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JEE Main 202225 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
25 June
Shift
Evening Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2022 · 25 June · Evening Shift · Physics · Dual Nature of Matter

A proton, a neutron, an electron and an α -particle have same...

A proton, a neutron, an electron and an α\alpha-particle have same energy. If λp,λn,λe{\lambda}_{p}, {\lambda}_{n}, {\lambda}_{e} and λα{\lambda}_{\alpha} are the de Broglie's wavelengths of proton, neutron, electron and α\alpha particle respectively, then choose the correct relation from the following

Options

  1. Aλp=λn>λe>λα{\lambda}_{p} = {\lambda}_{n} > {\lambda}_{e} > {\lambda}_{\alpha}
  2. Bλa<λn<λp<λe{\lambda}_{a} < {\lambda}_{n} < {\lambda}_{p} < {\lambda}_{e}
  3. Cλeλα{\lambda}_{e} {\lambda}_{\alpha}
  4. Dλe=λp=λn=λα{\lambda}_{e} = {\lambda}_{p} = {\lambda}_{n} = {\lambda}_{\alpha}.

Correct answer

B. λa<λn<λp<λe{\lambda}_{a} < {\lambda}_{n} < {\lambda}_{p} < {\lambda}_{e}

Step-by-step solution

The de-Broglie wavelength λ=h2m(K.E.)\lambda = \dfrac{h}{\sqrt{2m ( K . E . )}}

where, hh and K.E.K . E . are constant

λ∝1m\lambda ∝ \dfrac{1}{\sqrt{m}}

m=m = Mass of the particle

Thus, with increasing mass of particle de-Broglie wavelength decreases.

Order of mass me<mp<mn<mα{m}_{e} < {m}_{p} < {m}_{n} < {m}_{\alpha}

Order of de-Broglie wavelength is λa<λn<λp<λe{\lambda}_{a} < {\lambda}_{n} < {\lambda}_{p} < {\lambda}_{e}

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