Question

For the same value of kinetic energy, the momentum shall be maximum for

• A. a proton
• B. an electron
• C. a deutron
• D. an $\alpha -particle$

Answer 1

The correct option is D

an $\alpha -particle$

Step 1: Given data

Kinetic energy is constant, $k$

Step 2: Finding the maximum momentum of the particle

The relation between kinetic energy and momentum of the body is given by

$$\begin{gathered} E_k=\frac{p^2}{2m} \\ {p}^2=2m{E}_k \\ p=\sqrt{2m{E}_k} \\ p\propto \sqrt{m} \end{gathered}$$

Since $\alpha -particle$ has greater mass among the electron, proton and deuteron,

So, $\alpha -particle$ momentum will be maximum.

Hence, option (d) is correct.