Question

An electron of mass $m$ and a photon have same energy $E$. The ratio of wavelength of electron to that of photon is : ($c$ being the velocity of light)

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

Answer 1

Answer: (B)

$\lambda_{1}=\frac{ h }{\sqrt{2 mE }}$
$\lambda_{2}=\frac{ hc }{ E }$
$\frac{\lambda_{1}}{\lambda_{2}}=\frac{1}{ c }\left(\frac{ E }{2 m }\right)^{1 / 2}$