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A high-energy photon can spontaneously convert into an electron-positron pair (pair production) provided its energy exceeds 2m_e c² ≈ 1.022 MeV; this requires a nearby nucleus to conserve momentum. Conversely, an electron and positron annihilate to produce two back-to-back 0.511 MeV gamma-ray photons (annihilation). Both processes are direct manifestations of mass-energy equivalence and the existence of antimatter. Pair production and annihilation are exploited in PET scanners, where the coincident gamma rays allow precise localization of the annihilation event.
Apply conservation of energy and momentum to pair production to show why a single photon cannot produce a pair in free space (a nucleus must recoil). Verify that annihilation gamma-ray energies follow directly from E = mc².
From your study of mass-energy equivalence and the photon model, you know that E = mc² says energy and mass are interconvertible, and that photons carry energy E = hf. Pair production is the process that makes this conversion literal: a high-energy photon vanishes and in its place two particles materialize — an electron and its antiparticle, the positron. Each has rest-mass energy m_e c² ≈ 0.511 MeV, so the photon must supply at least 2m_e c² ≈ 1.022 MeV just to create the particles at rest, with any excess appearing as kinetic energy.
Why can a single photon not produce a pair in free space? Apply conservation of energy and momentum simultaneously. A photon has E = pc (massless), while the electron-positron pair at rest has E = 2m_e c² and p = 0. You cannot satisfy both E = 2m_e c² and p = 0 with a single photon (which requires E = pc ≠ 0 if E > 0). The numbers simply do not balance — it is a kinematic impossibility, not a matter of energy being insufficient. The way out is a nucleus nearby: the nucleus can absorb recoil momentum without taking much energy (its large mass means it moves very slowly), allowing the energy and momentum ledgers to balance simultaneously. The nucleus is a silent participant that enables the reaction without being consumed.
The reverse process, annihilation, occurs when an electron and positron meet. They convert entirely into radiation — typically two photons, each carrying exactly 0.511 MeV, emitted in exactly opposite directions. The back-to-back emission follows directly from momentum conservation: in the center-of-mass frame (where the total three-momentum is zero), the final state must also have zero total momentum, which requires two photons of equal energy traveling in opposite directions. A single-photon annihilation is forbidden by the same kinematic argument as single-photon pair production. (Three-photon annihilation is allowed but occurs with much lower probability.)
These processes illustrate antimatter as a genuine physical reality, not a theoretical abstraction. Every particle has a corresponding antiparticle with the same mass but opposite charges. When matter meets antimatter, the rest mass converts entirely to photon energy — the most complete form of mass-energy conversion possible. In medicine, PET scanning (Positron Emission Tomography) exploits annihilation directly: a radioactive tracer emits positrons that immediately annihilate with nearby electrons, producing back-to-back 0.511 MeV gamma-ray pairs. Detecting both photons in coincidence locates the annihilation event in three dimensions, revealing metabolically active tissue with millimeter precision.