Q. A photon and an electron have equal energy E. $\lambda_{photon}/\lambda_{electron}$ is proportional to
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.