A nucleus of uranium decays at rest into nucl | vedclass

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

Vedclass · Accepted Answer

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

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(D) If $\vec{p}_{Th}$ and $\vec{p}_{He}$ are the momenta of thorium and helium nuclei respectively,then according to the law of conservation of linear momentum:$0 = \vec{p}_{Th} + \vec{p}_{He}$ or $\vec{p}_{Th} = -\vec{p}_{He}$.The negative sign shows that both are moving in opposite directions. However,in magnitude,$p_{Th} = p_{He}$.If $m_{Th}$ and $m_{He}$ are the masses of thorium and helium nuclei respectively,then the kinetic energy of the thorium nucleus is $K_{Th} = \frac{p_{Th}^2}{2m_{Th}}$ and that of the helium nucleus is $K_{He} = \frac{p_{He}^2}{2m_{He}}$.Therefore,$\frac{K_{Th}}{K_{He}} = \left(\frac{p_{Th}}{p_{He}}\right)^2 \left(\frac{m_{He}}{m_{Th}}\right)$.Since $p_{Th} = p_{He}$ and $m_{He}  K_{Th}$.Thus,the helium nucleus has more kinetic energy than the thorium nucleus.

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

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