Question

A nucleus (mass no. $238$) initially at rest decay into another nucleus (mass no. $234$) emitting an $\alpha$ particle (mass no. $4$) with the speed of $1.17\times {10}^{7}m/sec$. Find the recoil speed of the remaining nucleus.

Answer 1

Given,

Mass of nucleus, $M_2=234u$

Mass of alpha, $m=4$ and velocity of alpha,$v=1.17\times {10}^{7}m/s$

From conservation of momentum

Initial momentum = final momentum

$M{V}_{initial}=M_{2}V+mv$

$\Rightarrow 0=234\times V+4\times 1.17\times {10}^7$

$\Rightarrow V=2\times {10}^{5}m/s$

Recoil speed is $2\times {10}^{5}m/s$