Ncert Exercises & Solutions

Question 5.17:

A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.

Let m, $m_{1}$ ,and $m_{2}$ be the respective masses of the parent nucleus and the two daughter nuclei. The parent nucleus is at rest.

Initial momentum of the system (parent nucleus) = 0

Let $v_{1}$ and $v_{2}$ be the respective velocities of the daughter nuclei having masses $m_{1}$ and $m_{2}$ .

Total linear momentum of the system after disintegration = $m_{1} v_{1} + m_{2} v_{2}$

According to the law of conservation of momentum:

Total initial momentum = Total final momentum

$0 = m_{1} v_{1} + m_{2} + v_{2}$
$v_{1} = \frac{- m_{2} v_{2}}{m_{1}}$

Here, the negative sign indicates that the fragments of the parent nucleus move in directions opposite to each other.

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