Question

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

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

Answer 1

The correct option is C $\frac{v}{2c}$

Given that,

${\lambda }_e={\lambda }_{ph}$

$\Rightarrow \frac{h}{p_e}=\frac{h}{p_{ph}}$

$\Rightarrow p_e=p_{ph}$

Now, $\frac{K.E_e}{E_{ph}}=\frac{\frac{1}{2}m{v}^2}{p_{ph}c}=\frac{\frac{1}{2}m{v}^2}{p_{e}c}$

$\Rightarrow \frac{K.E_e}{E_{ph}}=\frac{\frac{1}{2}m{v}^2}{mvc}$

$\Rightarrow \frac{K.E_e}{E_{ph}}=\frac{v}{2c}$

Hence, option $\left(C\right)$ is correct.