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

Why is it not possible for a photon to be completely absorbed by a free electron?

Options

  1. AThe electron would need to acquire a velocity greater than the speed of light.
  2. BThe photon cannot transfer its entire energy without also transferring its rest mass.
  3. CSimultaneous conservation of both energy and linear momentum cannot be achieved.
  4. DA free electron lacks the discrete energy levels required for photon absorption.

Correct answer

C. Simultaneous conservation of both energy and linear momentum cannot be achieved.

Step-by-step solution

Assume a photon of frequency is completely absorbed by a free electron initially at rest. Let the rest mass of the electron be m₀ and its final velocity be v . By conservation of energy: h + m₀ c^2 = mc^2 By conservation of linear momentum: h c = mv h = mvc Substituting h from the momentum equation into the energy equation: mvc + m₀ c^2 = mc^2 m₀ c^2 = mc(c - v) Using the relativistic mass formula m = m₀ 1 - v^2 c^2 : m₀ c^2 = m₀ c^2 (1 - v c ) 1 - v^2 c^2 1 = 1 - v c 1 + v c Squaring both sides: 1 + v c = 1 - v c

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