Question

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then

• A. The helium nucleus has more momentum than the thorium nucleus.
• B. The helium nucleus has less kinetic energy than the thorium nucleus.
• C. The helium nucleus has more kinetic energy than the thorium nucleus.
• D. The helium nucleus has less momentum than the thorium nucleus.

Answer 1

Answer: (C)

The helium nucleus has more kinetic energy than the thorium nucleus.

Answer 2

If $\vec{p}_{Th}$ and $\overrightarrow{p}_{He}$ are the momenta of thorium and helium nuclei respectively, then according to law of conservation of linear momentum

0=$\overrightarrow{p}_{Th}+\overrightarrow{p}_{He}$ or $\overrightarrow{p}_{Th}=-\overrightarrow{p}_{He}$

-ve sign shows that both are moving in opposite directions.

But in magnitude
$p_{Th}=p_{He}$

If m$_{Th}$ and m$_{He}$ are the masses of thorium and helium
nuclei respectively, then

Kinetic energy of thorium nucleus is $K_{Th}=\frac{p^{2}_{Th}}{2m_{Th}}$ and that of helium nucleus is
$K_{He}=\frac{p^{2}_{He}}{2m_{He}}$

$\therefore \, \, \frac{K_{Th}}{K_{He}}=\bigg(\frac{p_{Th}}{p_{He}}\bigg)^2 \bigg(\frac{m_{He}}{m_{Th}}\bigg)$

But $p_{Th}=p_{He}$ and $m_{He} \, K_{Th}$

Thus the helium nucleus has more kinetic energy than the thorium nucleus.