A neutron in a nuclear reactor collides head on elastically with the nucleus of a carbon atom initially at rest. The fraction of kinetic energy transferred from the neutron to the carbon atom is

Step-by-step solution

Let m and M be the masses of neutron and carbon nucleus (at rest) respectively. If u and v are the velocity of neutron before and after collision, then K_i= 1 2 m u^2 and K_f= 1 2 m v^2 , But v= (m-M) u m+M aligned & K_f= 1 2 m ( m-M m+M )^2 u^2 & K_f K_i = ( m-M m+M )^2 aligned The fraction of kinetic energy transferred from the neutron to the carbon atom is f= 4 m M (m+M)^2 But for carbon, M=12 ~m f= 4 m(12 m) (m+12 m)^2 = 48 169