Question

A proton and an $\alpha$ -particle are accelerated through a potential difference of 100 V. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is

• A. $\sqrt{2}:1$
• B. $2:1$
• C. $2\sqrt{2}:1$
• D. $\frac{1}{2\sqrt{2}}:1$

Answer 1

The correct option is C

$2\sqrt{2}:1$

$\lambda =\frac{h}{\sqrt{2mQV}}\Rightarrow \lambda \propto \frac{1}{\sqrt{mQ}}\Rightarrow \frac{{\lambda }_p}{{\lambda }_{\alpha }}=\sqrt{\frac{m_{\alpha }{Q}_{\alpha }}{m_p{Q}_p}}=\sqrt{\frac{4m_p\times 2Q_p}{m_p\times Q_p}}=2\sqrt{2}$