Fundamental Particles & Isotopes
Specification: OCR A H556 | Sections: 6.4.1–6.4.2 (core); baryon/lepton-number and strangeness conservation are enrichment | Teaching time: ~8 hours
- Use AZX notation and define isotopes; explain why some isotopes are unstable
- Classify particles as hadrons or leptons and describe the properties of each
- Describe the quark model — up, down, and strange quarks and their antiquarks
- Use conservation of charge, baryon number, lepton number, and strangeness in particle interactions
- Explain beta decay in terms of quark transformations
Isotopes & Nuclear Notation
Every element is defined by its atomic number Z — the number of protons in the nucleus. The mass number A is the total number of nucleons (protons + neutrons). These are written in the standard AZX notation:
For example, carbon-12 is written 126C — it has 6 protons and 6 neutrons. The number of neutrons N is always A − Z.
Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A). They have identical chemical properties because their electron configurations are the same, but different nuclear properties — some isotopes are stable while others are radioactive.
Common isotopes
| Isotope | Notation | Protons | Neutrons |
|---|---|---|---|
| Hydrogen-1 | 11H | 1 | 0 |
| Hydrogen-2 (deuterium) | 21H | 1 | 1 |
| Hydrogen-3 (tritium) | 31H | 1 | 2 |
| Carbon-12 | 126C | 6 | 6 |
| Carbon-14 | 146C | 6 | 8 |
| Uranium-235 | 23592U | 92 | 143 |
| Uranium-238 | 23892U | 92 | 146 |
The neutron-to-proton ratio gives a qualitative composition comparison. Many stable light nuclei have N/Z close to 1, while stable heavier nuclei generally have more neutrons than protons. These broad trends do not determine the stability or decay mode of an individual isotope; that requires verified nuclide data and a fuller nuclear model.
The relative atomic mass of an element is a weighted average of the masses of its naturally occurring isotopes, taking into account their relative abundances.
Classifying Subatomic Particles
Subatomic particles are divided into two broad categories: hadrons and leptons. This classification is based on whether particles experience the strong nuclear force.
Leptons
Leptons are fundamental particles — they are not composed of any smaller particles. They do not experience the strong nuclear force. Each lepton has a corresponding antilepton. OCR A core content requires the electron and neutrino, and their antiparticles. The muon, tau and their neutrino families in the table are enrichment; the lepton-number column is also extension material:
| Lepton | Symbol | Charge /e | Lepton number L | Antiparticle |
|---|---|---|---|---|
| Electron | e⁻ | −1 | +1 | e⁺ (positron) |
| Electron neutrino | νₑ | 0 | +1 | ν̄ₑ |
| Muon | μ⁻ | −1 | +1 | μ⁺ |
| Muon neutrino | νμ | 0 | +1 | ν̄μ |
| Tau | τ⁻ | −1 | +1 | τ⁺ |
| Tau neutrino | ντ | 0 | +1 | ν̄τ |
Hadrons
Hadrons do experience the strong nuclear force. Unlike leptons, hadrons are not fundamental — they are composed of smaller particles called quarks. Hadrons are subdivided into two groups:
- Baryons — made of three quarks (qqq). The proton and neutron are baryons. They have baryon number B = +1.
- Mesons — made of a quark–antiquark pair (qq̄). Pions (π) and kaons (K) are mesons. They have baryon number B = 0.
Every particle has a corresponding antiparticle with the same mass but opposite charge, baryon number, and lepton number. When a particle meets its antiparticle, they annihilate — their combined mass converts into photon energy. Antibaryons (like the antiproton p̄) are made of three antiquarks and have B = −1.
The Quark Model
Quarks are fundamental particles that combine to form hadrons. At A Level you need to know three types (called flavours): up, down, and strange. Each has a corresponding antiquark with opposite properties.
