Question

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

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

Answer 1

Answer: (D)

Since there is no external force acting on the uranium nucleus, momentum will be conserved in the reaction.
$P_{\text{iu }}=0$
Final momentum of the Thorium and He nuclei will be zero.
$pTh=pHe$
$K{E}_{Th}=\frac{p_{Th}^2}{2m_{Th}}$
$K{E}_{He}=\frac{p_{He}^2}{2m_{He}}$
$\Rightarrow \frac{K{E}_{Th}}{K{E}_{He}}=\frac{\frac{p_{Th}^2}{2m_{Th}}}{\frac{p_{He}^2}{2m_{He}}}$
$\Rightarrow \frac{K{E}_{Th}}{K{E}_{He}}=\frac{m_{He}}{m_{Th}}$
Since $m_{He}<m_{Th},K{E}_{He}>K{E}_{Th}$