Question

A photon and an electron have equal energy E. Then the ratio of wavelength of photon to that of electron is proportional to

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

Answer 1

The correct option is B $\frac{1}{\sqrt{E}}$

Wavelength of photon ${\lambda }_p=\frac{hc}{E}$ .....(1)
Wavelength of electron ${\lambda }_e=\frac{h}{\sqrt{2mE}}$ ....(2)
$\Rightarrow \frac{{\lambda }_p}{{\lambda }_e}=\frac{hc}{E}\times \frac{\sqrt{2mE}}{h}=C\sqrt{\frac{2m}{E}}\Rightarrow \frac{{\lambda }_p}{{\lambda }_e}\propto \frac{1}{\sqrt{E}}$