Question

A proton and an electron have same kinetic energy. Which one has smaller de-Broglie wavelength and why?

Answer 1

de-Broglie wavelength $\lambda =\frac{h}{p}$ where $p=\sqrt{2mE}$

$\therefore$ $\lambda =\frac{h}{\sqrt{2mE}}$ $⟹\lambda \propto \frac{1}{\sqrt{m}}$ $(\because E=constant)$

As $m_e<m_p$ $⟹$ ${\lambda }_p<{\lambda }_e$

Thus proton has smaller wavelength.