First slide

The steps in collision

Question

A moving neutron collides with a stationary $α$ -particle. The fraction of the kinetic energy lost by the neutron is

Moderate

A

1/4
B

1/16
C

9/25
D

16/25

Solution

Hero, we have
$E_{i} = \frac{1}{2} {mu}^{2} and E_{f} = \frac{1}{2} {mv}^{2} As shown in the above question v = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) u or v = (\frac{m - 4 m}{m + 4 m}) u Fraction of energy lost = (E_{i} - E_{f}) / E_{i} = 1 - {(\frac{v}{u})}^{2} = 1 - {(\frac{m - 4 m}{m + 4 m})}^{2} = 1 - \frac{9}{26} = \frac{16}{25}$

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