Annihilation and Pair Production Revision Notes | A Level AQA Physics

1. Matter Meets Antimatter

Picture two identical particles hurtling towards each other — except one is made of matter and the other of antimatter. The moment they touch, both vanish completely, replaced by pure energy. That is not science fiction; it is one of the most precisely tested phenomena in physics.

This lesson covers two processes — annihilation and pair production — that sit at the heart of particle physics and demonstrate Einstein's equivalence of mass and energy. You do not need to use $E = mc^2$ in calculations for AQA, but you do need to understand the energy bookkeeping involved and be able to apply rest-energy values given in MeV.

2. Annihilation: Mass Becomes Radiation

When a particle meets its antiparticle, both are destroyed and their combined rest energy is released as electromagnetic radiation in the form of photons. The most common example at A Level is an electron ($e^-$) meeting a positron ($e^+$).

The reason two photons are produced rather than one comes down to conservation of momentum. A single photon always carries momentum, so if the electron and positron approach with equal and opposite momenta (i.e. they are effectively at rest relative to each other), a single photon cannot satisfy both conservation of energy and conservation of momentum simultaneously. Two photons emitted in opposite directions solve this neatly — their momenta cancel.

Each photon produced carries a minimum energy equal to the rest energy of one electron (or positron), which is $0.511 \text{ MeV}$. If the particles also had kinetic energy before colliding, each photon carries more than this minimum. The two photons travel in exactly opposite directions to conserve momentum.

3. Pair Production: Radiation Becomes Mass

Pair production is the inverse of annihilation in terms of energy conversion, although the photon count differs. A single photon with sufficient energy, usually near a nucleus, can convert into a particle-antiparticle pair. Again, the most common A Level example is a photon producing an electron-positron pair.

There is a critical condition: pair production cannot happen in a vacuum in isolation. The process must occur near a nucleus (or another charged particle). The nucleus absorbs some momentum, which allows both energy and momentum to be conserved simultaneously — something a lone photon converting into two particles in empty space cannot achieve on its own.

Any photon energy above the minimum threshold does not disappear — it becomes kinetic energy shared between the newly created particle and antiparticle. So if a photon carries $1.50 \text{ MeV}$ and produces an electron-positron pair, the $1.50 - 1.02 = 0.48 \text{ MeV}$ surplus becomes kinetic energy of the two particles.

4. Worked Examples: Applying the Energy Bookkeeping

AQA questions on this topic typically ask you to calculate photon energies in annihilation or the minimum photon energy for pair production. The key is treating rest energy values (given in MeV) as your currency and applying conservation of energy carefully. Here are two exam-style walkthroughs.

Worked example: Annihilation: Finding the energy of each photon produced

An electron and a positron, both effectively at rest, undergo annihilation. Calculate the energy of each photon produced. (Rest energy of electron = $0.511 \text{ MeV}$) [3 marks]

1. Electron + positron $\rightarrow$ two photons — Both particles are destroyed; all their rest energy becomes photon energy. [B1] for identifying two photons are produced.
2. $E_{\text{total}} = 0.511 + 0.511 = 1.022 \text{ MeV}$ — Each particle contributes its rest energy. Since both are at rest, there is no kinetic energy to add. [M1] for summing both rest energies.
3. $E_{\text{each photon}} = \dfrac{1.022}{2} = 0.511 \text{ MeV}$ — By symmetry (equal and opposite momenta), each photon carries half the total energy. [A1] for correct answer with unit.

Answer: Each photon has energy $0.511 \text{ MeV}$

Worked example: Pair Production: Minimum photon energy and kinetic energy surplus

A photon of energy $2.20 \text{ MeV}$ undergoes pair production near a nucleus, creating an electron-positron pair. (a) State the minimum photon energy required. (b) Calculate the total kinetic energy of the produced pair. [3 marks]

1. $E_{\text{min}} = 2 \times 0.511 = 1.022 \text{ MeV}$ — The photon must supply at least the rest energy of both particles. [B1] for stating $1.022 \text{ MeV}$ (or $2 \times 0.511 \text{ MeV}$).
2. $2.20 \text{ MeV} > 1.022 \text{ MeV}$ ✓ — The photon exceeds the threshold, so pair production can occur. The surplus becomes kinetic energy.
3. $E_{\text{KE total}} = 2.20 - 1.022 = 1.178 \text{ MeV} \approx 1.18 \text{ MeV}$ — By conservation of energy, the excess above the rest-energy threshold becomes kinetic energy shared between the electron and positron. [M1] for correct subtraction, [A1] for answer with unit.

Answer: (a) Minimum photon energy = $1.022 \text{ MeV}$. (b) Total kinetic energy of the pair = $1.18 \text{ MeV}$

5. Comparing Annihilation and Pair Production

These two processes are genuinely inverse operations of each other. Annihilation converts mass into radiation; pair production converts radiation into mass. Both are governed by the same conservation laws: energy, momentum, and charge must all be conserved in each process.

Notice that charge is conserved in both processes. In annihilation, $-e + (+e) = 0$ charge before, and photons carry no charge after. In pair production, the photon has zero charge, and the electron ($-e$) plus positron ($+e$) also sum to zero.

6. Conservation Laws: The Underlying Logic

Every interaction in particle physics must satisfy a set of conservation laws. Annihilation and pair production are no exception, and AQA questions often ask you to verify or apply these laws explicitly.

• Conservation of energy: total energy (rest energy + kinetic energy) is the same before and after the interaction
• Conservation of momentum: total momentum before equals total momentum after (this is why two photons are needed in annihilation and why a nucleus is needed in pair production)
• Conservation of charge: net charge is unchanged (both processes start and end with zero net charge for electron-positron interactions)
• Conservation of lepton number: in pair production, one lepton ($e^-$, lepton number $+1$) and one antilepton ($e^+$, lepton number $-1$) are created together, keeping the total lepton number at zero

Lepton number conservation is particularly worth noting for pair production. A photon has lepton number zero. The electron produced has lepton number $+1$ and the positron has lepton number $-1$, so the total remains zero. You cannot produce two electrons from a photon — that would violate lepton number conservation.

7. Exam Technique and Common Mistakes

This topic is relatively compact, but the marks are easy to lose through imprecise language or forgetting the factor of two. The guidance below is drawn from common patterns in AQA mark schemes.

For extended-response questions that ask you to compare annihilation and pair production, structure your answer around the direction of conversion, the number of photons involved, the energy conditions, and the conservation laws satisfied. A conclusion that explicitly states they are inverse processes of each other will typically secure the top mark band.

Together, annihilation and pair production demonstrate the AQA specification requirement that energy and mass are interconvertible, and that every particle interaction must satisfy conservation of energy, momentum, and charge — a principle that underpins the entire particle physics section of the course.

For AQA A level you should link pair production and annihilation to mass-energy equivalence, but you are not expected to use E = mc^2 in calculations in this topic. The key idea is qualitative: sufficient photon energy can be converted into rest mass and kinetic energy, usually when a photon passes close to a nucleus so momentum can be conserved.