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Particle physics

A-Level Physics 9702 · Topic 11 revision notes · AS

Inside the atom and beyond: the nuclear model, nuclide notation, alpha, beta and gamma radiation, decay equations, quarks, hadrons and leptons.

20 definitions to learn word for word, 12 equations in their own column, 8 diagrams and graphs. Read it, cover it, test yourself.

  1. 11.1a Alpha-particle scattering and the nuclear atom
  2. 11.1b Nuclides, isotopes and nuclear equations
  3. 11.1c Alpha, beta and gamma radiation
  4. 11.2a Quarks and hadrons
  5. 11.2b Leptons and beta decay at quark level
Definitions (mark-scheme wording)EquationsExam traps

11.1aAlpha-particle scattering and the nuclear atom

Definitions

Nucleus
the tiny, dense, positively charged centre of the atom containing almost all of its mass.
Nucleon
a proton or a neutron (a particle in the nucleus).

Key points

  • Alpha particles fired at thin gold foil in a vacuum; detector moved round to count at each angle.
  • Most pass straight through: the atom is mostly empty space.
  • A few deflect through large angles: charge is concentrated in a small positive region that repels them.
  • Very few rebound (> 90°): the nucleus is very small but contains most of the mass.
  • Nucleus diameter ~10-15 m to 10-14 m; atom diameter ~10-10 m.
  • Electrons occupy the space around the nucleus; atom is neutral overall.
nucleus (+) most: straight through few: large angle very few rebound α
Alpha scattering: the closer an alpha passes the nucleus, the larger its deflection; a head-on approach bounces back.

Watch out!

  • The few large deflections show the nucleus is small and dense; the many undeflected show empty space. Do not swap the conclusions.
  • Deflection is by electrostatic repulsion, not collision with electrons.

11.1bNuclides, isotopes and nuclear equations

Definitions

Proton number (Z)
the number of protons in the nucleus.
Nucleon number (A)
the total number of protons and neutrons in the nucleus.
Nuclide
a nucleus with a particular number of protons and a particular number of neutrons.
Isotopes
nuclei of the same element with the same number of protons but different numbers of neutrons.
Unified atomic mass unit (u)
one twelfth of the mass of an atom of carbon-12; 1 u = 1.66 × 10-27 kg.

Key points

  • Notation AZX: nucleon number on top, proton number below; neutrons N = A - Z.
  • Isotopes have the same chemistry (same electrons) but different nuclear stability.
  • In every nuclear equation, nucleon number and charge (proton number) are conserved.
  • Alpha decay: A falls by 4, Z falls by 2.
  • Beta-minus decay: A unchanged, Z rises by 1 (a neutron becomes a proton).
  • Beta-plus decay: A unchanged, Z falls by 1 (a proton becomes a neutron). Gamma: A and Z unchanged.
14 6 C nucleon number A proton number Z neutrons N = A - Z = 8
Nuclide notation for carbon-14: 6 protons, 14 nucleons, so 8 neutrons.
NZ α: Z-2, N-2 β⁻: Z+1, N-1 β⁺: Z-1, N+1
Decay on an N-Z chart: alpha moves 2 down and 2 left; beta-minus moves one neutron to a proton (down 1, right 1); beta-plus the reverse.

Watch out!

  • Beta-minus raises Z by one; the electron is written 0-1e so the charges balance.
  • Isotopes differ in neutron number, not proton number.

11.1cAlpha, beta and gamma radiation

Definitions

Alpha particle
a helium-4 nucleus: two protons and two neutrons, charge +2e.
Beta-minus particle
a fast-moving electron emitted from the nucleus, charge -e.
Beta-plus particle
a positron (the antiparticle of the electron) emitted from the nucleus, charge +e.
Gamma radiation
high-energy electromagnetic radiation (photons) emitted from the nucleus; no charge, no mass.
Antiparticle
a particle with the same mass as its partner but opposite charge (and other opposite quantum numbers).

