Question

A nucleus with mass number $220$ initially at rest emits an $\alpha particle$. If the $Q$ value of the reaction is $5.5MeV$, calculate the kinetic energy of the $\alpha particle$

• A. $4.4MeV$
• B. $5.4MeV$
• C. $5.6MeV$
• D. $6.5MeV$

Answer 1

The correct option is B $5.4MeV$

$M\to X+\alpha$
$E=\frac{p^2}{2m}$
Let Total energy = $T$
$T=E_{\alpha }+E_X$
$M=M_{\alpha }+M_X$
$M_X=216$
Conservation of momentum
$p_{\alpha }=p_X$
$m_{\alpha }{E}_{alpha}=m_X{E}_X$
$E_{\alpha }=\frac{m_x}{M}T$
$E_{\alpha }=\frac{216}{220}5.5=5.4MeV$