Question

A photon and an electron have equal energy $E$. ${\lambda }_{photon}/{\lambda }_{electron}$ is proportional to

• A. $\sqrt{E}$
• B. $1/\sqrt{E}$
• C. $1/E$
• D. Does not depend upon $E$

Answer 1

Answer: (B)

$1/\sqrt{E}$

As we know,

${\lambda }_{photon}=\frac{hc}{E}$ and ${\lambda }_{photon}=\frac{h}{\sqrt{2mE}}$
$\Rightarrow \frac{{\lambda }_{photon}}{{\lambda }_{electron}}=c\sqrt{\frac{2m}{E}}\Rightarrow \frac{{\lambda }_{photon}}{{\lambda }_{electron}}\propto \frac{1}{\sqrt{E}}$