A Level Physics 9702 · AS Level · Topic 11 · ~7 min read
Particle physics
What α-particle scattering tells us about the nucleus, nuclide notation and isotopes, α, β⁻, β⁺ and γ radiation, antiparticles and neutrinos, decay equations, and quarks, hadrons and leptons with the quark changes in β decay.
α-particle scatteringNuclear modelNucleon & proton numberIsotopesα, β⁻, β⁺, γAntiparticlesNeutrinosDecay equations
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In 30 seconds
- α-particle scattering showed that an atom's positive charge and almost all its mass are concentrated in a tiny nucleus.
- Nuclide notation AZX: A = nucleon number (protons + neutrons), Z = proton number. Isotopes have the same Z but different numbers of neutrons.
- In every nuclear process nucleon number and charge are conserved.
- β⁻ decay emits an electron and an electron antineutrino (a neutron becomes a proton: d → u). β⁺ decay emits a positron and an electron neutrino (u → d).
- Quarks (up, down, strange, charm, top, bottom) are fundamental. Baryons are three quarks; mesons are a quark and an antiquark. Electrons and neutrinos are leptons, also fundamental.
By the end you can
- Infer the size and nature of the nucleus from α-particle scattering.
- Use nuclide notation and the terms nucleon number, proton number and isotope.
- Describe α, β⁻, β⁺ and γ radiation and write balanced decay equations.
- Explain antiparticles, and why β-particles have a continuous energy spectrum.
- Describe protons and neutrons in terms of quarks and the quark changes in β decay.
1The nuclear atom
α-particle scattering
| Observation | Inference |
|---|---|
| Most α-particles pass straight through the gold foil | most of the atom is empty space |
| A few are deflected through small angles | there is a concentration of positive charge that repels them |
| A very small fraction (about 1 in 8000) are deflected by more than 90° | the positive charge and most of the mass are concentrated in a very small, dense nucleus |
- The simple nuclear model: a tiny nucleus (diameter about 10⁻¹⁵ to 10⁻¹⁴ m) of protons and neutrons, surrounded by orbital electrons (atom diameter about 10⁻¹⁰ m).
Nuclides and isotopes
Nucleon number (A) — the total number of protons and neutrons in a nucleus.
Proton number (Z) — the number of protons in a nucleus.
Isotopes — nuclides of the same element (same proton number) with different numbers of neutrons.
- Example: 5626Fe has 26 protons and 56 − 26 = 30 neutrons; a neutral atom also has 26 electrons.
- Unified atomic mass unit: 1 u = 1.66 × 10⁻²⁷ kg (one-twelfth of the mass of a carbon-12 atom). A proton or neutron is about 1 u.
Common mistakePutting the nucleon and proton numbers the wrong way round, or writing the neutron number as the nucleon number. Both were 2024 Paper 2 errors.
2Radiation and decay
α, β and γ
| Radiation | Composition | Charge | Mass | Typical speed |
|---|---|---|---|---|
| α | helium nucleus, 2 protons + 2 neutrons | +2e | 4 u | about 0.05c |
| β⁻ | electron | −e | 1/1840 u | up to about 0.99c |
| β⁺ | positron (antielectron) | +e | 1/1840 u | up to about 0.99c |
| γ | electromagnetic radiation (photon) | 0 | 0 | c |
Antiparticle — a particle with the same mass as its corresponding particle but opposite charge (and other opposite quantum numbers). The positron is the antiparticle of the electron.
Decay equations
- Balance both rows: the top numbers (nucleon number) and the bottom numbers (charge/proton number) must add up on each side.
23892U → 23490Th + 42α
α decay: A − 4, Z − 2146C → 147N + 0−1e + ν̄
β⁻ decay: A unchanged, Z + 1, an electron antineutrino is emitted²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + ν
β⁺ decay: A unchanged, Z − 1, an electron neutrino is emitted- γ emission changes neither A nor Z; the nucleus loses energy (often just after α or β decay).
Energy spectra
- α-particles from one nuclide have discrete (fixed) energies, because the decay produces only two products, which share the energy in a fixed way.
- β-particles have a continuous range of energies, because a third particle (the antineutrino or neutrino) is emitted and shares the released energy in varying proportions.
Common mistakeDescribing β energies as discrete, or describing the continuous spectrum without saying that another particle (the (anti)neutrino) must be emitted. Both lost marks in 2024 Paper 2.
3Fundamental particles
Quarks
| Quark | Symbol | Charge |
|---|---|---|
| up | u | +⅔e |
| down | d | −⅓e |
| strange | s | −⅓e |
| charm | c | +⅔e |
| top | t | +⅔e |
| bottom | b | −⅓e |
- Antiquarks (ū, d̄, …) have the opposite charge: ū is −⅔e, d̄ is +⅓e.
- Hadrons are made of quarks: a baryon has three quarks (proton uud, neutron udd); a meson has a quark and an antiquark (e.g. π⁺ = ud̄, charge +⅔ + ⅓ = +1).
- Leptons are fundamental and are not made of quarks: electrons, positrons and neutrinos.
Quark changes in β decay
- β⁻: a neutron becomes a proton: udd → uud, so one d quark changes to a u quark: d → u + e⁻ + ν̄.
- β⁺: a proton becomes a neutron: uud → udd, so one u quark changes to a d quark: u → d + e⁺ + ν.
- Check the charge: d (−⅓) → u (+⅔) + e⁻ (−1) + ν̄ (0): −⅓ = +⅔ − 1 ✓.
Common mistakeSwapping β⁺ and β⁻ (2024 Paper 1). β⁻: neutron → proton, electron and antineutrino. β⁺: proton → neutron, positron and neutrino.
Linking questionMass–energy and binding energy explain why nuclei decay in Nuclear physics; positrons annihilate with electrons in PET scanning in Medical physics; and charge quantisation links to Electricity.
Test yourself — cover the answers first
Quick check
- State one conclusion from the fact that most α-particles pass straight through gold foil.
- How many neutrons are in 23592U?
- Which particle is emitted with the electron in β⁻ decay?
- What is the quark composition of a neutron?
- What is the charge of a meson made of s and ū?
Exam-style
- Polonium-210 (Z = 84) emits an α-particle. Write the decay equation and name the daughter's proton number.
- Explain why the energy of β-particles from a sample is continuous, while α-particles have discrete energies.
- A particle consists of an up quark and an anti-down quark. State whether it is a baryon or meson and find its charge.
Show answers
- most of the atom is empty space
- 143
- an electron antineutrino
- udd
- −⅓ − ⅔ = −1 (e)
- 21084Po → 20682Pb + 42α; Z = 82
- β decay produces three particles (daughter, β, (anti)neutrino) sharing the energy in variable proportions; α decay has two products with fixed shares
- meson; +⅔ + ⅓ = +1e
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