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JEE MainPhysicsDual Nature of Matter

A metal surface with a work function of 2 eV is illuminated by light of wavelength ₁ , yielding a maximum kinetic energy of 1 eV for the emitted photoelectrons. When the same surface is illuminated by light of wavelength ₂ , the maximum kinetic energy of the emitted photoelectrons becomes 4 eV . The ratio ₁ : ₂ is

Options

  1. A1 : 4
  2. B2 : 1
  3. C1 : 2
  4. D4 : 1

Correct answer

B. 2 : 1

Step-by-step solution

According to Einstein's photoelectric equation, the energy of the incident photon is E = K_ + . For the first wavelength ₁ : E₁ = 1 eV + 2 eV = 3 eV For the second wavelength ₂ : E₂ = 4 eV + 2 eV = 6 eV The energy of a photon is inversely proportional to its wavelength ( E = hc ), which means 1 E . Therefore, the ratio of the wavelengths is: ₁ ₂ = E₂ E₁ = 6 eV 3 eV = 2 1 The ratio ₁ : ₂ is 2 : 1 . Answer: 2 : 1

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