Every particle has an antiparticle with the same mass and opposite charge. Paul Dirac's 1928 relativistic equation for the electron implied that it must have a partner, and in 1932 Carl Anderson found it, the positron, in cosmic-ray tracks. When matter meets its antimatter, both can vanish into pure energy, and energy can make new pairs. Relativistic energy and momentum decide exactly when.
🔑 Key idea
Pair production: a photon near a nucleus can become a particle–antiparticle pair if its energy is at least $$E_\gamma \ge 2mc^2\qquad(1.022\ \text{MeV for an electron–positron pair}).$$ Annihilation: an electron and a positron at rest turn into (at least) two photons of $m_ec^2 = 0.511$ MeV each, flying in opposite directions. A single photon cannot make a pair in empty space, and a pair at rest cannot make a single photon: momentum would not be conserved.
💡 Why it works
Conservation of energy says the photon must supply at least the two rest energies, $2mc^2$. Momentum is the subtle part. A photon with energy $E$ carries momentum $p = E/c$. A pair with that total momentum has energy at least $\sqrt{(pc)^2 + (2mc^2)^2}$, which is always more than $pc$. So a lone photon in empty space never has enough energy for its momentum. Near a nucleus, the nucleus absorbs some momentum (taking almost no energy, since it is heavy), and the pair can form. For annihilation at rest, the total momentum is zero; one photon always has momentum, so at least two photons must come out, back to back, sharing the energy equally.
For any momentum, the pair (red) needs more energy than a photon with that momentum has (blue). The curves never meet, so a photon can only make a pair if something else, such as a nucleus, takes up momentum.
Worked examples
✏️ Worked example: Thresholds
What is the smallest photon energy that can create an electron–positron pair? A proton–antiproton pair ($m_pc^2 = 938.3$ MeV)?
Answer: 1.022 MeV and 1.88 GeV (ignoring the small recoil energy of the nucleus)
✏️ Worked example: Sharing the leftover energy
A 2.50 MeV photon makes an electron–positron pair near a heavy nucleus. If the two share the leftover energy equally, how much kinetic energy does each get?
Rest energy used: 1.022 MeV. Left for motion: $2.50 - 1.022 = 1.478$ MeV.
Each: $1.478/2 = 0.739$ MeV.
Answer: About 0.74 MeV each
✏️ Worked example: Annihilation photons
An electron and a positron, both nearly at rest, annihilate. What is the wavelength of each photon? ($hc = 1240$ eV·nm.)
Answer: $2.43$ pm, exactly the electron's Compton wavelength $h/m_ec$; PET scanners detect these photon pairs
⚠️ Common mistake
Thinking a single photon can turn into a pair in empty space whenever it has 1.022 MeV. Energy alone is not enough: momentum must be conserved too, and a lone photon always has too much momentum for its energy. That is why pair production happens near nuclei (or electrons) that can recoil. Check with any photon energy: $\sqrt{(pc)^2 + (1.022)^2} > pc$ always.
Practice
Pass with 3 right answers, the last 2 in a row. Each right answer earns 2 XP.