First slide

Types of collision

Question

A neutron traveling 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

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 the neutron be v₁ Then
$v_{1} = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) u_{1} + (\frac{2 m_{2}}{m_{1} + m_{2}}) u_{2} Hero u_{1} = u and u_{2} = 0, m_{1} = 1 and m_{2 = A} v_{1} = (\frac{1 - A}{1 + A}) u For neutron, final K . E . = E' ∴ E^{'} = \frac{1}{2} (1) v_{1}^{2} = \frac{1}{2} {(\frac{1 - A}{1 + A})}^{2} u^{2} Initial K.E. = E ∴ E = \frac{1}{2} (1) u^{2} From eqs . (i) and [ii), we have \frac{E^{'}}{E} = {(\frac{1 - A}{1 + A})}^{2} E^{'} = {(\frac{1 - A}{1 + A})}^{2} E$

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