molecules of the gas in which the ions occur, 

 they will be moving with very considerable velocities. Consider 

 two ions the one positively the other negatively electrified ; 

 they will attract each other with a force varying inversely as the 

 square of the distance between them ; we know from the theory 

 of central forces that if when the ions are at a distance r apart, 

 the kinetic energy due to their relative motion is greater than 

 e 2 \r (where e is the charge on an ion), the ions will not describe 

 closed orbits round each other, but will separate and ultimately 

 get an infinite distance apart, they will therefore not recombine. 

 If, however, the kinetic energy T is less than e 2 /r, the particles 

 will revolve round each other and recombine. Thus for recom- 

 bination to take place the ions must approach within a distance r, 



e 2 e 2 . 



such that T<— or r < ™ . Since T only depends upon the 



temperature, the limiting distance will be the same for all ions. 



Since T is the average kinetic energy of two ions, we have, 

 by the Kinetic Theory of Gases, if N is the number of molecrles 

 in a cubic centimetre of gas at a pressure p, 



p = lNT, thus T=3p/N and e 2 /T=Ne 2 /3p. 



At atmospheric pressure and 0° C, 



p = 10 6 , Ne = l'22xl0 10 , e = 3-5xl0- 10 ; 



thus Ne 2 /Sp = r = 1 -4 x 1 0- 6 cm. 



Thus for recombination to take place the two ions must 

 approach within a distance l - 4xl0~ 6 cm. This distance is ex- 

 ceedingly small compared with the average distance between the 

 ions in any known case of ionization. 



To find how long an ion will be before it comes within this 

 distance of an oppositely charged ion, let V be the average 



