### Pair production and annihilation, notes and video tutorial

In particle physics pair production and annihilation are opposite processes converting energy to particles and the reverse, all revolving around Einstein’s famous equation E=mc^{2}

**Pair production**

In pair production a high energy photon interacts with the nucleus of an atom producing two particles. The two have to be one of each of matter and antimatter, following the rules of conservation of lepton number, momentum, energy and strangeness.

The most common pair production is of electron and positron. More massive particles can be produced but they would require exceptionally energetic/high frequency photons.

**Annihilation**

Annihilation occurs when a particle and an anti-particle meet producing two photons. (It is always two photons

since the production of only one would break the law of conservation of momentum.)

To find out what kind of photon is needed for pair production or which photons are produced in an annihilation we have to do a couple of calculations using, you guessed, E=mc^{2}

**Energy to mass**

To calculate the **minimum** **energy** required to produce the mass of an electron and a positron from E=mc^{2}

If an electron and a positron are produced then they both have a mass of 9.109

× 10^{-31} kilograms so that is a total of 1.822 x 10^{-30} kg

The **minimum** **energy** required (this does not take into account the kinetic energy of the particles produced) to do that is 1.822 x 10^{-30} x 9×10^{16}

=1.63×10^{-13} joules

##### What kind of radiation could cause this mass to be created?

The energy of a photon is from E = hf where h is Planck’s Constant

so 1.63×10^{-13} = 6.62607004 × 10^{-34} x f

giving f = 2.46 x 10^{20 }Hz which is well into the gamma ray band of the e/m spectrum

In the reverse annihilation – the calculation would be the same except that since the energy is split between two photons the energy of each would be halved and therefore the frequency would be halved but still well within the gamma band of radiation.