a, Particles ivith Light Atoms. 557 



range of a. particles of this velocity v is 2*7 cm. This result 

 means that « particles of range less than 2*7 cm., acted on 

 by the forces given by the simple theory, are unable to 

 approach within the critical distance D of the nucleus of the 

 hydrogen atom. 



Since the number of H atoms produced is proportional to 

 the value of p 2 given in equation 



7? 2 



n __ 9 ° 

 Number of H atoms of velocity v ~ r' 1 



''o 



D-2i 



Substituting the values of D, /x, vjv, the relative number of 

 H atoms to be expected for different values of v are given 

 below : — 



Range of incident oc par- 

 ticles in cms 7 6 5 4 3-5 3-0 2-7 



Relative number of 



H atoms 100 88 72 50 35 15 



It has been previously pointed out that the observed 

 number of H atoms shows a rapid decrease for ranges 

 between 3 and 2 cm., a result in general accord with these 

 calculations. It is, however, not to be expected that there 

 would be any close agreement between theory and experi- 

 ment, for the theory supposes that there is an abrupt 

 variation in the magnitude and direction of the forces for an 

 apsidal distance D, a condition which is physically im- 

 probable. We may, however, conclude that the variations 

 of number of H atoms with velocity is not inconsistent with 

 the view that the forces between colliding atoms augment 

 rapidly for values of D<3*5 x 10 -13 cm. 



From the known values of D and /a, we are able to cal- 

 culate the value of 0, i. e., the angle of deflexion of the 

 H atom for a collision of apsidal distance D = 3'5 x 10~ 13 cm. 

 For a. rays of range 7 cm., # = 69° ; the corresponding 

 effective range of the H atom is 28 cos 4 6 or 4*6 mm. It is 

 thus clear that, on the assumptions made, no atoms for which 

 D>3*5xlO~ 13 should be detected under the experimental 

 conditions. 



The general results are consistent with the view that the 

 field of force between the a particle and hydrogen nucleus 

 undergoes rapid changes in magnitude and probably also in 

 direction when the nuclei approach within 3*5 X 10~ 13 cm. 

 of each other. 



