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

• A

  ${\left(\frac{\mathrm{A}-1}{\mathrm{A}+1}\right)}^2$

• B

  ${\left(\frac{\mathrm{A}+1}{\mathrm{A}-1}\right)}^2$

• C

  ${\left(\frac{\mathrm{A}-1}{\mathrm{A}}\right)}^2$

• D

  ${\left(\frac{\mathrm{A}+1}{\mathrm{A}}\right)}^2$