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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. The surface of the plate facing the cesium piece carries a charge density of 1.0 10⁻⁹ C m ⁻² . Monochromatic light with a wavelength of 400 nm illuminates the cesium piece. Considering the fastest electron emitted parallel to the large metal plate, determine its displacement parallel to its initial velocity right before it h

Options

  1. A9.2 cm
  2. B4.6 cm
  3. C13.0 cm
  4. D14.8 cm

Correct answer

A. 9.2 cm

Step-by-step solution

The energy of the incident photon is given by: E = hc = 1240 eV nm 400 nm = 3.1 eV Using Einstein's photoelectric equation, the maximum kinetic energy of the emitted electron is: K_ = E - = 3.1 eV - 1.9 eV = 1.2 eV The fastest electron emitted parallel to the plate has its entire kinetic energy in the direction parallel to the plate. Its initial velocity v is: v = 2 K_ m For a large metal plate, the electric field just outside the surface carrying a local surface charge density is given by Gauss's law as: E_ field

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