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

A metal plate with a work function of 2.2 eV is illuminated by a light beam having a wavelength of 400 nm . A particular electron absorbs a photon. Assuming that 10 % of the extra energy is lost to the metal during each collision, determine the maximum number of collisions the electron can undergo before it becomes unable to emerge from the metal.

Options

  1. A4
  2. B5
  3. C3
  4. D2

Correct answer

C. 3

Step-by-step solution

The energy of the incident photon is given by: E = hc Substituting hc = 1240 eV nm and = 400 nm : E = 1240 400 = 3.1 eV When the electron absorbs the photon, it gains an extra energy of 3.1 eV . During each collision, the electron loses 10 % of its energy, meaning it retains 90 % of its energy. After n collisions, the remaining energy of the electron is: E_n = E (0.9)^n For the electron to emerge from the metal, its remaining energy must be greater than the work function of the metal ( = 2.2 eV ). Thus, we require:

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