Question

An electron with speed $v$ and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are $E_e$ and $p_e$ and that of photon are $E_{ph}$ and $p_{ph}$ respectively. Which of the following is correct?

• A. $\frac{E_e}{E_{ph}}=\frac{2c}{v}$
• B. $\frac{E_e}{E_{ph}}=\frac{v}{2c}$
• C. $\frac{p_e}{p_{ph}}=\frac{2c}{v}$
• D. $\frac{p_e}{p_{ph}}=\frac{v}{2c}$

Answer 1

Answer: (B)

${\lambda }_e={\lambda }_{\text{photon }}$
$\frac{h}{mv}=\frac{h}{P_{\text{photon }}}$
$\Rightarrow P_{\text{photon }}=mv$
$\frac{E_c}{E_{ph}}=\frac{\frac{1}{2}m{v}^2}{\frac{hc}{\lambda }}=\frac{1}{2}\frac{mv}{P_{Ph}C}\times v=\frac{v}{2C}$