Artificial Disintegration of Light Elements. 823 



account the energy derived from the disintegration o£ the 

 nucleus. If we suppose, however, that the law of con- 

 servation of momentum is valid in this problem, we can, on 

 certain assumptions, calculate the final distribution of energy 

 between the three bodies involved in the collision. 



We shall suppose that, in addition to the conservation 

 of momentum, the resultant kinetic energy of the three 

 bodies involved is the same whether the H atom is liberated 

 in the forward or backward direction, and in -particular that 

 the final energy of escape of the a particle is not sensibly 

 different in the two cases. Both of these assumptions seem 

 not unreasonable. 



Let M, m, /ul be the masses of the u particle, H atom, and 

 residual nucleus respectively ; V, V the initial and final 

 velocities of the « particle ; i? l5 v 2 the maximum velocities of 

 the H atoms in the forwards and backwards direction ; u i} 

 u 2 the corresponding velocities of the residual nucleus. The 

 velocities are all measured in the direction of the a particle. 



Then 



M(V-V')=™«i + M 

 = mv a + fiu 2 , 



while the equivalence of energy in the two cases gives 

 mvi + fjMi = mv 2 2 ~\- /jLU 2 2 . 



From these three equations we can determine the three 

 unknowns — viz., V, u u and u 2 . 

 In the case of aluminium, 



m = l; ^ = 26, ^ = 2'37V, v 2 = 2'13V. 



It can be calculated that in this case 



V' = \L9V, 



^ Wl =-87V, 



/am s =5'37V. 



It is thus seen that the u particle escapes with '19 of its 

 initial velocity, and so gives 96"! per cent, of its energy to the 

 system. The residual nucleus is shot forward in the direction 

 of the ol particle, but with slower velocity in the case of the 

 escape of a forward particle. 



The relative energies in terms of the initial energy of the 



