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
- AThe electron would need to acquire a velocity greater than the speed of light.
- BThe photon cannot transfer its entire energy without also transferring its rest mass.
- CSimultaneous conservation of both energy and linear momentum cannot be achieved.
- 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