Question

In an $\alpha$-decay, the kinetic energy of $\alpha$ particle is $48\, MeV$ and $Q$ value of the reaction is $50\, MeV$. The mass number of the mother nucleus is (Assume that daughter nucleus is in ground state)

Answer 1

We have, $K_{\alpha}=\frac{m_{y}}{m_{y}+m_{\alpha}} \cdot Q$
$\Rightarrow K_{\alpha}=\frac{A-4}{A} \times Q$
$\Rightarrow 48=\frac{A-4}{A} \times 50$
$\Rightarrow A=100$