Question

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

• A. $\sqrt{E^3}$
• B. $\frac{1}{E}$
• C. $\frac{1}{\sqrt{E}}$
• D. $DoesnotdependuponE$

Answer 1

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

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