A neutron traveling with a velocity u and  kinetic energy  E.collides perfectly elastically head-on with the nucleusof an atom of mass number A at rest. The fraction of total energy retained by neutron is

Let the final velocity of neutron be v1  According to theory of collisionv1=m1−m2m1+m2u1+2m2m1+m2u2  Here u1=u and u2=0. Further m1=1 and m2=A ∴ v1=1−A1+Au  Final K.E. of neutron =12mv12 =12m1−A1+A2u2  Initial K.E. of neutron =12mu2 ∴  Fraction of energy retained  =1−A1+A2