3.2.1.3ParticlesCore

Particles, Antiparticles and Photons

Beta decay hides a puzzle: if a neutron simply became a proton and an electron, energy and momentum wouldn’t balance — experiments showed the emitted electrons came out with a whole range of energies, not one fixed value. The fix was to propose a new, almost undetectable particle carrying away the missing energy: the $neutrino$ . It is one of a whole family of $antiparticles$ — mirror images of ordinary matter — and, alongside them, the particle of light itself, the $photon$ , which is central to how particles interact and annihilate.

40 min Video by Science Shorts 3.2.1 Particles

Particle Physics — A-level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

State that every particle has a corresponding antiparticle with the same mass but opposite charge
Describe the properties of the neutrino and antineutrino, and why they were proposed
Use the photon energy equation $E = h f$
Describe annihilation and pair production in terms of energy and momentum conservation
Calculate threshold photon energies and frequencies for pair production

Antiparticles

Every particle has a corresponding $antiparticle$ : same mass and same magnitude of any other property such as baryon or lepton number, but opposite charge (where the particle has a charge at all). The positron $e^{+}$ is the antiparticle of the electron — identical mass, but charge $+ e$ instead of $- e$ . The antiproton has the mass of a proton but charge $- e$ . Even the uncharged neutron has a distinct antineutron, distinguished by opposite baryon number rather than charge.

When a particle meets its own antiparticle, they can undergo $annihilation$ : both are destroyed and their entire rest mass–energy converts into photons. The reverse process, $pair production$ , sees a single photon convert into a particle–antiparticle pair — direct evidence that mass and energy are interchangeable, exactly as $E = m c^{2}$ predicts.

Tip — A quick way to write an antiparticle: keep the same symbol but flip the sign of the charge superscript, or add a bar — e.g. $e^{-}$ and $e^{+}$ , or $p$ and $\overset{p}{ˉ}$ .

The neutrino and antineutrino

In $β^{-}$ decay, careful measurement shows the emitted electrons have a continuous range of kinetic energies up to some maximum — not the single fixed value you’d expect if the neutron simply split into a proton and an electron. Wolfgang Pauli proposed a third, near-massless, uncharged particle emitted alongside the electron, sharing the available energy and momentum: the $antineutrino$ ( $\overset{ν}{ˉ}_{e}$ ).

The neutrino $ν_{e}$ (emitted in $β^{+}$ decay) and antineutrino $\overset{ν}{ˉ}_{e}$ (emitted in $β^{-}$ decay) have (almost) zero mass, no charge, and interact so weakly with matter that they pass through entire planets almost undetected. Their existence was inferred purely from the requirement that energy, momentum and lepton number must be conserved in beta decay — a good example of a conservation law predicting a new particle before it was ever directly observed.

Tip — Don’t confuse the neutrino with the neutron — completely different particles. The neutrino has (almost) no mass at all; the neutron has almost the same mass as a proton.

The photon model

Electromagnetic radiation can be modelled as a stream of discrete packets of energy called $photons$ . A photon has no mass, travels at the speed of light $c$ , and carries an amount of energy set only by the frequency of the radiation.

This is why high-frequency radiation (gamma rays, X-rays) is so much more energetic — and dangerous — than low-frequency radiation (radio waves) of the same intensity: each individual photon carries far more energy, even though intensity depends on the number of photons too.

E = h f = \frac{h c}{λ}

Photon energy; h = 6.63 × 10⁻³⁴ J s is the Planck constant.

1Use

E = \frac{h c}{λ}

E = \frac{6.63 \times 1 0 ^{- 34} \times 3.00 \times 1 0 ^{8}}{450 \times 1 0 ^{- 9}}

E = 4.42 \times 1 0^{- 19}

Answer

E \approx 4.42 \times 1 0^{- 19}

Annihilation and pair production

When an electron and a positron meet at rest, their combined rest mass–energy ( $2 m_{e} c^{2}$ ) converts entirely into $two$ photons travelling in opposite directions, each carrying half the total energy. Two photons (not one) are required so that momentum is conserved: the electron–positron pair had zero total momentum, and a single photon can never have zero momentum.

In $pair production$ , a single high-energy photon passing close to a nucleus converts into a particle–antiparticle pair, most commonly an electron and a positron. The nucleus is needed nearby to absorb some recoil momentum — without it, energy and momentum cannot both be conserved. The photon must carry at least the combined rest energy of the pair it creates; this minimum is the $threshold energy$ .

E_{photon} \geq 2 m_{e} c^{2} (m_{e} c^{2} = 8.19 \times 1 0^{- 14} J = 0.511 MeV)

Threshold photon energy for electron–positron pair production.

1Total energy released

= 2 m_{e} c^{2} = 2 \times 9.11 \times 1 0^{- 31} \times (3.00 \times 1 0^{8})^{2}

= 1.64 \times 1 0^{- 13}

3This splits equally between two photons: each photon has

\frac{1.64 \times 1 0 ^{- 13}}{2} = 8.2 \times 1 0^{- 14}

AnswerEach photon carries

\approx 8.2 \times 1 0^{- 14}

J (0.511 MeV).

Tip — Pair production always needs a nucleus (or another particle) nearby to take up recoil momentum — a photon travelling through empty space can never spontaneously turn into a pair on its own.

Equation recap

E = h f = \frac{h c}{λ}

Photon energy from frequency or wavelength.

E_{photon} \geq 2 m_{X} c^{2}

Threshold energy for pair production of a particle X and its antiparticle.

Common mistakes to avoid

Thinking annihilation produces just one photon.

At least two photons are needed so that momentum — not just energy — is conserved; a single photon can never carry zero net momentum.

Believing a photon can pair-produce anywhere in empty space.

A nearby nucleus (or other particle) is essential to absorb recoil momentum; pair production cannot happen in isolation.

Confusing the neutrino with the neutron because the names look similar.

The neutrino has (almost) zero mass and no charge; the neutron has a mass close to the proton’s. They are unrelated particles that happen to share a root word.

Key takeaways

Every particle has an antiparticle of equal mass but opposite charge (and opposite other properties like baryon/lepton number).
The (anti)neutrino was proposed to conserve energy, momentum and lepton number in beta decay, and has (almost) zero mass and no charge.
A photon carries energy E = hf = hc/λ and has no mass.
Annihilation converts a particle–antiparticle pair into (at least) two photons; pair production is the reverse, needing a photon energy of at least 2mc² and a nearby nucleus for momentum conservation.

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Particles, Antiparticles and Photons

neutrino

. It is one of a whole family of

antiparticles

— mirror images of ordinary matter — and, alongside them, the particle of light itself, the

photon

, which is central to how particles interact and annihilate.

40 min Video by Science Shorts 3.2.1 Particles