Question

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. $\sqrt{\frac{m}{E}}$

Answer 1

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

Energy of photon, $E=h\nu =\frac{hc}{{\lambda }_{Ph}}$

Where, ${\lambda }_{Ph}$ is the wavelength of a photon $\Rightarrow {\lambda }_{Ph}=\frac{hc}{E}$

Wavelength of the electron, ${\lambda }_e=\frac{h}{\sqrt{2mE}}$
$\therefore \frac{{\lambda }_{Ph}}{{\lambda }_e}=\frac{hc}{E}\times \frac{\sqrt{2mE}}{h}=c\sqrt{\frac{2m}{E}}$

Hence, $\left(A\right)$ is the correct answer.