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NEETPhysicsDual Nature of Matter

Light of wavelength is incident on a metal surface having a threshold wavelength ₀ (where < ₀ ). The de-Broglie wavelength _d of the emitted photoelectrons with maximum kinetic energy is given by:

Options

  1. Ah ₀ 2mc( ₀ + )
  2. Bh ₀ 2mc( ₀ - )
  3. Ch ₀ 2mc( ₀ - )
  4. Dhc ₀ 2m( ₀ - )

Correct answer

C. h ₀ 2mc( ₀ - )

Step-by-step solution

According to Einstein's photoelectric equation, the maximum kinetic energy K_ max of the emitted photoelectrons is: K_ max = hc - hc ₀ K_ max = hc ( ₀ - ₀ ) The de-Broglie wavelength of an electron with kinetic energy K_ max is given by: _d = h 2m K_ max Substituting the expression for K_ max into the de-Broglie wavelength formula: _d = h 2m [ hc( ₀ - ) ₀ ] _d = h^2 ₀ 2mhc( ₀ - ) _d = h ₀ 2mc( ₀ - ) Answer: h ₀ 2mc( ₀ - )

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