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JEE Main 202315 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
15 April
Shift
Morning Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2023 · 15 April · Morning Shift · Physics · Dual Nature of Matter

The de Broglie wavelength of an electron having kinetic energy E is...

The de Broglie wavelength of an electron having kinetic energy EE is λ\lambda. If the kinetic energy of electron becomes E4\dfrac{E}{4}, then its de-Broglie wavelength will be:

Options

  1. A2λ\sqrt{2}\lambda
  2. Bλ2\dfrac{\lambda}{\sqrt{2}}
  3. Cλ2\dfrac{\lambda}{2}
  4. D2λ2\lambda

Correct answer

D. 2λ2\lambda

Step-by-step solution

The de-Broglie wavelength in the first case is

λ=h2mE\lambda = \dfrac{h}{\sqrt{2mE}}

In the second case the kinetic energy is K=E4K = \dfrac{E}{4}.

Let the de-Broglie wavelength be λ′\lambda '.

The value of wavelength is

λ′=h2mE4=2h2mE=2λ\lambda ' = \dfrac{h}{\sqrt{2m\dfrac{E}{4}}} = \dfrac{2h}{\sqrt{2mE}} = 2\lambda

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