Question

In an $\alpha$-decay the kinetic energy of $\alpha$-particle is $48MeV$ and $Q$-value of the reaction is $50MeV$. The mass number of the molecular nucleus is $X$. Find value of $X/25$.
(Assume that daughter nucleus is in ground state.)

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (B)

$4$

We have: $K_a=\frac{m_y}{m_y+m_{\alpha }}Q$

$\Rightarrow K_{\alpha }=\frac{A-4}{A}Q$

$\Rightarrow 48=\frac{A-4}{A}\times 50$

$\Rightarrow A=100$