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NEETPhysicsDual Nature of Matter

In two separate photoelectric experiments, light beams of energies 6.0 eV and 18.0 eV are incident on a metal surface having a work function of 2.0 eV . The ratio of the de Broglie wavelengths of the fastest emitted photoelectrons in the first case to that in the second case is:

Options

  1. A4 : 1
  2. B1 : 4
  3. C1 : 2
  4. D2 : 1

Correct answer

D. 2 : 1

Step-by-step solution

By Einstein's photoelectric equation, the maximum kinetic energy of emitted photoelectrons is K = E - . For the first case: K₁ = 6.0 eV - 2.0 eV = 4.0 eV For the second case: K₂ = 18.0 eV - 2.0 eV = 16.0 eV The de Broglie wavelength of an electron is related to its kinetic energy by the relation = h 2mK . This implies that 1 K . Taking the ratio of the wavelengths for the two cases: ₁ ₂ = K₂ K₁ = 16.0 4.0 = 4 = 2 Thus, the ratio ₁ : ₂ is 2 : 1 . Answer: 2 : 1

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