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MHT CET202520 Apr 2025Evening ShiftPhysicsDual Nature of MatterActual

A light of wavelength is incident on a photosensitive surface of negligible work function. The photoelectrons emitted from the surface have de-Broglie wavelength ₁ . Then ratio : ₁^2 is ( h = Planck's constant, c = velocity of light, m = mass of electron)

Options

  1. A4 mc : h
  2. B2 c: h
  3. C2 mc : h
  4. D2 mh : c

Correct answer

C. 2 mc : h

Step-by-step solution

The incident photon energy E = hc becomes the photoelectron's kinetic energy since the work function is negligible, so KE = hc . The photoelectron's kinetic energy also equals p^2 2m where p is its momentum. Equating these expressions: hc = p^2 2m Using the de Broglie relation ₁ = h p , we substitute p = h ₁ into the energy equation: hc = (h/ ₁)^2 2m = h^2 2m ₁^2 Solving for the ratio : ₁^2 : ₁^2 = 2mc h Thus : ₁^2 = 2mc : h , matching option C .

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