Question

An $\alpha$ particle is emitted from a heavy radioactive nucleus. Compare the kinetic energies of the $\alpha$ particle ${KE}_{\alpha }$ and the daughter nucleus ${KE}_D$.

• A. ${KE}_{\alpha }>{KE}_D$
• B. ${KE}_{\alpha }={KE}_D$
• C. ${KE}_D>{KE}_{\alpha }$
• D. ${KE}_{\alpha }={4KE}_D$

Answer 1

The correct option is A ${KE}_{\alpha }>{KE}_D$

$\begin{array}{c}\text{Parent nucleus is heavy}\Rightarrow \text{Daughter nucleus is heavy.}\\ \text{Now,}{K}_{\alpha }=\frac{\text{mass of daughter nucleus)}}{(\text{mass of Parent nucleus)}}\times K\end{array}$

$\begin{array}{cc}\text{O),}& K_{\alpha }=\frac{m_D}{m_{{\alpha }^{+}}{m}_D}\times K\\ \because & m_2>m_{\alpha }\\ \Rightarrow & K_{\alpha }>K_D.\end{array}$