A neutron makes a head-on elastic collisio

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A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is

A

$16/81$

B

$8/9$

C

$8/27$

D

$2/3$

A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is

Fractional decrease in kinetic energy of neutron
=$1 - {\left( {\frac{{{m_1} - {m_2}}}{{{m_1} + {m_2}}}} \right)^2}$[As $m_1=1$ and $m_2 = 2$]
$ = 1 - {\left( {\frac{{1 - 2}}{{1 + 2}}} \right)^2}$$ = 1 - {\left( {\frac{1}{3}} \right)^2} = 1 - \frac{1}{9} = \frac{8}{9}$