Question

The ratio of momenta of an electron and an α-particle which are accelerated from rest by a potential difference of 100 volt 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

Answer: (D)

$\sqrt{\frac{m_{e}}{2m_{\alpha}}}$

Answer 2

Momentum $p = \sqrt{2mK};$

where K = kinetic energy = Q.V

⇒$p = \sqrt{2mQV}$⇒$p \propto \sqrt{mQ} \Rightarrow \frac{p_{e}}{p_{\alpha}} = \sqrt{\frac{m_{e}Q_{e}}{m_{\alpha}Q_{\alpha}}} = \sqrt{\frac{m_{e}}{2m_{\alpha}}}$