Question

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

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

Answer 1

The correct option is B The helium nucleus has more kinetic energy than the thorium nucleus.

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