# Electron and positron pair production and annihilation

An electron and a positron arise from an energetic gamma photon. However during annihilation of an electron and positron, two gamma photons are released.

Is this a violation of law of conservation of energy or is the energy of the two emergent photons less than that of the photon from which the electron-positron pair arose?

• Where did you read that An electron and a positron arises from an energetic gamma photon? You might need to keep reading to the part where it says that the photon has to hit something before the pair is created otherwise momentum would not be conserved. Jun 30, 2019 at 12:18
• Yes it does hit a nucleus. Thank you for the correction Jun 30, 2019 at 12:19
• Note that number of photons after annihilation is even, mostly 2, if mutual electron + positron spins are antiparallel, or odd, mostly 3, if parallel. See also positronium Jun 30, 2019 at 13:28
• for feynman diagram see en.wikipedia.org/wiki/Pair_production#Cross_section Jul 2, 2019 at 4:33

## 2 Answers

A lone photon will never decay into an electron-positron pair. This process is kinematically not allowed because of 3-momentum conservation. You need a nucleus nearby for the process to materialize.

An electron-positron pair can scatter into 2 photons, yes. Energy and 3-momentum conservation holds here.

• What is 3 momentum conservation? Jun 30, 2019 at 12:23
• @Orion73 The spatial part of 4-momentum. Aka just momentum, the zeroth part of 4-momentum being energy. Jun 30, 2019 at 13:03

You can't have a violation of the 1st Law of Thermodynamics (mass/energy can neither be created nor destroyed), it is an inviolable law. Gamma wavelengths cover a wide band of the electromagnetic spectrum; there are soft gamma rays through to hard gamma rays. You hit on the answer yourself. An electron-positron pair could not, during annihilation, give rise to a pair of gamma photons with a higher combined energy than the one which gave birth to the electron-positron pair in the first place.

• PS a cosmic ray nucleus can materialise a photon which would not normally be energetic enough to produce an electron/positron pair,but that is because from the cosmic ray's point of view the weak photon is blue shifted into gamma wavelength and can therefore be materialised. The cosmic ray loses a little energy in the process,so the 1st Law is not violated.. Jun 30, 2019 at 12:32