Key points

  • Ionising power: α strongly, β moderately, γ weakly. Penetration is the reverse order.
  • Stopped by: α a sheet of paper or a few cm of air; β a few mm of aluminium; γ reduced by several cm of lead.
  • Speeds: α about 0.05c; β up to about 0.99c; γ travels at c.
  • In a field, α and β are deflected in opposite directions; γ is undeflected.
  • Alpha particles from one nuclide have discrete energies (a few MeV).
  • Beta particles have a continuous range of energies because the (anti)neutrino carries away a variable share.
source paper Al (mm) lead (cm) αβγ
Penetration: paper stops alpha, a few mm of aluminium stops beta, several cm of lead only reduces gamma.
numberenergy α: discrete numberenergy Emax β: continuous
Energy spectra: alpha particles have a single discrete energy; beta particles have a continuous range up to a maximum.

Watch out!

  • A continuous beta spectrum is the evidence for the (anti)neutrino; energy is shared between two particles.
  • Gamma emission does not change A or Z; it follows another decay that leaves the nucleus excited.

11.2aQuarks and hadrons

Definitions

Fundamental particle
a particle that is not made of other particles (e.g. quarks, leptons).
Quark
a fundamental particle that combines with others to form hadrons; six flavours: up, down, strange, charm, top, bottom.
Hadron
a particle made of quarks (baryons and mesons).
Baryon
a hadron made of three quarks (e.g. proton, neutron).
Meson
a hadron made of a quark and an antiquark.

Key points

  • Up, charm, top: charge +⅔e. Down, strange, bottom: charge -⅓e.
  • Each quark has an antiquark with the opposite charge (e.g. anti-up: -⅔e).
  • Proton = uud (charge +e); neutron = udd (charge 0).
  • Antibaryons are three antiquarks, e.g. antiproton = anti-u anti-u anti-d (charge -e).
  • Mesons: quark + antiquark, e.g. π+ = u + anti-d (charge +e).
  • Hadron charges are always whole numbers of e; quarks are never found alone.
  • Protons and neutrons are not fundamental.
charge +1e charge 0 u u d u d d proton = uud neutron = udd ⅔ + ⅔ - ⅓ = 1 ⅔ - ⅓ - ⅓ = 0
Quark content: uud gives +1e (proton); udd gives 0 (neutron). Three quarks each, so both are baryons.
uup ccharm ttop ddown sstrange bbottom +⅔e -⅓e quarks antiquarks: opposite charge
The six quark flavours and their charges; antiquarks have the opposite charge.

Watch out!

  • A meson is a quark and an antiquark, not two quarks.
  • Down quark charge is -⅓e, not -⅔e: check that uud sums to exactly +1.

11.2bLeptons and beta decay at quark level

Definitions

Lepton
a fundamental particle that is not made of quarks, e.g. the electron and the (electron) neutrino.
Neutrino
a lepton with no charge and almost zero mass, emitted in beta decay.
Weak interaction
the fundamental interaction responsible for beta decay (changing one quark flavour into another).

Key points

  • Leptons (electron, neutrino) and quarks are fundamental.
  • Beta-minus: a down quark becomes an up quark, so udd (neutron) becomes uud (proton).
  • Beta-plus: an up quark becomes a down quark, so uud (proton) becomes udd (neutron).
  • Beta-minus emits an electron and an electron antineutrino; beta-plus emits a positron and an electron neutrino.
  • Charge is conserved at quark level: -⅓ = +⅔ + (-1) + 0.
  • Beta decay is caused by the weak interaction.
d → u + e⁻ + ν̄ u d d u d u e⁻ ν̄ neutron (udd) proton (uud)
Beta-minus at quark level: one down quark (circled) becomes an up quark; the neutron becomes a proton and an electron and an antineutrino are emitted.

Watch out!

  • Match the neutrino to the decay: beta-minus with the antineutrino, beta-plus with the neutrino.
  • Electrons are leptons: they are not made of quarks and not found in the nucleus before the decay.
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