Question

The wavelength $\lambda_e$ of an electron and $\lambda_P$ of a photon of same energy E are related by:

• A. $\lambda_P \propto \frac{1}{\sqrt{\lambda_e}}$
• B. $\lambda_P \propto \lambda^2_e$
• C. $\lambda_P \propto \lambda_e$
• D. $\lambda_P \propto \sqrt{ \lambda_e}$

Answer 1

Answer: (B)

$\lambda_P \propto \lambda^2_e$

Answer 2

$\lambda_P = \frac{h}{p} = \frac{hc}{E}$ and $\lambda_e = \frac{h}{p} = \frac{h}{\sqrt{2mE}}$
$\Rightarrow \lambda_P \propto \lambda^2_e$