132 ADVENTURES IN RADIOISOTOPE RESEARCH 



It must be home in mind that in the present instance the recoil par- 

 ticles are expelled in all directions, such that the particle can reach the 

 surface only when the distance x of iis starting point from the surface 

 satisfies the condition 



x/at t^ cos a (4) 



where a is the angle between the normal to the surface and the ray. 

 The ratio of the number of particles reaching the surface from a point 

 C to the total number of particles issuing from that point in all directions 

 is equal to the ratio of the surface of the spherical cap of height a~x to 

 the surface of a sphere of radius a, whence it follows that 



2 7t a(a — x) , X 



^ ^^^ = 1 (5) 



2 7ia^ a 



To take account of this concept the integrand in (equation (1) must be 

 multiplied by {l—x/a), and thus 



a 



A=.\-J 



]f{7ii)Z) 



1 e- •'"''^*^ • dx 1 6) 



a 



or, by substituting 

 the result is 



I = a/2y{DZ) 



A = ^p{^)-^{}-e-''} (8) 



This equation is evaluated graphically and from the value of | thus 

 obtained D is calculated by means of equation (7). 



Since the diffusion constant has been calculated in some cases from the 

 decrease in the a-ionization it may be appropriate to discuss the calcula- 

 tion for that method. The a-activity was measured by selecting a parallel 

 ])eam normal to the pellet surface such that equation (1) could be applied. 

 The shutter had an air gap of 5.3 cm and thus only the a-rays of Th('", 

 with a range of 8.4 cm, were able to penetrate. The conditions for the 

 calculation were thus simplified. In measuring D by means of a-racliation 

 it must l)e noted that the particles entering the electroscope do not all 

 have the same ionizing effect since this is dependent on the path already 

 travelled by a particle. A particle which has come from the interior of the 

 pellet has less effect than one which has started from the surface. If the 

 decrease in ionization due to a particle which has travelled a distance 

 X in the Pbia pellet in relation to the effect of one which has started from 

 the surface is represented by 



J = (fix) (9) 



