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

Let mass of neutron = m (say) then mass of nucleus = mAIn head on elastic collision, velocity of neutron (after collision)v1=m−mAm+mAv=1−A1+AvThe fraction of total energy retained by the neutron=12mv1212mv2=1−A1+A2=A−1A+12