676 Prof. E. ItutherforJ on the 



Let m be mass of the particle, 

 v x = velocity of approach, 

 i\, = velocity of recession, 

 M = mass of atom, 



V = velocity communicated to atom as result of 

 encounter. 



Fig. 2. 



Let OA (fig. 2) represent in magnitude and direction the 

 momentum mv^ of the entering particle, 

 and OB the momentum of the receding 

 particle which has been turned through an 

 angle AOB = <£. Then BA represents in 

 magnitude and direction the momentum 

 MV of the recoiling atom. 



{MV) 2 = (mv l ) 2 +(i7iv 2 ) 2 -2m 2 v 1 v 2 coscl). (1) 



By the conservation of energy 

 M V 2 = mv 2 — mv 2 2 . 



(2) 



Suppose M/?n = K and v 2 =pv L , where /\ 

 p is <1. 



From (1) and (2), 



(K + l)p 2 ~2/>cos(£ = K-l, 



or 



COS(/> 



^K + l + K + 1 VK'-sin'*. 



Consider the case of an a particle of atomic weight 4, 

 deflected through an angle of 90° by an encounter with an 

 atom of gold of atomic weight 197. 



Since K=49 nearly, 



P = 



K-l 



K+l 



= •979, 



or the velocity of the particle is reduced only about 2 per 

 cent, by the encounter. 



In the case of aluminium K = 27/4 and for cj> = 90° 

 p = 'S6. 



It is seen that the reduction of velocity of the a particle 

 becomes marked on this theory for encounters with the 

 lighter atoms. Since the range of an a particle in air or 

 other matter is approximately proportional to the cube of 

 the velocity, it follows that an a particle of range 7 cms. 

 has its range reduced to 4' 5 cms. after incurring a single 



