Question

The ratio of the wavelengths of a photon and that of an electron of same energy $E$ will be [$m$ is mass of electron]:

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

Answer 1

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

Wavelength of photon:

$E=\frac{hc}{\lambda }$

${\lambda }_p=\frac{hc}{E}$

Wavelength of electron:

${\lambda }_e=\frac{h}{mv}$

$\frac{1}{2}m{v}^2=E$

$mv=\sqrt{2Em}$

So ${\lambda }_e=\frac{h}{\sqrt{2Em}}$

$\frac{{\lambda }_p}{{\lambda }_e}=c\sqrt{\frac{2m}{E}}$