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JEE Main 202324 JanuaryEvening Shift
Exam
JEE Main
Year
2023
Date
24 January
Shift
Evening Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2023 · 24 January · Evening Shift · Physics · Dual Nature of Matter

An α particle, a proton and an electron have the same kinetic...

An α\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:

Options

  1. Aλα>λp>λe{\lambda}_{\alpha} > {\lambda}_{p} > {\lambda}_{e}
  2. Bλα<λp<λe{\lambda}_{\alpha} < {\lambda}_{p} < {\lambda}_{e}
  3. Cλα=λp=λe{\lambda}_{\alpha} = {\lambda}_{p} = {\lambda}_{e}
  4. Dλα>λp<λe{\lambda}_{\alpha} > {\lambda}_{p} < {\lambda}_{e}

Correct answer

B. λα<λp<λe{\lambda}_{\alpha} < {\lambda}_{p} < {\lambda}_{e}

Step-by-step solution

As we know, de-Broglie wavelength is given by,

λ=hp\lambda = \dfrac{h}{p}

and p=2mKp = \sqrt{2mK}

Therefore,

λ=h2mK\lambda = \dfrac{h}{\sqrt{2mK}}

As kinetic energy is the same for all particles,

∴λ∝1m∴ \lambda ∝ \dfrac{1}{\sqrt{m}}

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

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

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