JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Modern Physics

The parent nucleus is at rest, so the $\alpha$-particle and the residual nucleus fly apart with equal and opposite momenta of magnitude $p$. Their kinetic energies are $K_{\alpha }=\frac{p^2}{2m_{\alpha }}$ and $K_d=\frac{p^2}{2m_d}$, so the released energy divides inversely as the masses:

With mass numbers $m_d=180$ and $m_{\alpha }=4$,

The $\alpha$-particle carries away $5.38$ MeV.