Question

The de Brogue wavelengths for an electron and a photon are $\lambda_{e}$ and $\lambda_{p}$ respectively. For the same kinetic energy of electron and photon. which of the following presents the correct relation between the de Brogue wavelengths of two ?

• A. $\lambda_{ p } \propto \lambda_{ e }^{2}$
• B. $\lambda_{p} \propto \lambda_{e}$
• C. $\lambda_{p} \propto \sqrt{\lambda_{e}}$
• D. $\lambda_{p} \propto \sqrt{\frac{1}{\lambda_{e}}}$

Answer 1

Answer: (A)

$\lambda_{ e }=\frac{ h }{\sqrt{2 mk }}$
Also for photon $k =\frac{ hc }{\lambda_{ p }}$
$\lambda_{ e }=\frac{ h \sqrt{\lambda_{ p }}}{\sqrt{2 mhc }} $
$\lambda_{ p } \propto \lambda e ^{2}$