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QPages 365-366: Q12: HC Verma: Concepts of Physics - Volume 2 Photoelectric Effect and Wave-Particle Duality Pages 365-366: Q12 Solution: Show that it is not possible for a photon to be completely…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often equate the photon’s energy to the electron’s non‑relativistic kinetic energy while also setting the photon momentum equal to the electron momentum; this violates the relativistic relation $E=\sqrt{p^2c^2+m^2c^4}$ and leads to the impossible $m_0^2c^4=0$. Always apply both energy and momentum conservation with the full relativistic expressions to see the contradiction.

Show that it is not possible for a photon to be completely absorbed by a free electron.

Step-by-Step Verified Solution

**Answer:** It is not possible for a photon to be completely absorbed by a free electron. **Step-by-Step Explanation:** Consider a photon of energy EE and momentum p=E/cp = E/c colliding with a free electron at rest. Conservation of momentum: p=pep = p_e. Conservation of energy: E=Ee−m0c2=pe2c2+m02c4−m0c2E = E_e - m_0c^2 = \sqrt{p_e^2c^2 + m_0^2c^4} - m_0c^2. Substituting pe=E/cp_e = E/c: E=E2+m02c4−m0c2E = \sqrt{E^2 + m_0^2c^4} - m_0c^2. This gives m02c4=0m_0^2c^4 = 0, which is impossible. Hence, a photon cannot be completely absorbed by a free electron.

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