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

Answer 1

Answer: (C)

$\lambda_{e}=\lambda_{p h}$
$\frac{h}{p_{e}}=\frac{h}{p_{p h}}$
$\sqrt{2 m k_{e}}=\frac{E_{p h}}{c}$
$2 m k_{e}=\frac{\left(E_{p h}\right)^{2}}{c^{2}}$
$\frac{k_{e}}{E_{p h}}=\frac{E_{p h}}{c^{2}}\left(\frac{1}{2 m}\right)$
$=\frac{p_{p h}}{c}\left(\frac{1}{2 m}\right)$
$=\frac{p_{e}}{c}\left(\frac{1}{2 m}\right)$
$=\frac{m v}{c} \frac{1}{2 m}$
$=\frac{v}{2 c}$