Scattering of a and -ft Particles by Matter. 673 



Let angle POA = 0. 



Let V = velocity of particle on entering the atom, v its 

 velocity at A, then from consideration of angular momentum 



pY = $A.v. 



From conservation of energy 



NeE 



Since the eccentricity is sec #, 



SA = SO + OA =p cosec 0(1 -f cos 6) 

 =p cot 6/2, 

 f = S A(S A - b) =p cot 6/2(p cot 6/2 - b) , 

 /. b = 2p cot (9. 

 The angle of deviation cf> of the particle is it — 20 and 



cot<£/2=^* (1) 



This gives the angle of deviation of the particle in terms 

 of b, and the perpendicular distance of the direction of 

 projection from the centre of the atom. 



For illustration, the angle of deviation cf> for different 

 values of p/b are shown in the following table : — 



p/b.... 10 5 2 1 -5 -25 -125 



4> 5°-7 ll°-4 28° 53° 90° 127° 152° 



§ 3. Probability of single deflexion through any angle. 



Suppose a pencil of electrified particles to fall normally on 

 a thin screen of matter of thickness t. With the exception 

 of the few particles which are scattered through a large 

 angle, the particles are supposed to pass nearly normally 

 through the plate with only a small change of velocity. 

 Let n = number of atoms in unit volume of material. Then 

 the number of collisions of the particle with the atom of 

 radius R is 7r~R?nt in the thickness t. 



* A simple consideration shows that the deflexion is unaltered if the 

 forces are attractive instead of repulsive. 



