Q76 / 90 · JEE Main 2021 (25 Jul Shift 2) · Physics

An electron moving with speed $v$ and a photon moving with speed $c$ , have the same D-Broglie wavelength. The ratio of the kinetic energy of the electron to that of a photon is:

Solution

$λ_{e} = λ_{Ph}$

$\frac{h}{p_{e}} = \frac{h}{p_{ph}}$

$\sqrt{2 m k_{e}} = \frac{E_{ph}}{c}$

$2 m k_{e} = \frac{{(E_{ph})}^{2}}{c^{2}}$

$\frac{k_{e}}{E_{ph}} = \frac{E_{ph}}{c^{2}} (\frac{1}{2 m})$

$= \frac{p_{ph}}{c} (\frac{1}{2 m})$

$= \frac{p_{e}}{c} (\frac{1}{2 m})$

$= \frac{m v}{c} \frac{1}{2 m}$

$= \frac{v}{2 c}$

Hence, the correct answer is option: 'C'.