A neutron collides elastically with the stationary nucleus of an...

Let us assume the mass of the neutron is& ${m}_{n} = m$~and mass of the nucleus is& ${m}_{A} = Am$

Also, let us assume that the initial and the final velocities~of the neutron are& ${v}_{i}$~and& ${v}_{f}$~respectively.&

Using the formula of& final velocity for a perfectly elastic collision we get,

${v}_{f} = \left(m - Am\right)( m + Am ){v}_{i} = \left(\dfrac{1 - A}{1 + A}\right){v}_{i}$

$⇒ \dfrac{vf}{vi} = \left(\dfrac{1 - A}{1 + A}\right)<br /><br />$⇒ $\dfrac{Kfinal}{Kinitial} = \left(\dfrac{1 - A}{1 + A}\right)$2$</p>$