Question

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

• A. $\frac{3c}{v}$
• B. $\frac{v}{3c}$
• C. $\frac{v}{2c}$
• D. $\frac{2c}{v}$

Answer 1

Answer: (C)

${\lambda }_e={\lambda }_{ph}$
$\frac{h}{p_e}=\frac{h}{p_{ph}}$
$\sqrt{2m{k}_e}=\frac{E_{ph}}{c}$
$2m{k}_e=\frac{{\left(E_{ph}\right)}^2}{c^2}$
$\frac{k_e}{E_{ph}}=\frac{E_{ph}}{c^2}\left(\frac{1}{2m}\right)$
$=\frac{p_{ph}}{c}\left(\frac{1}{2m}\right)$
$=\frac{p_e}{c}\left(\frac{1}{2m}\right)$
$=\frac{mv}{c}\frac{1}{2m}$
$=\frac{v}{2c}$