Question

If a nucleus such as ${}^{226}\text{Ra}$ that is initially at rest undergoes alpha decay, then which of the following statement is true?

• A. The alpha particle has more kinetic energy than the daughter nucleus.
• B. The alpha particle has less kinetic energy than the daughter nucleus.
• C. The alpha particle and daughter nucleus both have the same kinetic energy.
• D. We cannot say anything about kinetic energy of alpha particle and daughter nucleus.

Answer 1

The correct option is A The alpha particle has more kinetic energy than the daughter nucleus.

As the parent nucleus is at rest, according to the conservation of momentum,

$0=P_D+P_{\alpha }$

$\Rightarrow |P_{\alpha }|=|P_D|=P$

We know that,

$K_{\alpha }=\frac{P^2}{2m_{\alpha }}$ and $K_D=\frac{P^2}{2m_D}$

Also, Mass of the nucleus is proportional to mass number.

$\Rightarrow m_D>m_{\alpha }\to K_{\alpha }>K_D$.

Hence, option $\left(A\right)$ is correct.

Why this Question? We can apply conservation of momentum when the net external force on a system is zero.