Question

A photon and an electron have equal energy E. The ratio of \(λ\)(electron) to \(λ\)(photon) is proportional to

• A. \(1:\sqrt{E}\)
• B. \(\sqrt{E}:1\)
• C. \(1:E\)
• D. \(1:E^2\)

Hint:

Electron: $\lambda=\frac{h}{\sqrt{2mE}}$. Photon: $\lambda=\frac{hc}{E}$.

Answer 1

The Correct Option is B

Step 1: Use momentum
$p_e=\sqrt{2mE}\propto\sqrt E$ while $p_{ph}=\frac Ec\propto E$. Since $\lambda=\frac hp$, $\frac{\lambda_e}{\lambda_{ph}}=\frac{p_{ph}}{p_e}\propto\frac{E}{\sqrt E}=\sqrt E$.

Final Answer:
Option (B). \[ \boxed{\text{(B)}} \]