JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
An \(\alpha\)-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength:
- A \(\lambda_\alpha>\lambda_{ p }>\lambda_{ e }\)
- B \(\lambda_\alpha<\lambda_{ p }<\lambda_{ e }\)
- C \(\lambda_\alpha=\lambda_{ p }=\lambda_{ e }\)
- D \(\lambda_\alpha>\lambda_{ p }<\lambda_{ e }\)
Answer & Solution
Correct Answer
(B) \(\lambda_\alpha<\lambda_{ p }<\lambda_{ e }\)
Step-by-step Solution
Detailed explanation
\(\lambda_{ D }=\frac{ h }{ p }=\frac{ h }{\sqrt{2 mK }}\) \(\therefore \lambda \propto \frac{1}{\sqrt{ m }}\) \(\because m _\alpha > m _{ p } > m _{ e }\) \(\lambda_{ e } > \lambda_{ p } > \lambda_\alpha\)
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