Question

The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of $100V$ is

• A. $1$
• B. $\sqrt{\frac{2m_e}{m_{\alpha }}}$
• C. $\sqrt{\frac{m_e}{m_{\alpha }}}$
• D. $\sqrt{\frac{m_e}{2m_{\alpha }}}$

Answer 1

The correct option is D $\sqrt{\frac{m_e}{2m_{\alpha }}}$

We have, $p=\sqrt{2mqV}$
$\therefore \frac{P_e}{P_{\alpha }}=\sqrt{\frac{m_e{q}_e}{m_{\alpha }{q}_{\alpha }}}=\sqrt{\frac{m_{e}e}{m_{\alpha }2C}}=\sqrt{\frac{m_e}{2m_{\alpha }}}$