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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
$\lambda_P \propto \lambda_e^2$
C
$\lambda_P \propto \lambda_e$
D
$\lambda_P \propto \sqrt{\lambda_e}$
Detailed Solution
Photon: $\lambda_P = \frac{h}{p} = \frac{hc}{E}$
Electron: $\lambda_e = \frac{h}{p} = \frac{h}{\sqrt{2mE}} \Rightarrow E = \frac{h^2}{2m\lambda_e^2}$
So $\lambda_P \propto \lambda_e^2$
Electron: $\lambda_e = \frac{h}{p} = \frac{h}{\sqrt{2mE}} \Rightarrow E = \frac{h^2}{2m\lambda_e^2}$
So $\lambda_P \propto \lambda_e^2$