Discover antimatter, pair production, annihilation and conservation laws
AQA A-Level Physics 2
🔁State the properties of antiparticles for each particle
✨Describe pair production and the conditions required
💥Describe pair annihilation and calculate photon energies
⚖️Apply conservation of mass-energy (E = mc²)
🛡️State the conservation laws obeyed in particle interactions
📐Use E = hf to find photon energies in annihilation
Antiparticles
Every particle has a corresponding antiparticle with the same mass but opposite charge (and opposite quantum numbers). Antiparticles were predicted by Paul Dirac in 1928 from his relativistic quantum equation.
Particle
Symbol
Antiparticle
Symbol
Charge
Electron
e⁻
Positron
e⁺
+e
Proton
p
Antiproton
p̄
−e
Neutron
n
Antineutron
n̄
0
Neutrino
ν_e
Antineutrino
ν̄_e
0
The photon is its own antiparticle (γ = γ̄). The antineutron has the same mass and zero charge as the neutron, but opposite baryon number and quark content.
Antimatter is matter composed of antiparticles. When matter and antimatter meet, they annihilate — converting all their rest mass energy into photons.
Pair Production
Pair production occurs when a high-energy photon spontaneously converts into a particle-antiparticle pair (most commonly an electron-positron pair) in the presence of a nucleus (which absorbs recoil momentum).
Any energy above 1.02 MeV becomes kinetic energy of the produced particles. The photon must have energy ≥ 2m_e c² for pair production to occur.
Pair production conserves: charge (0 = −e + e), lepton number, baryon number, and mass-energy. A nucleus must be nearby to conserve momentum.
Pair Annihilation
Annihilation occurs when a particle meets its antiparticle. Their combined rest mass energy is converted entirely into two photons emitted in opposite directions (to conserve momentum).
e⁻ + e⁺ → γ + γ
Each photon has minimum energy: E = m_e c²
E = 9.11 × 10⁻³¹ × (3.00 × 10⁸)² = 8.19 × 10⁻¹⁴ J = 0.511 MeV
If the particles are at rest, both photons have equal energy (0.511 MeV each) and travel in exactly opposite directions. If the particles have kinetic energy, the photons have more energy than the minimum.
Two photons are produced (not one) to satisfy conservation of momentum. One photon alone could not have zero total momentum as required when a particle and antiparticle at rest annihilate.
Conservation Laws in Particle Physics
Every particle interaction must obey these conservation laws. If any is violated, the interaction cannot occur:
Check whether the following interaction is possible by applying all conservation laws: p + p̄ → π⁺ + π⁻ + γ. (Pions π have baryon number 0 and lepton number 0.)
1Charge: left = +1 + (−1) = 0; right = +1 + (−1) + 0 = 0 ✓
2Baryon number: left = 1 + (−1) = 0; right = 0 + 0 + 0 = 0 ✓
3Lepton number: all particles are non-leptons → L = 0 on both sides ✓
All conservation laws satisfied → this interaction is allowed
A photon of energy 2.50 MeV undergoes pair production. What is the kinetic energy available for the produced electron and positron? (1 MeV = 1.60 × 10⁻¹³ J)
1Rest mass energy of one electron = 0.511 MeV. Two particles = 2 × 0.511 = 1.022 MeV
3Shared between electron and positron (symmetrically if identical): each gets ~0.739 MeV
Total KE available = 1.48 MeV (to 3 s.f.)
1. What is the antiparticle of the neutron?
The antiparticle of the neutron is the antineutron. It has the same mass and zero charge, but opposite baryon number (−1) and quark composition.
2. Why are two photons produced in electron-positron annihilation rather than one?
A particle-antiparticle pair at rest has zero total momentum. A single photon cannot have zero momentum (it always carries momentum p = E/c). Two photons emitted in opposite directions have equal and opposite momenta that sum to zero — conserving momentum.
3. What is the minimum photon energy (in MeV) required for electron-positron pair production?
Minimum energy = 2 × m_e c² = 2 × 0.511 MeV = 1.02 MeV. Both particles must be created with at least their rest mass energy.
4. The baryon number of an antiproton is:
Baryons have B = +1; antibaryons have B = −1. The antiproton has B = −1.
5. Two photons are produced when a proton and antiproton annihilate at rest. Each photon has energy equal to m_p c². Calculate this energy in MeV. (m_p = 1.673 × 10⁻²⁷ kg; 1 MeV = 1.60 × 10⁻¹³ J)
1. A photon of wavelength 1.80 × 10⁻¹² m undergoes pair production. Calculate (a) the energy of the photon in joules and eV, and (b) the kinetic energy shared by the produced pair.
(a) E = hc/λ = (6.63×10⁻³⁴ × 3.00×10⁸) / 1.80×10⁻¹² = 1.105×10⁻¹³ J = 1.105×10⁻¹³ / 1.60×10⁻¹⁹ = 6.91×10⁵ eV = 0.691 MeV. (b) Rest mass energy of pair = 2 × 0.511 MeV = 1.022 MeV. But photon energy = 0.691 MeV < 1.022 MeV — this photon does NOT have enough energy for pair production! The minimum required wavelength is λ = hc/(2m_e c²) = hc/1.022 MeV = 1.22 × 10⁻¹² m. Since 1.80 pm > 1.22 pm, the photon energy is too low → pair production cannot occur.
2. Determine whether the following interaction conserves all laws: n → p + e⁻ + ν_e. Check charge, baryon number and electron lepton number.
Charge: left = 0; right = +1 + (−1) + 0 = 0 ✓. Baryon number: left = 1; right = 1 + 0 + 0 = 1 ✓. Electron lepton number: left = 0; right = 0 + 1 + (−1) = 0 — wait: e⁻ has L_e = +1, ν_e has L_e = +1. So right = 0 + 1 + 1 = 2? ✗ — WAIT. This is beta-minus decay: n → p + e⁻ + ν̄_e (antineutrino, not neutrino). L_e: left = 0; right = 0 + (+1) + (−1) = 0 ✓. The correct equation uses an antineutrino. The question as written with ν_e (neutrino) would violate lepton number: right would give 0 + 1 + 1 = 2 ≠ 0. So the interaction as stated (with ν_e) is NOT allowed — it should be ν̄_e.
3. PET (Positron Emission Tomography) scanners rely on annihilation photons. Explain why the two photons are detected at exactly 180° to each other, and suggest why this is useful in medical imaging.
When a positron emitted from a radiotracer annihilates with an electron at rest (approximately), the total momentum is approximately zero. By conservation of momentum, the two photons must travel in exactly opposite directions (180° apart) with equal energies of 0.511 MeV each. The scanner detects both photons simultaneously (coincidence detection) — the annihilation event must have occurred somewhere on the line connecting the two detectors. By computing many such lines from different detector pairs, the scanner can reconstruct a 3D image of where the positron-emitting tracer is concentrated — giving detailed functional information about metabolic activity in organs such as the brain or tumours.