572 Sir E. Rutherford on Collision of 



a particle of range R in hydrogen is given by 



m E 2 



■/»-£• i?-. w 



where M is the mass and E the charge on the a particle. 



It is to be expected that this relation would hold approxi- 

 mately for the passage of electrified atoms through light 

 substances like air and aluminium. Since M — 4 and E = 2<? 

 where e is the unit charge, the range x of a particle carrying 

 a single charge is obviously x — m 1 ^. The velocity!* acquired 

 by an atom of mass m due to a close collision with an 

 « particle of velocity r is given by 



2M 



u= ^ — . r COS 0, 



M + m 



where 6 is the angle of deflexion of the atom after the 

 collision. Assuming that the range of electrified atoms 

 in general like the range of a particles varies as the cube 

 of the velocity, the range x after collision of an atom 

 carrying unit charge is given by 



x = mT{[^ ) cos d <9. 



R^Y 



Applying this result to H atoms, the maximum velocity 

 should be (8/5) 3 R = 4'lR, while the observed value is about 

 4R. As a further test of this relation, consider the range 

 to be expected for the recoil atom of radium B of mass m 

 resulting from the expulsion of an a particle of range 

 4*75 cm. from radium A. Bv the principle of momentum 



M 



Mr = m» and the velocity of recoil w= — v where ??i = 214 



m 



Consequently the range in air x 



= 214. (A)' x 4-75 = -067 



The value found by Wertenstein * is '12 mm., but, con- 

 sidering the very wide range of velocity, the agreement is 

 fairly satisfactory. If it be assumed that the range is pro- 

 portional to the power 2'85 instead of 3, this is a good 

 agreement both for the hydrogen and recoil aloms. 



If the atom after collision with an a particle carries a 

 charge of two units, its range from (1) should be only about 

 1/4 of the same atom carrying a single charge. For 



* Wertenstein, C. R. cl. p. 869 (1910) ; cli. p. 469 (1910). 



cm. 



