510 Collisions of Electrons ivith Molecules of a Gas. 



been adopted it is most improbable that ionization takes 

 place in all collisions in which the velocity exceeds the value 

 corresponding to the voltage P, or that ionization does not 

 take place in a collision in which the velocity is less than 

 the value. 



The potentials P do not therefore represent a critical 

 potential, and the minimum potential required to ionize a 

 molecule when the collision occurs under the most favourable 

 conditions should be less than the above values. In air, the 

 minimum ionizing potential as found by Lenard * by a 

 different method is 11 volts; but it may be concluded that 

 ionization is produced in a comparatively small number of 

 cases when electrons collide with a velocity corresponding to 

 this voltage. In air at one millimetre pressure the observed 

 increase of conductivity due to the motion of electrons would 

 be accounted for if ionization took place in about 2 per cent, 

 of all the collisions in which the velocity was greater than 

 that corresponding to 11 volts, when Z is 100 volts per 

 centimetre, and in about -I per cent of these collisions when 

 Z is 50 volts per centimetre. 



6. The numbers obtained for the velocities W and the 

 factor k provide a simple means of measuring the proportion 

 of the energy of an electron which is lost on colliding with 

 a molecule. Thus with air at a pressure of one millimetre, 

 and a force of 20 volts per centimetre, the value of k is 56'3, 

 so that the mean final velocity of agitation corresponds to a 

 potential of 2'1 volts, and in passing through a distance of 

 one centimetre in the direction of the force the electron 

 makes 290 collisions with molecules. Thus in the final 

 steady state of motion the energy corresponding to a potential 

 fall of 20 volts is dissipated in 290 collisions, so that the 

 average loss of energy at each collision is 1/14*5 volt. Thus 

 about 3 per cent, of the energy is lost on each collision, or 

 about 1*5 per cent, of the velocity, when collisions take place 

 with velocities of 8'5 x 10 7 centimetre per second. 



The exact value of the elasticity has been found by 

 Pidduckt taking into consideration the distribution of the 

 velocities. If the collisions are perfectly elastic the following 

 relation is obtained between the values of TV and k : 



f! being the mean velocity of agitation of the molecules of 

 the gas. 



* P. Lenard, Ann. der Phys. (4) viii. p. 194 (1902). 



t F. B. Pidduck, Proc. Roy. Soc. A. lxxxviii. p. 296 (1913). 



