546 Sir E. Rutherford on Collision of 



If Q ex. particles pass normally through a layer of 

 gas thickness dx ; which contains N atoms per c.c. at 

 N.T.P.. then the number dn of H atoms projected between 

 the angles and 6 is given by 



dn = QNirp*d t v 



= ttNQ^ 2 tan 2 . d,v. 



Since the reduction of velocity of the a. particle in passing- 

 through 1 cm. of hydrogen is small, the number n of H atoms 

 produced per cm. of path is given by 



n/Q =7rlVtan 2 (4) 



In this case v>/Q is the fraction of ot particles which give rise 

 to an H atom between and 6. 



Taking e=4E=4'77 x lO" 10 e.s. unit, r?=l'922xl0 9 cm. 

 per sec, N = 5*41x 10 19 , and e/m = 9570 for hydrogen, 



then fi= 9-27 xlO" 11 



and n/Q = 1*46 X 10" 6 tan 2 6 (5) 



It was found experimentally that the swiftest H atoms due 

 to an a. particle from radium had a range corresponding to 

 28 cm. of air or four times the range of the a. particle. 

 Generally it was found that the maximum range of the 

 H atom was four times the range of the a particle producing 

 it. Since the range of a particles varies as the cube of their 

 velocity, it follow,s that the range of H atoms is proportional, 

 at any rate approximately, to the cube of their velocity. 

 Since the velocity of an H atom projected at an angle with 

 the a particle is n cos where v is the maximum velocitv 

 of the H atom, the range R of an H atom projected at angle 6 

 is given by R/R = cos 3 # where R is the maximum range. 

 Since, however, the a. particles fall nearly normally on the 

 screen, the H atoms deflected at an angle 6 travel a distance 

 Rsec#. Consequently the range R in the direction of the 

 a particles is given by R/R = cos 4 6. Substituting the value 

 of in equation (5), 



n/Q = 1*46 xl0- 6 (^/^°~l). 



This equation only applies to a particles of velocity v G 

 emitted by radium C. Since p cc 1/r 2 , it is seen that the 

 number of H atoms varies as 1/v 4 . Remembering that 

 the range of the a particle varies as v 3 , it is easily seen 



