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JEE MainPhysicsDual Nature of Matter

A metallic surface of work function is illuminated by light of wavelength . The minimum de Broglie wavelength of the emitted photoelectrons is _d . When the wavelength of the incident light is decreased to 2 , the minimum de Broglie wavelength of the emitted photoelectrons becomes _d 3 . The value of the initial incident wavelength is :

Options

  1. Ahc 2
  2. B17hc 8
  3. C7hc 8
  4. D5hc 2

Correct answer

C. 7hc 8

Step-by-step solution

The minimum de Broglie wavelength _d of the emitted photoelectrons corresponds to the maximum kinetic energy K , given by the relation: _d = h 2mK K = h^2 2m _d^2 Thus, the maximum kinetic energy is inversely proportional to the square of the minimum de Broglie wavelength ( K 1 _d^2 ). When the minimum de Broglie wavelength becomes _d 3 , the new maximum kinetic energy K₂ is: K₂ = h^2 2m( _d/3)^2 = 9 ( h^2 2m _d^2 ) = 9K₁ Using Einstein's photoelectric equation for the two cases: K₁ = hc - K₂ = hc /2 - = 2hc - Subs

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