Question

An electron and a proton are moving in the same direction with same direction with same kinetic energy. The ratio of the de-Broglie wavelength associated with these particles is?

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

Answer 1

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

de-Broglie wavelength
${\lambda }_e=\frac{hc}{E_e}$ and ${\lambda }_p=\frac{hc}{E_p}$

Here, ${\lambda }_e=\frac{h}{\sqrt{2m_{e}E}}$ and ${\lambda }_p=\frac{h}{\sqrt{2m_{p}E}}$

$\therefore \frac{{\lambda }_e}{{\lambda }_p}=\sqrt{\frac{m_p}{m_e}}$.