Particles and antiparticles

Every particle type has a corresponding antiparticle. A particle and its antiparticle have the same mass and therefore the same rest energy: the energy each has because of its mass.

Their electric charges are opposite. For example, the electron has a negative charge, while its antiparticle, the positron, has an equally large positive charge. If a particle has zero electric charge, its antiparticle also has zero electric charge.

The following are particle–antiparticle pairs:

• Electron and positron
• Proton and antiproton
• Neutron and antineutron
• Neutrino and antineutrino

The neutron and antineutron are both electrically neutral, as are the neutrino and antineutrino.

Rest energy can be expressed in megaelectronvolts, written $$\mathrm{MeV}$$. The megaelectronvolt is a unit of energy.

Photon energy

Electromagnetic radiation can be modelled as a stream of photons. Each photon is a discrete packet of energy. The energy of an individual photon depends on its frequency.

Here, $$E$$ is photon energy, $$f$$ is frequency and $$h$$ is the Planck constant. Photon energy is directly proportional to frequency: doubling the frequency doubles the energy of each photon.

When $$h$$ is given in joule-seconds and $$f$$ in hertz, the calculated energy is in joules.

Photon energy and wavelength

For electromagnetic radiation in a vacuum, frequency and wavelength are related by:

Here, $$c$$ is the speed of electromagnetic radiation in a vacuum and $$\lambda$$ is its wavelength in a vacuum. Since $$f = c/\lambda$$, substituting into $$E = hf$$ gives:

Photon energy is therefore inversely proportional to wavelength: a longer-wavelength photon has lower energy. For example, doubling the wavelength in a vacuum halves the photon energy.

Particle–antiparticle annihilation

When a particle meets its corresponding antiparticle, they can annihilate: the particle and antiparticle disappear, and their energy is transferred to radiation, typically photons.

Electron–positron annihilation

An electron and its antiparticle, a positron, each have rest energy because they have mass. If both particles are at rest before annihilation, their total rest energy is transferred to the photons. For a particle of mass $$m$$, its rest energy is $$E = mc^2$$, where $$c$$ is the speed of light.

If the electron and positron also have kinetic energy, that energy contributes to the photon energy. The total energy of the photons equals the combined rest energies and kinetic energies of the two particles before annihilation.

Momentum conservation in annihilation

Momentum as well as energy must be conserved. An electron and a positron at rest have zero total momentum before annihilation, so the photons must have zero total momentum afterwards.

A single photon carries momentum, so it cannot have zero momentum on its own. At least two photons are therefore produced. If exactly two are produced, they travel in opposite directions with equal momenta, so their momenta cancel.

Pair production

A photon can be absorbed and its energy used to create a particle and its corresponding antiparticle. For example, pair production can create an electron and a positron, the electron’s antiparticle.

A particle and its antiparticle have the same rest mass. The photon must supply at least their combined rest energy. For a pair in which each particle has rest mass $$m$$, the photon energy must therefore satisfy:

Here $$E_{\gamma}$$ is the photon energy and $$c$$ is the speed of light. Energy above the combined rest energy can appear as kinetic energy of the products.

Momentum conservation in pair production

Both energy and momentum must be conserved. A photon cannot produce a particle–antiparticle pair on its own in empty space while conserving both. Pair production can occur near a nucleus because the nucleus can take up momentum and recoil.

The recoiling nucleus also gains kinetic energy. For a nucleus initially at rest, the photon therefore needs slightly more energy than the combined rest energies of the pair.