Question

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

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

Answer 1

Answer: (B)

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