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JEE Main 20206 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Morning Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2020 · 6 September · Morning Shift · Physics · Dual Nature of Matter

An electron, a doubly ionized helium ion ( He^ ++ ) and proton are...

An electron, a doubly ionized helium ion (He++He^{++}) and proton are having the same kinetic energy. The relation between their respective de-Broglie wavelength λe∗λHe++\lambda{e}^{*}\lambda{He}^{+ +} and λp{\lambda}_{p} is :

Options

  1. Aλe>λHe++>λp\lambda_e>\lambda_{{He}^{++}}>\lambda_p
  2. Bλe<λHe++==λp\lambda_e<\lambda_{{He}^{++}}==\lambda_p
  3. Cλe>λp>λHe++\lambda_e>\lambda_p>\lambda_{{He}^{++}}
  4. Dλe<λp<λHe++\lambda_e<\lambda_p<\lambda_{{He}^{++}}

Correct answer

C. λe>λp>λHe++\lambda_e>\lambda_p>\lambda_{{He}^{++}}

Step-by-step solution

λ=hmv=h2mk\lambda=\frac{h}{m v}=\frac{h}{\sqrt{2 m k}}
λe:λp:λHe++=1me:1mp:1He++\lambda_{\mathrm{e}}: \lambda_{\mathrm{p}}: \lambda_{{He}^{++}}=\frac{1}{\sqrt{\mathrm{m}_{\mathrm{e}}}}: \frac{1}{\sqrt{\mathrm{m}_{\mathrm{p}}}}: \frac{1}{\sqrt{\mathrm{He}^{++}}}
19.1×10−31:11.6×10−27:14×1.6×10−27=84:2:1\frac{1}{\sqrt{9.1 \times 10^{-31}}}: \frac{1}{\sqrt{1.6 \times 10^{-27}}}: \frac{1}{\sqrt{4 \times 1.6 \times 10^{-27}}}=84: 2: 1
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