Scattering of a and /3 Particles by Matter. 683 



Taking the probability of single scattering ='46 and 

 substituting the above values in the formula, the value of N 

 for gold comes out to be 97. 



For a thickness of gold equivalent in stopping power to 

 2*12 cms. of air, Geiger found the most probable angle to be 

 3° 40'. In this case £ = '00047, = 4°'4, and average u = 

 1*7 X 10 9 , and N comes out to be 114. 



Geiger showed that the most probable angle of deflexion 

 for an atom was nearly proportional to its atomic weight. It 

 consequently follows that the value of N for different atoms 

 should be nearly proportional to their atomic weights, at any 

 rate for atomic weights between gold and aluminium. 



Since the atomic weight of platinum is nearly equal to that 

 of gold, it follows from these considerations that the 

 magnitude of the diffuse reflexion of a particles through more 

 than 90° from gold and the magnitude of the average small 

 angle scattering of a pencil of rays in passing through gold- 

 foil are both explained on the hypothesis of single scattering 

 by supposing the atom of gold has a central charge of about 

 100*. 



(d) Experiments of CrowtTier on scattering of /3 rays. — ■ 

 We shall now consider how far the experimental results of 

 Crowther on scattering of j3 particles of different velocities 

 by various materials can be explained on the general theory 

 of single scattering. On this theory, the fraction of 8 

 particles p turned through an angle greater than is 

 given by 



p= j-n .t .b 2 cot 2 0/2. 



In most of Crowther's experiments is sufficiently small 

 that tan 0/2 may be put equal to <j)/2 without much error. 

 Consequently 



4> 2 = 2irn.t.b 2 if i? = 1/2. 



On the theory of compound scattering, we have already 

 seen that the chance p l that the deflexion of the particles 

 is greater than <fi is given by 



9tt 3 

 (j) 2 l\oorp 1 =—~~n.t.b' 2 . 



Since in the experiments of Crowther the thickness / of 

 matter was determined for which p 1 = l/2, 



2 =:'9G7r n t lr. 



For a probability of 1/2, the theories of single and compound 



2 Y 2 



