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JEE Main 20249 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Morning Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2024 · 9 April · Morning Shift · Physics · Dual Nature of Matter

A proton, an electron and an alpha particle have the same energies....

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :

Options

  1. Aλα<λp<λe\lambda_\alpha < \lambda_{\mathrm{p}} < \lambda_{\mathrm{e}}
  2. Bλe>λα>λp\lambda_{\mathrm{e}}>\lambda_\alpha>\lambda_{\mathrm{p}}
  3. Cλp>λe>λα\lambda_{\mathrm{p}}>\lambda_{\mathrm{e}}>\lambda_\alpha
  4. Dλp<λe<λα\lambda_{\mathrm{p}} < \lambda_{\mathrm{e}} < \lambda_\alpha

Correct answer

A. λα<λp<λe\lambda_\alpha < \lambda_{\mathrm{p}} < \lambda_{\mathrm{e}}

Step-by-step solution

λDB=hp=h2mk⇒λDBα1m⇒λa<λp<λe\begin{aligned} & \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{e}}\end{aligned}
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