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NEET 2014
Exam
NEET
Year
2014
Subject
Physics
Chapter
Dual Nature of Matter

NEET 2014 · Physics · Dual Nature of Matter

If the kinetic energy of the particle is increased to 16 times its...

If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is:

Options

  1. A2525
  2. B7575
  3. C6060
  4. D5050

Correct answer

B. 7575

Step-by-step solution

KEfinal=16KEinitialK{E}_{final} = 16K{E}_{initial}

⇒12mvf2=16×12mvi2⇒ \dfrac{1}{2}m{{v}_{f}}^{2} = 16 \times \dfrac{1}{2}m{{v}_{i}}^{2}(mass remains same because the particle remains same)

⇒vf=4vi⇒ {v}_{f} = 4{v}_{i}
We know that, De-broglie wavelength (λ)=hmv( \lambda ) = \dfrac{h}{mv}

∴λf=hmvf=h4mvi∴ {\lambda}_{f} = \dfrac{h}{m{v}_{f}} = \dfrac{h}{4m{v}_{i}}

So De-Broglie wave will decreased to 7575%

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