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Concepts Of Physics MCQ Edition [Volume 2]PhysicsPhotoelectric Effect and Wave–Particle Duality

A small piece of cesium metal ( = 1.9 eV ) is positioned 20 cm away from a large metal plate, which has a charge density of 1.0 10⁻⁹ C m ⁻² on the surface facing the cesium. Monochromatic light with a wavelength of 400 nm is incident on the cesium piece. Determine the minimum and maximum kinetic energy of the photoelectrons upon reaching the large metal plate. Neglect any change in the electric field due to the prese

Options

  1. A22.6 eV and 23.8 eV
  2. B0 eV and 1.2 eV
  3. C22.6 eV and 25.7 eV
  4. D11.3 eV and 12.5 eV

Correct answer

A. 22.6 eV and 23.8 eV

Step-by-step solution

The energy of the incident photons is given by: E = hc = 1240 eV nm 400 nm = 3.1 eV According to Einstein's photoelectric equation, the maximum kinetic energy of the emitted photoelectrons is: K_ = E - = 3.1 eV - 1.9 eV = 1.2 eV The minimum kinetic energy of the emitted photoelectrons is: K_ = 0 eV For a large metal plate, the electric field just outside the surface with a local charge density is given by Gauss's law as: E_f = ₀ = 1.0 10⁻⁹ 8.85 10⁻¹² 113 V/m The potential difference between the large metal plate an

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