Question

An electron with speed υ and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are Ee and pe and that of photon are Eph and pph respectively. Which of the following is correct?

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

Answer 1

Answer: (B)

$\frac{E_e}{E_{\text{ph}}} = \frac{v}{2c}$

Answer 2

$\lambda_e = \lambda_{\text{ph}}$

$⇒$ $\frac{h}{p_e} = \frac{hc}{E_{\text{ph}}}$

$⇒$ $E_{\text{ph}} = p_e \cdot c = 2E_e \left(\frac{c}{v}\right)$

$⇒$ $\frac{E_e}{E_{\text{ph}}} = \frac{v}{2c}$
So, Option (B)