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JEE Main 20238 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
8 April
Shift
Morning Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2023 · 8 April · Morning Shift · Physics · Dual Nature of Matter

Proton ( P ) and electron ( e ) will have same de-Broglie...

Proton (P)( P ) and electron (e)( e ) will have same de-Broglie wavelength when the ratio of their momentum is (assume, mp=1849{m}_{p} = 1849 me{m}_{e})

Options

  1. A1:11: 1
  2. B1:18491: 1849
  3. C1:431: 43
  4. D43:143: 1

Correct answer

A. 1:11: 1

Step-by-step solution

The De Broglie wavelength is λ=hmv\lambda = \dfrac{h}{mv}

The momentum is given by p=mvp = mv

The momentum of proton is pp=mpvp{p}_{p} = {m}_{p}{v}_{p}

The momentum of electron is p′=mevep ' = {m}_{e}{v}_{e}

Since hh is the Planck's constant and it is given that both wavelengths are same, i.e.

λp=λe{\lambda}_{p} = {\lambda}_{e}, so pp=p′{p}_{p} = p '.

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