| Quark | Symbol | Charge /e | Strangeness S | Baryon number B |
|---|---|---|---|---|
| Up | u | +⅔ | 0 | +⅓ |
| Down | d | −⅓ | 0 | +⅓ |
| Strange | s | −⅓ | −1 | +⅓ |
| Anti-up | ū | −⅔ | 0 | −⅓ |
| Anti-down | d̄ | +⅓ | 0 | −⅓ |
| Anti-strange | s̄ | +⅓ | +1 | −⅓ |
Quark composition of familiar particles
| Particle | Type | Quark composition | Charge check | Baryon number |
|---|---|---|---|---|
| Proton (p) | Baryon | uud | +⅔ + ⅔ − ⅓ = +1 | +1 |
| Neutron (n) | Baryon | udd | +⅔ − ⅓ − ⅓ = 0 | +1 |
| π⁺ (pion plus) | Meson | ud̄ | +⅔ + ⅓ = +1 | 0 |
| π⁻ (pion minus) | Meson | ūd | −⅔ − ⅓ = −1 | 0 |
| K⁺ (kaon plus) | Meson | us̄ | +⅔ + ⅓ = +1 | 0 |
| K⁰ (kaon zero) | Meson | ds̄ | −⅓ + ⅓ = 0 | 0 |
Notice the pattern: baryons always have B = +1 (three quarks, each with B = +⅓). Mesons always have B = 0 (quark with B = +⅓ plus antiquark with B = −⅓). Antibaryons have B = −1 (three antiquarks). The only hadrons you need to know at A Level are baryons and mesons.
Conservation Laws & Beta Decay
OCR 6.4.2 requires leptons, hadrons, the u/d/s quark model, beta decays and charge-balanced quark transformations. The additional baryon/lepton-number and strangeness accounting below is optional enrichment. Core beta-minus: d → u + e⁻ + ν̄ₑ; beta-plus: u → d + e⁺ + νₑ.
In all particle interactions and decays, the following quantities are always conserved (the total before = total after):
- Charge — measured in units of the elementary charge e
- Baryon number B — baryons: +1, antibaryons: −1, everything else: 0
- Lepton number L — leptons: +1, antileptons: −1, everything else: 0
- Strangeness S — conserved in the strong interaction but can change by ±1 in the weak interaction
Beta-minus decay
In β⁻ decay, a neutron inside a nucleus converts into a proton, emitting an electron and an electron antineutrino:
At the quark level, a down quark transforms into an up quark via the weak interaction:
Beta-plus decay
In β⁺ decay, a proton converts into a neutron, emitting a positron and an electron neutrino:
At the quark level, an up quark transforms into a down quark:
Question: A nucleus of carbon-14 undergoes beta-minus decay. Write the nuclear equation and verify charge and baryon number conservation.
Question: A K⁻ meson (sū) decays into a μ⁻ and a μ antineutrino. Verify charge, lepton number, and strangeness conservation.
Students often forget that the electron antineutrino (ν̄ₑ) is emitted in β⁻ decay, and the electron neutrino (νₑ) is emitted in β⁺ decay. Without the neutrino/antineutrino, lepton number would not be conserved. Remember: the bar over the ν means it's an antiparticle with L = −1.
Quark Builder · core practice and enrichment
Select quarks to build a baryon (3 quarks) or meson (quark + antiquark). The tool checks conservation laws and identifies the particle.
Isotope Builder
Adjust the number of protons and neutrons to form isotope notation and compare the composition. This qualitative N/Z comparison cannot determine nuclear stability or decay mode.
Knowledge Check
State the quark composition of (a) a proton and (b) a neutron. Verify the charge of each using the quark charges.
- Proton: uud [1 mark]
- Neutron: udd [1 mark]
- Charge check: Proton = +⅔ + ⅔ − ⅓ = +1 ✓; Neutron = +⅔ − ⅓ − ⅓ = 0 ✓ [1 mark]
Explain the difference between a hadron and a lepton. Give one example of each.
- Hadrons experience the strong nuclear force; leptons do not [1 mark]
- Hadrons are composite (made of quarks); leptons are fundamental [1 mark]
- Example hadron: proton, neutron, pion; Example lepton: electron, muon, neutrino [1 mark]
What is an isotope? Explain why isotopes of the same element have identical chemical properties but different nuclear stability.
- Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons [1 mark]
- Chemical properties depend on electron configuration, which is the same for all isotopes of an element [1 mark]
- Nuclear stability depends on the neutron-to-proton ratio; different neutron numbers change this ratio, making some isotopes unstable [1 mark]
Exam-Style Questions
(a) A Σ⁺ baryon has a strangeness of −1 and charge +1. Deduce its quark composition. [3 marks]
(b) The Σ⁺ decays via the weak interaction into a proton and a pion (π⁰). State the quark composition of π⁰ and verify that charge and baryon number are conserved in this decay. [4 marks]
(c) Explain why strangeness is not conserved in this decay. [1 mark]
(a)
- Σ⁺ is a baryon, so three quarks [1 mark]
- Strangeness −1 means one strange quark (s) [1 mark]
- Need charge +1 with s (−⅓): remaining two quarks must give +4/3, so two up quarks: uus [1 mark]
(b)
- In this extension, π⁰ is a flavour mixture of uū and dd̄, rather than either pure pair alone [1 mark]
- Charge: before = +1 (Σ⁺); after = +1 (p) + 0 (π⁰) = +1 ✓ [1 mark]
- Baryon number: before = +1 (Σ⁺); after = +1 (p) + 0 (π⁰) = +1 ✓ [1 mark]
- The final proton has valence composition uud; either component of the neutral-pion flavour mixture has net charge 0 and baryon number 0 [1 mark]
(c)
- Strangeness changes from −1 (Σ⁺) to 0 (p + π⁰); this is allowed because the decay is via the weak interaction, which can change strangeness by ±1 [1 mark]
Sodium-22 (2211Na) undergoes beta-plus decay.
(a) Write the full nuclear equation for this decay. [2 marks]
(b) Describe what happens at the quark level during this decay. [2 marks]
(c) Verify that charge, baryon number, and lepton number are conserved. [3 marks]
(a)
- 2211Na → 2210Ne + e⁺ + νₑ [2 marks]
(b)
- An up quark in the proton converts to a down quark via the weak interaction [1 mark]
- Quark equation: u → d + e⁺ + νₑ [1 mark]
(c)
- Charge: Before = +11; After = +10 + (+1) + 0 = +11 ✓ [1 mark]
- Baryon number: Before = +22; After = +22 + 0 + 0 = +22 ✓ [1 mark]
- Lepton number: Before = 0; After = (−1) + (+1) = 0 ✓ [1 mark]
A student states: "A positron is a type of lepton with the same mass as an electron but with a positive charge."
(a) Is this statement correct? Justify your answer. [2 marks]
(b) State the lepton number of a positron. [1 mark]
(c) When a positron and an electron meet, they annihilate each other. Write an equation for this annihilation and state what is produced. [2 marks]
(a)
- Yes, the statement is correct [1 mark]
- The positron (e⁺) is the antiparticle of the electron (e⁻); it is a lepton with identical mass (0.511 MeV/c²) and opposite charge (+1e) [1 mark]
(b)
- Lepton number of positron = −1 (it is an antilepton) [1 mark]
(c)
- e⁻ + e⁺ → 2γ (two photons) [1 mark for correct equation]
- The rest mass energy of both particles is converted into photon energy (gamma rays) [1 mark]
The table shows four hypothetical particles with their quark compositions. For each, determine the charge, baryon number, and strangeness. State whether each is a baryon, meson, or neither, and show one explicit quark-charge sum.
A: uds B: ss̄ C: uuu D: ud̄
[6 marks]
| Particle | Charge | Baryon number | Strangeness | Type |
|---|---|---|---|---|
| A: uds | +⅔ − ⅓ − ⅓ = 0 | +1 | −1 | Baryon (Λ⁰) |
| B: ss̄ | −⅓ + ⅓ = 0 | 0 | −1 + 1 = 0 | Meson (η-type) |
| C: uuu | +⅔ + ⅔ + ⅔ = +2 | +1 | 0 | Baryon (Δ⁺⁺) |
| D: ud̄ | +⅔ + ⅓ = +1 | 0 | 0 | Meson (π⁺) |
Six integer mark points: [1] all four charges correct; [1] all four baryon numbers correct; [1] all four strangeness values correct; [1] A and C identified as baryons; [1] B and D identified as mesons; [1] at least one explicit quark-charge sum, e.g. uds: +⅔ − ⅓ − ⅓ = 0. Particle names are enrichment and are not required.
Topic Summary
Isotopes
Same Z, different N; A = Z + N. N/Z is a qualitative comparison, not a stability or decay-mode prediction. Nuclear stability and decay mode are not determined by the composition builder.
Particle Classification
OCR core leptons: fundamental, no strong force (electron and neutrino, with antiparticles). Other lepton families are enrichment. Hadrons: composite, strong force. Baryons (qqq, B=+1) and mesons (qq̄, B=0).
Quark Properties
u: +⅔, s=0, B=+⅓. d: −⅓, s=0, B=+⅓. s: −⅓, s=−1, B=+⅓. Antiquarks: flip all signs.
Conservation Laws
Charge, baryon number, and lepton number are always conserved. Strangeness is conserved in strong interactions but can change in weak interactions.