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NEETPhysicsDual Nature of Matter

Two monochromatic light beams of photon energies 4 eV and 7 eV are incident sequentially on the same metal surface. If the ratio of the maximum speeds of the emitted photoelectrons is 1 : 2 respectively, the work function of the metal is:

Options

  1. A1 eV
  2. B8 eV
  3. C3 eV
  4. D2 eV

Correct answer

C. 3 eV

Step-by-step solution

Let the work function of the metal be . According to Einstein's photoelectric equation, the maximum kinetic energy is K_ = E - . For the two incident beams, the maximum kinetic energies are: K₁ = 4 eV - K₂ = 7 eV - The kinetic energy is proportional to the square of the maximum speed ( K v^2 ). Therefore, the ratio of their kinetic energies is: K₁ K₂ = ( v₁ v₂ )^2 = ( 1 2 )^2 = 1 4 Substituting the expressions for K₁ and K₂ : 4 - 7 - = 1 4 Cross-multiplying yields: 16 - 4 = 7 - 3 = 9 = 3 eV Answer: 3 eV

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