Question

The ratio of momenta of an electron and an alpha particle which are accelerated from rest by potential difference of 100 V 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 $\sqrt{\frac{m_e}{2m_{\alpha }}}$

Work done in accelerating a charge of magnitude $q$ through a potential of $V$ is $qV$
This work is converted into $KE$ of charged particle.

The magnitude of charge on alpha particle is twice that of electron.
So,

$K{E}_{\alpha }=2\times K{E}_e$
$\frac{{p_{\alpha }}^2}{2m_{\alpha }}=2\times \frac{{p_e}^2}{2m_e}$

$\therefore \frac{p_e}{p_{\alpha }}=\sqrt{\frac{m_e}{2m_{\alpha }}}$