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

Placed 1 m apart, two initially neutral particles undergo a process where charge is transferred from one particle to the other. Assuming the lost electric potential energy is entirely transformed into a photon, determine the longest and the next smaller possible wavelengths of the photon.

Options

  1. A860 m , 215 m
  2. B860 m , 430 m
  3. C1720 m , 430 m
  4. D430 m , 108 m

Correct answer

A. 860 m , 215 m

Step-by-step solution

When charge is transferred between two initially neutral particles, one acquires a charge +q and the other -q . The charge must be an integer multiple of the elementary charge, so q = ne where n = 1, 2, 3, The initial electric potential energy of the system is zero. The final electric potential energy is: U_f = - 1 4 ₀ q^2 r = - n^2 e^2 4 ₀ r The lost electric potential energy is converted into a photon of wavelength . Thus, we have: U = 0 - U_f = n^2 e^2 4 ₀ r Equating this to the energy of the photon, hc : hc = n

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