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NEETPhysicsDual Nature of Matter

A photoelectric surface is illuminated by light of wavelength , producing photoelectrons with a maximum kinetic energy K . When the wavelength of the incident light is reduced to 2 , the maximum kinetic energy of the emitted photoelectrons becomes 3K . The threshold wavelength for this surface is:

Options

  1. A2
  2. B3 2
  3. C4
  4. D2

Correct answer

A. 2

Step-by-step solution

According to Einstein's photoelectric equation, the maximum kinetic energy is given by: K = hc - hc ₀ ... (i) For the second case, when the wavelength is 2 , the maximum kinetic energy is 3K : 3K = hc ( 2 ) - hc ₀ 3K = 2hc - hc ₀ ... (ii) Substituting the value of K from equation (i) into equation (ii): 3 ( hc - hc ₀ ) = 2hc - hc ₀ 3hc - 3hc ₀ = 2hc - hc ₀ Rearranging the terms, we get: 3hc - 2hc = 3hc ₀ - hc ₀ hc = 2hc ₀ ₀ = 2 Answer: 2

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