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

Determine the maximum magnitude of the linear momentum of a photoelectron emitted when light of wavelength 400 nm is incident on a metal having a work function of 2.5 eV .

Options

  1. A8.4 10⁻²⁵ kg m/s
  2. B9.5 10⁻²⁵ kg m/s
  3. C4.2 10⁻²⁵ kg m/s
  4. D2.1 10⁻²⁵ kg m/s

Correct answer

C. 4.2 10⁻²⁵ kg m/s

Step-by-step solution

The energy of the incident photon is given by: E = hc = 6.63 10⁻³⁴ 3 10^8 400 10⁻⁹ J = 4.97 10⁻¹⁹ J The work function of the metal in Joules is: = 2.5 eV = 2.5 1.6 10⁻¹⁹ J = 4.0 10⁻¹⁹ J Using Einstein's photoelectric equation, the maximum kinetic energy of the emitted photoelectron is: K_ max = E - = 4.97 10⁻¹⁹ J - 4.0 10⁻¹⁹ J = 0.97 10⁻¹⁹ J The maximum magnitude of the linear momentum is related to the maximum kinetic energy by: p_ max = 2 m_e K_ max Substituting the mass of an electron m_e = 9.1 10⁻³¹ kg : p_ max

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