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MHT CET202523 Apr 2025Morning ShiftPhysicsDual Nature of MatterActual

The energy that should be added to an electron to reduce its de-Broglie wavelength from to 2 is n times the initial energy. The value of ' n ' is

Options

  1. A4
  2. B3
  3. C2
  4. D1

Correct answer

B. 3

Step-by-step solution

The de-Broglie wavelength ₁ = corresponds to kinetic energy E₁ = h^2 2m ^2 derived from = h p and E = p^2 2m . When the wavelength decreases to ₂ = 2 , the new kinetic energy becomes E₂ = h^2 2m( /2)^2 = 4E₁ . The required energy addition is E = E₂ - E₁ = 3E₁ , yielding n = 3 since E = nE₁ . Final answer: 3

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