Q. A photon and an electron have an equal energy$E$.
A) $\sqrt{E}$
B) $1/\sqrt{E}$
C) $1/E$
D) Does not depend upon $E$
Explanation
(b) $\ \lambda_{photon} = \ \frac{hc}{E}$
and $\lambda_{electron\ } = \frac{h}{\sqrt{2mE}}\ $
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{\lambda_{photon}}{\ \lambda_{electron}} = c\sqrt{\frac{2m}{E}}\ $
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{\lambda_{photon}}{\ \lambda_{electron}} \propto \frac{1}{\sqrt{E}}\ \ \ \ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.