Q. If $m$ is the mass of an electron and $c$ is the speed of light, the ratio of the wavelength of a photon of energy $E$ to that of the electron of the same energy is
A) $c\sqrt{\frac{2m}{E}}$
B) $\sqrt{\frac{2m}{E}}$
C) $\sqrt{\frac{2m}{cE}}$
D) $\sqrt{\frac{m}{E}}$
Explanation
(a) Energy of photon, $E = hv = \frac{hc}{\lambda_{Ph}}$
where $\lambda_{Ph}$ is the wavelength of a photon $\lambda_{ph} = \frac{hc}{E}$
Wavelength of the electron, $\lambda_{e} = \frac{h}{\sqrt{2mE}}$
$\therefore\frac{\lambda_{Ph}}{\lambda_{e}} = \frac{hc}{E} \times \frac{\sqrt{2mE}}{h} = c\sqrt{\frac{2m}{E}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.