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

\(0 = {\vec p_{{\text{Th}}}} + {\vec p_{{\text{He}}}}\) or \({\vec p_{{\text{Th}}}} =  - {\vec p_{{\text{He}}}}\)

\(-ve\) sign shows that both are moving in opposite directions. But in magnitude

\(p_{\mathrm{Th}}=p_{\mathrm{He}}\)

If \({m_{{\text{Th}}}}\) and \(m_{\mathrm{He}}\) are the masses of thorium and helium nuclei respectively, then Kinetic energy of thorium nucleus is \(K_{\mathrm{Th}}=\frac{p_{\mathrm{Th}}^{2}}{2 m_{\mathrm{Th}}}\) and that of helium nucleus is

\(K_{\mathrm{He}}=\frac{p_{\mathrm{He}}^{2}}{2 m_{\mathrm{He}}}\)

\(\therefore \quad \frac{K_{\mathrm{Th}}}{K_{\mathrm{He}}}=\left(\frac{p_{\mathrm{Th}}}{p_{\mathrm{He}}}\right)^{2}\left(\frac{m_{\mathrm{He}}}{m_{\mathrm{Th}}}\right)\)

But \(p_{\mathrm{Th}}=p_{\mathrm{He}}\) and \({m_{{\text{He}}}}\, < \,{m_{_{{\text{Th}}}}}\)

\(\therefore \) \({K_{{\text{Th}}}}\, < \,{K_{{\text{He}}}}\) or \({K_{{\text{He}}}}\, > \,{K_{{\text{Th}}}}\)

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