Question:
A photon and an electron have equal energy E. The ratio of \(λ\)(electron) to \(λ\)(photon) is proportional to
A photon and an electron have equal energy E. The ratio of \(λ\)(electron) to \(λ\)(photon) is proportional to
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Electron: $\lambda=\frac{h}{\sqrt{2mE}}$. Photon: $\lambda=\frac{hc}{E}$.
Updated On: Oct 1, 2026
- \(1:\sqrt{E}\)
- \(\sqrt{E}:1\)
- \(1:E\)
- \(1:E^2\)
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The Correct Option is B
Solution and Explanation
Step 1: Wavelengths
\(\lambda_e=\frac{h}{\sqrt{2mE}}\) and \(\lambda_{ph}=\frac{hc}{E}\).
Step 2: Ratio
\(\frac{\lambda_e}{\lambda_{ph}}=\frac{E}{c\sqrt{2mE}}=\frac{\sqrt E}{c\sqrt{2m}}\).
Step 3: Proportion
The ratio is proportional to \(\sqrt E\), that is \(\sqrt E:1\). Option (B).
Final Answer:
The ratio is proportional to \(\sqrt E:1\), option (B). \[ \boxed{\text{(B)}} \]
\(\lambda_e=\frac{h}{\sqrt{2mE}}\) and \(\lambda_{ph}=\frac{hc}{E}\).
Step 2: Ratio
\(\frac{\lambda_e}{\lambda_{ph}}=\frac{E}{c\sqrt{2mE}}=\frac{\sqrt E}{c\sqrt{2m}}\).
Step 3: Proportion
The ratio is proportional to \(\sqrt E\), that is \(\sqrt E:1\). Option (B).
Final Answer:
The ratio is proportional to \(\sqrt E:1\), option (B). \[ \boxed{\text{(B)}} \]
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