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JEE Main 20209 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
9 January
Shift
Morning Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2020 · 9 January · Morning Shift · Physics · Dual Nature of Matter

A particle moving with kinetic energy E has de Broglie wavelength λ...

A particle moving with kinetic energy EE has de Broglie wavelength λ\lambda . If energy \DeltaE\DeltaE is added to its energy, the wavelength become λ2\dfrac{\lambda}{2} . Value of \DeltaE,\DeltaE, is:

Options

  1. AEE
  2. B4E4E
  3. C3E3E
  4. D2E2E

Correct answer

C. 3E3E

Step-by-step solution

λ=h2(KE)m⇒λ∝1KE\lambda = \dfrac{h}{\sqrt{2\left(KE\right)m}} ⇒ \lambda ∝ \dfrac{1}{\sqrt{KE}}
λλ2=KEfKEi\dfrac{\lambda}{\dfrac{\lambda}{2}} = \sqrt{\dfrac{KE{}_{f}}{K{E}_{i}}}
4KEi=KEf4K{E}_{i} = K{E}_{f}
⇒\DeltaE=4KEi−KEi=3KE=3E⇒ \DeltaE = 4K{E}_{i} - K{E}_{i} = 3KE = 3E
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