Annihilation is the process in which a particle and its corresponding antiparticle collide and their entire mass is converted into energy in the form of gamma-ray photons, in accordance with Einstein's mass-energy equivalence:
The most common example studied at this level is electron–positron annihilation.
A positron () is the antiparticle of the electron. It has:
Positrons are produced in pair production (the reverse of annihilation) and in decay.
When an electron and a positron meet, they annihilate and produce two gamma-ray photons:
A single photon cannot be produced because it would violate the Law of Conservation of Momentum. In the centre-of-mass frame, the total momentum of the electron–positron pair is zero. A single photon always carries momentum (), so it cannot conserve zero net momentum. Two photons emitted in exactly opposite directions have momenta that cancel, satisfying conservation of momentum.
Annihilation must satisfy:
| Conservation Law | How it is satisfied |
|---|---|
| Mass-Energy | Total rest-mass energy + kinetic energy of both particles = total energy of both photons |
| Linear Momentum | Two photons travel in opposite directions; their momenta are equal and opposite |
| Charge | has charge , has charge ; total charge = 0; photons carry no charge |
If the electron and positron are both at rest, all energy comes from rest mass:
This energy is shared equally between the two photons, so each photon has energy:
This is the minimum energy each photon can have.
If the electron has kinetic energy and the positron has kinetic energy , the energy conservation equation becomes:
where is the energy of each photon (assuming equal sharing).
Worked Example:
An electron and positron, each with kinetic energy , annihilate. Find the energy of each photon.