Question

An electron and a proton are accelerated through the same potential difference. The ratio of their de Broglie wavelengths ($\frac{{\lambda }_e}{{\lambda }_p}$ ) is

• A. 1
• B. $\frac{m_e}{m_p}$
• C. $\frac{m_p}{m_e}$
• D. $\sqrt{\frac{m_p}{m_e}}$

Answer 1

The correct option is D $\sqrt{\frac{m_p}{m_e}}$

${\lambda }_e=\frac{h}{\sqrt{2m_{e}eV}}$

${\lambda }_p=\frac{h}{\sqrt{2m_{p}eV}}$

$\frac{{\lambda }_e}{{\lambda }_p}=\sqrt{\frac{m_p}{m_{{}_e}}}$

So, the answer is option (D).