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 mother nucleus is: (Assume that the daughter nucleus is in ground state)

• A. $96$
• B. $100$
• C. $104$
• D. none of these

Answer 1

The correct option is B $100$

Let,

${}_Z^{A}X{\to }_{A-2}^{A-1}Y{+}_2^{4}He$

$K_{\alpha }=\frac{m_y}{m_y+m_{\alpha }}Q$

$\Rightarrow \frac{A-4}{A}Q$

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

$\Rightarrow A=100$