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JEE Main 202125 JulyMorning Shift
Exam
JEE Main
Year
2021
Date
25 July
Shift
Morning Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2021 · 25 July · Morning Shift · Physics · Dual Nature of Matter

What should be the order of arrangement of de-Broglie wavelength of...

What should be the order of arrangement of de-Broglie wavelength of electron (λe)\left({\lambda}_{e}\right), an α\alpha-particle \left({\lambda}_{\alpha}\right)andproton(λp)and proton \left({\lambda}_{p}\right) given that all have the same kinetic energy ?

Options

  1. Aλe=λp=λα{\lambda}_{e} = {\lambda}_{p} = {\lambda}_{\alpha}
  2. Bλe<λp<λα{\lambda}_{e} < {\lambda}_{p} < {\lambda}_{\alpha}
  3. Cλe>λp>λα{\lambda}_{e} > {\lambda}_{p} > {\lambda}_{\alpha}
  4. Dλe=λp>λα{\lambda}_{e} = {\lambda}_{p} > {\lambda}_{\alpha}

Correct answer

C. λe>λp>λα{\lambda}_{e} > {\lambda}_{p} > {\lambda}_{\alpha}

Step-by-step solution

λ=hp=h2mE∝1m\lambda = \dfrac{h}{p} = \dfrac{h}{\sqrt{2mE}} ∝ \dfrac{1}{\sqrt{m}}

mα>mp>me{m}_{\alpha} > {m}_{p} > {m}_{e}

so λe>λp>λα{\lambda}_{e} > {\lambda}_{p} > {\lambda}_{\alpha}

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