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Electron and positron annihilate and produce a single photon only when :

  • A.Electron and positron are at rest
  • B.Electron is at rest
  • C.Positron is at rest
  • D.At least one particle is in a bound state

Answer: D

A single photon can be produced only when at least one particle is in a bound state.

For a free electron and positron, energy and momentum cannot both be conserved if only one photon is emitted. In the centre-of-momentum frame the total momentum is zero but the energy is at least \(2m_{e}c^{2}\); a single photon with that energy would carry momentum \(E/c \neq 0\). So free-pair annihilation gives at least two photons.

If one of the particles is bound, for example an electron bound in an atom, the nucleus or the rest of the atom can take up the recoil momentum, and one-photon annihilation becomes possible. Having one or both particles at rest does not help, since the centre-of-momentum argument still applies.

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