Question

For some energy find the ratio of $\lambda photon$ and ${\lambda }_{\text{electron}}$ (Here m is mass of electron)

• A. $c\sqrt{\frac{2m}{E}}$
• B. $\frac{1}{c}\sqrt{\frac{2m}{E}}$
• C. $\frac{1}{c^2}\sqrt{\frac{2m}{E}}$
• D. $\frac{1}{c}\sqrt{\frac{2m}{E^2}}$

Answer 1

The correct option is A $c\sqrt{\frac{2m}{E}}$

$\begin{array}{c}Forelectron:\\ mv=\frac{h}{{\lambda }_e}\\ v=\frac{h}{m{\lambda }_e}\\ \frac{m{v}^2}{2}=\frac{m}{2}\cdot \frac{h^2}{m^2{{\lambda }_e}^2}\\ E=\frac{h^2}{2m{{\lambda }_e}^2}\\ {\lambda }_e=\sqrt{\frac{h^2}{2mE}}=\frac{h}{\sqrt{2mE}}\\ Forphoton:{\lambda }_p=\frac{hc}{E}\\ \frac{{\lambda }_p}{{\lambda }_e}=\frac{hc}{E}\times \frac{\sqrt{2mE}}{h}\\ =c\sqrt{\frac{2m}{E}}\end{array}$

Hence,

option $\left(A\right)$ is correct answer.