A photon and an electron have equal energy $E$. $\lambda_{\mathrm{photon}} / \lambda_{\mathrm{electron}}$ is proportional to
Show Hint
- $\sqrt{E}$
- $\frac{1}{\sqrt{E}}$
- $\frac{1}{E}$
- does not depend upon $E$
The Correct Option is B
Solution and Explanation
For photon, $\lambda_p = \frac{hc}{E}$. For electron, $\lambda_e = \frac{h}{\sqrt{2mE}}$.
Step 2: Detailed Explanation:
Ratio $\frac{\lambda_p}{\lambda_e} = \frac{hc/E}{h/\sqrt{2mE}} = c\sqrt{\frac{2m}{E}} \propto \frac{1}{\sqrt{E}}$.
Step 3: Final Answer:
The ratio is proportional to $\frac{1}{\sqrt{E}}$.
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