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JEE MainPhysicsDual Nature of Matter

A metallic surface is illuminated successively by monochromatic light of frequencies f and 2f . The maximum speed of the emitted photoelectrons for the incident frequency 2f is observed to be 3 times the maximum speed of the photoelectrons for the incident frequency f . The threshold frequency of the metallic surface is :

Options

  1. Af 2
  2. B7f 8
  3. C17f 8
  4. D5f 2

Correct answer

B. 7f 8

Step-by-step solution

Let the threshold frequency of the metallic surface be f₀ . According to Einstein's photoelectric equation, the maximum kinetic energy K of the emitted photoelectrons is given by K = hf - hf₀ . For incident frequency f , the maximum kinetic energy is K₁ = hf - hf₀ . For incident frequency 2f , the maximum kinetic energy is K₂ = h(2f) - hf₀ . The maximum kinetic energy is related to the maximum speed v by K = 1 2 mv^2 . Given that the ratio of maximum speeds is v₂ = 3v₁ , the ratio of their maximum kinetic energies

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