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JEE MainPhysicsDual Nature of Matter

A metallic surface has a threshold wavelength of 5 . When it is illuminated by light of wavelength , the stopping potential is measured to be V . If the surface is then illuminated by a new light source such that the stopping potential becomes V 2 , what is the wavelength of the new incident light?

Options

  1. A2
  2. B2
  3. C5 3
  4. D5

Correct answer

C. 5 3

Step-by-step solution

According to Einstein's photoelectric equation, the maximum kinetic energy (and thus the stopping potential) is given by: eV = hc - hc ₀ Given that the threshold wavelength is ₀ = 5 , for the first incident wavelength : eV = hc - hc 5 = 4hc 5 For the second case, the stopping potential is V 2 . Let the new incident wavelength be ' . The photoelectric equation becomes: e ( V 2 ) = hc ' - hc 5 Substituting the value of eV from the first equation: 1 2 ( 4hc 5 ) = hc ' - hc 5 2hc 5 = hc ' - hc 5 hc ' = 2hc 5 + hc 5 = 3

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