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QPage 458: Q23: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 458: Q23 Solution: An electron and a positron moving at small speeds collide and…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume the electron‑positron pair can produce a single gamma ray of $2m_ec^2$, overlooking momentum conservation; in reality at least two photons are emitted (or additional photons if kinetic energy is present) to satisfy both energy and momentum.

An electron and a positron moving at small speeds collide and annihilate each other. Find the energy of the resulting gamma photon.

Step-by-Step Verified Solution

**Answer:** Energy of gamma photon = 1.02 MeV. **Step-by-Step Explanation:** Electron and positron annihilate. Total rest mass energy = 2mec2=2×0.511=1.0222m_e c^2 = 2 \times 0.511 = 1.022 MeV. This energy is carried by the gamma photon(s). For a single photon, energy = 1.022 MeV.

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