Question

An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is :

• A. $\bigg( \frac{E}{2m} \bigg)^{\frac{1}{2}}$
• B. $c(2mE )^{\frac{1}{2}}$
• C. $\frac{1}{c} \bigg( \frac{2m}{E} \bigg)^{\frac{1}{2}}$c
• D. $\frac{1}{c} \bigg( \frac{E}{2m} \bigg)^{\frac{1}{2}}$c

Answer 1

Answer: (D)

$\frac{1}{c} \bigg( \frac{E}{2m} \bigg)^{\frac{1}{2}}$c

Answer 2

For electron $\lambda_e = \frac{h}{\sqrt{2mE}}$
for Photon $E = pc \, \Rightarrow \, \lambda_{Ph} = \frac{hc}{E}$
$\Rightarrow \, \frac{\lambda_e}{\lambda_{Ph}} = \frac{h}{\sqrt{2mE}} \times \frac{E}{hc} = \left( \frac{E}{2m} \right)^{1/2} \frac{1}{c}$