Question

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

• A. $ 1 $
• B. $ \sqrt{\frac{2{{m}_{e}}}{{{m}_{\alpha }}}} $
• C. $ \sqrt{\frac{{{m}_{e}}}{{{m}_{\alpha }}}} $
• D. $ \sqrt{\frac{{{m}_{e}}}{2{{m}_{\alpha }}}} $

Answer 1

Answer: (D)

Momentum, $ p=mv $
and $ F=\sqrt{\frac{2QV}{m}} $
$ \Rightarrow $ $ p=\sqrt{2QmV} $
$ p\propto \sqrt{Qm} $
$ \therefore $ $ \frac{{{p}_{e}}}{{{p}_{\alpha }}}=\sqrt{\frac{e{{m}_{e}}}{2e{{m}_{\alpha }}}}=\sqrt{\frac{{{m}_{e}}}{2{{m}_{\alpha }}}} $