Question

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

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

Answer 1

The correct option is B $\frac{1}{\sqrt{E}}$

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