A neutron makes a head on elastic collision with a lead nucleus. The ratio of nuclear mass to neutron mass is 206 . The fractional change in kinetic energy of a neutron is

Step-by-step solution

Let m be the mass of the neutron and M be the mass of the lead nucleus. Given M = 206m . In a head-on elastic collision, the final velocity v₁' of the neutron is given by v₁' = m - M m + M v₁ , where v₁ is the initial velocity of the neutron. The ratio of the final kinetic energy K' to the initial kinetic energy K is K' K = ( v₁' v₁ )^2 = ( m - M m + M )^2 . Substituting M = 206m , we get K' K = ( m - 206m m + 206m )^2 = ( -205m 207m )^2 = ( 205 207 )^2 . The fractional change in kinetic energy is K K = K' - K K =