Question

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

Answer 1

Given:
$Q=50\text{MeV};K{E}_{\alpha }=48\text{MeV}$

Let the decay be represented as,

$X^A\to Y^{A^{\prime }}+\alpha$

So, kinetic energy of $\alpha -$ particle is given by,

$K{E}_{\alpha }=\frac{m_{\alpha }}{m_X}Q$

$\Rightarrow 48=\frac{(A-4)u}{Au}\times 50$

$\therefore A=100$