JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as _______.
- A \(\lambda_{\mathrm{e}}>\lambda_\alpha>\lambda_{\mathrm{p}}\)
- B \(\lambda_\alpha<\lambda_p<\lambda_c\)
- C \(\lambda_p<\lambda_e<\lambda_a^p\)
- D \(\lambda_p>\lambda_c^p>\lambda_a\)
Answer & Solution
Correct Answer
(B) \(\lambda_\alpha<\lambda_p<\lambda_c\)
Step-by-step Solution
Detailed explanation
\(\lambda_{\mathrm{DB}}=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mk}}}\) \(\Rightarrow \lambda_{\mathrm{DB}} \alpha \frac{1}{\sqrt{\mathrm{m}}}\) \(\Rightarrow \lambda_{\mathrm{a}}<\lambda_{\mathrm{p}}<\lambda_{\mathrm{c}}\)
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