Particles and radiation: A-level Physics revision
From the structure of the atom to the quantum behaviour of light, this sheet covers the whole of AQA section 3.2 with worked examples, key diagrams and a quick self-check.
Work through it in three passes
Learn the particles
Start with the atom, the strong force, and the difference between hadrons and leptons.
Apply conservation laws
Use charge, baryon number, lepton number and strangeness to decide whether an interaction is allowed.
Link quantum ideas
Connect photon energy to the photoelectric effect and atomic line spectra, then check your recall.
- Use proton, neutron and electron properties and write nuclide notation.
- Explain the strong nuclear force and write alpha and beta decay equations.
- Compare particles and antiparticles, and calculate photon energies.
- Identify exchange particles and draw simple Feynman diagrams.
- Classify hadrons, baryons, mesons and leptons and apply conservation laws.
- Use the quark model for protons, neutrons, pions and kaons.
- Apply the photoelectric equation and interpret threshold frequency and work function.
- Explain excitation, ionisation and line spectra using discrete energy levels.
- Use the de Broglie equation to find the wavelength of a particle.
What is inside the atom?
A simple model of the atom has protons and neutrons in the nucleus, with electrons in orbitals outside. The table below gives the charge and mass you need to recall.
| Particle | Charge / C | Relative charge | Mass / kg | Relative mass |
|---|---|---|---|---|
| Proton | +1.60 × 10⁻¹⁹ | +1 | 1.673 × 10⁻²⁷ | 1 |
| Neutron | 0 | 0 | 1.675 × 10⁻²⁷ | 1 |
| Electron | −1.60 × 10⁻¹⁹ | −1 | 9.11 × 10⁻³¹ | ~1/1840 |
Specific charge is charge divided by mass. For a nucleus or ion it is the total charge divided by the total mass. For a proton it is about 9.58 × 10⁷ C kg⁻¹.
ᵃ𝓍 where A is the nucleon (mass) number and Z is the proton (atomic) number. Isotopes have the same Z but different A.
Worked example — specific charge of an alpha particle
An alpha particle is a helium nucleus, ⁴₂He. Calculate its specific charge.
Charge = 2 × 1.60 × 10⁻¹⁹ C = 3.20 × 10⁻¹⁹ C.
Mass ≈ 4 × 1.673 × 10⁻²⁷ kg = 6.69 × 10⁻²⁷ kg (ignore electron masses).
What holds the nucleus together?
The electrostatic force would push protons apart, so there must be an attractive strong nuclear force acting between nucleons (protons and neutrons). Its key properties are:
- Attractive from about 0.5 fm up to about 3 fm.
- Repulsive below about 0.5 fm, stopping the nucleus from collapsing.
- Negligible beyond about 3 fm.
The strong nuclear force between two nucleons.
Alpha and beta decay
Unstable nuclei decay to become more stable. The two equations you must be able to write are:
The antineutrino in β⁻ decay is needed to conserve energy and lepton number. In β⁺ decay a neutrino is emitted.
Every particle has a partner
Every particle has a corresponding antiparticle with the same mass and rest energy but opposite charge. For example, the positron is the antielectron.
Annihilation
A particle meets its antiparticle and their mass-energy becomes photons.
The minimum photon energy from electron-positron annihilation is 0.511 MeV each.
Pair production
A photon with enough energy can create a particle-antiparticle pair.
The photon must have at least E = 2 mₑc² ≈ 1.022 MeV.
A photon is a quantum of electromagnetic radiation. Its energy is linked to frequency and wavelength by:
where h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹.
Forces are mediated by exchange particles
Forces between particles are explained by the exchange of virtual particles. For AQA you need to know:
| Interaction | Acts on | Exchange particle |
|---|---|---|
| Strong nuclear | Hadrons (quarks) | Pion (between nucleons); gluon (between quarks) |
| Electromagnetic | Charged particles | Virtual photon |
| Weak nuclear | Quarks and leptons | W⁺ or W⁻ boson |
| Gravitational | Mass–energy | Graviton (not examined) |
Feynman diagrams
A Feynman diagram shows incoming particles, outgoing particles and the exchange particle. Time usually runs left to right. Below is β⁻ decay: a neutron changes to a proton and emits a W⁻ boson, which decays into an electron and an antineutrino.
β⁻ decay: n → p + e⁻ + ν̄ₑ
Hadrons, baryons, mesons and leptons
Hadrons
Particles that feel the strong interaction. They are made from quarks.
- Baryons: three quarks (qqq), e.g. proton, neutron.
- Mesons: quark-antiquark pair (qq̄), e.g. pions, kaons.
Leptons
Particles that do not feel the strong interaction. They are fundamental.
- Electron e⁻, muon μ⁻ and their neutrinos νₑ, νᵤ.
- Each has a corresponding antiparticle.
