First slide

The steps in collision

Question

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

Moderate

A

${(\frac{1 - A}{A + 1})}^{2}$
B

${(\frac{A + 1}{A - 1})}^{2}$
C

${(\frac{A - 1}{A})}^{2}$
D

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

Solution

Let the final velocity of neutron be v₁ According to theory of collision
$v_{1} = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) u_{1} + (\frac{2 m_{2}}{m_{1} + m_{2}}) u_{2} Here u_{1} = u and u_{2} = 0 . Further m_{1} = 1 and m_{2} = A ∴ v_{1} = (\frac{1 - A}{1 + A}) u Final K.E. of neutron = \frac{1}{2} {mv}_{1}^{2} = \frac{1}{2} m {(\frac{1 - A}{1 + A})}^{2} u^{2} Initial K.E. of neutron = \frac{1}{2} {mu}^{2} ∴ Fraction of energy retained = {(\frac{1 - A}{1 + A})}^{2}$

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