Conservation laws
In any particle interaction the following are conserved:
| Quantity | Rule |
|---|---|
| Charge | Total charge before = total charge after. |
| Baryon number | +1 for baryons, −1 for antibaryons, 0 for mesons and leptons. |
| Lepton number | Conserved separately for electron and muon families. |
| Strangeness | Conserved in strong interactions; can change by 0, ±1 in weak interactions. |
Strange particles are produced in pairs by the strong interaction and decay individually by the weak interaction. They contain a strange quark or antiquark.
Three quarks build the hadrons you need
| Quark | Symbol | Charge | Baryon number | Strangeness |
|---|---|---|---|---|
| Up | u | +2/3 | +1/3 | 0 |
| Down | d | −1/3 | +1/3 | 0 |
| Strange | s | −1/3 | +1/3 | −1 |
For antiquarks all three values are reversed.
Common hadron compositions
Baryons
Mesons
β⁻ decay is really d → u + e⁻ + ν̄ₑ. The down quark in the neutron becomes an up quark, turning the neutron into a proton.
Worked example — is this interaction allowed?
π⁻ + p → K⁰ + Λ⁰
Quark compositions: π⁻ = dū, p = uud, K⁰ = ds̄, Λ⁰ = uds.
Charge: (−1 + 1) → (0 + 0). Conserved.
Baryon number: (0 + 1) → (0 + 1). Conserved.
Strangeness: (0 + 0) → (−1 + −1) = −2. Not conserved.
Because strangeness is not conserved, this cannot be a strong interaction. It could be weak (strangeness changes by 1 per strange particle).
Light behaves as a stream of photons
When light shines on a metal surface, electrons are emitted only if each photon carries enough energy to overcome the metal’s work function φ.
The photoelectric effect. If the photon energy is below the work function, no electrons are released.
- Threshold frequency f₀: the minimum frequency for emission, where hf₀ = φ.
- Stopping potential Vₛ: the voltage needed to stop the fastest electrons; eVₛ = Eₖ(max).
- Intensity affects the number of photons per second, not the energy of each photon.
Worked example — photoelectric calculations
A metal has a work function of 2.9 eV. Light of wavelength 4.5 × 10⁻⁷ m is incident on it. Calculate the maximum kinetic energy of the emitted electrons.
Because the result is negative, the photon energy is below the work function. No photoelectrons are emitted.
Electrons occupy discrete energy levels
Electrons in an atom can only have certain energies. A photon is emitted or absorbed when an electron moves between levels.
A photon is emitted when an electron drops to a lower energy level.
Excitation is when an electron moves to a higher level without leaving the atom. Ionisation is when an electron is removed completely (to n = ∞).
Hot gases emit a line spectrum because only certain photon energies are produced. Each element has a unique pattern of lines, which is evidence for discrete energy levels.
Worked example — wavelength of an emitted photon
An electron drops from −1.5 eV to −3.4 eV. Calculate the wavelength of the emitted photon.
Particles can show wave behaviour
The photoelectric effect shows that electromagnetic waves have a particle nature. Electron diffraction shows that particles can show wave behaviour.
where mv is momentum. Higher momentum means a shorter wavelength.
Worked example — de Broglie wavelength
Calculate the de Broglie wavelength of an electron travelling at 3.0 × 10⁶ m s⁻¹.
Classify and conserve
For each particle, select the correct classification.
Mistakes to avoid
Antiparticles are not just negative
The antiproton has charge −1, but the antineutron has charge 0. Antiparticles have opposite quantum numbers, not just opposite charge.
Lepton number is family-specific
Electron lepton number and muon lepton number are conserved separately. A muon decaying to an electron must also produce a muon neutrino and an electron antineutrino.
Strangeness only applies to some particles
Only particles containing strange quarks have strangeness. It is conserved in strong interactions but can change by 0 or ±1 in weak decays.
Threshold frequency means zero kinetic energy
At the threshold frequency the emitted electrons have zero maximum kinetic energy, not zero speed on average.
Self-check
1. State the quark composition of a neutron and an antiproton.
Neutron = udd. Antiproton = ūūđ.
2. Explain why a neutrino is emitted in β⁻ decay.
It carries away lepton number (lepton number must be conserved) and shares the energy released so that the electron energy can vary.
3. Calculate the energy of a photon with wavelength 600 nm.
E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / (600 × 10⁻⁹) = 3.32 × 10⁻¹⁹ J
4. State two pieces of evidence for discrete energy levels in atoms.
Line emission spectra contain only certain wavelengths, and the photon energies match differences between energy levels.
Before the exam
- Know the charge, mass and specific charge of the proton, neutron and electron.
- Write alpha and beta decay equations and explain the role of the neutrino.
- Use E = hf = hc/λ for photons.
- Apply annihilation and pair-production energy calculations.
- Name the exchange particle for each interaction and sketch simple Feynman diagrams.
- Classify particles as hadrons, baryons, mesons or leptons.
- Use conservation of charge, baryon number, lepton number and strangeness.
- Recall quark combinations for protons, neutrons, pions and kaons.
- Apply the photoelectric equation and interpret graphs of Eₖ(max) against frequency.
- Explain excitation, ionisation and line spectra using energy levels.
- Use the de Broglie equation and explain electron diffraction.