The Quark Model

The quark model explains the internal structure of hadrons (protons, neutrons, pions, and many other particles). It was proposed independently by Murray Gell-Mann and George Zweig in 1964 and is a cornerstone of the Standard Model of particle physics. This lesson covers quarks, antiquarks, hadrons, baryons, mesons, and the quantum numbers used to classify particles. This is assessed in AQA section 3.2.1.

Specification mapping. This lesson develops the AQA A-Level Physics (7408) Particles and Radiation strand, specifically the sub-strand covering hadrons, baryons, mesons and the quark model (section 3.2.1.6), and the strangeness quantum number introduced in 3.2.1.7. Refer to the official AQA 7408 specification document for the authoritative wording. The lesson is sequenced after our treatments of constituents of the atom (order 0), nuclear stability (order 1), antiparticles and photons (order 2), so that the quark substructure of hadrons is introduced once students already know the constituents of the nucleus at the nucleon level.

Synoptic links. The quark model connects across the specification in three principal directions. First, to leptons and exchange particles (3.2.1.5, 3.2.1.4) — quarks and leptons together form the two fermion families of the Standard Model, and the force-mediating bosons act on both. Second, to conservation laws (3.2.1.7) — quark composition determines baryon number, charge and strangeness, all of which must be conserved across an interaction; questions on whether a proposed interaction is allowed reduce to quark-counting arguments. Third, back to nuclear physics (course 6, 3.8) — beta decay at the nucleon level is fundamentally a quark-level transformation (d → u with W⁻ emission for β⁻ decay), so the half-life and decay-mode content of the nuclear-physics course rests on this lesson. A fourth, looser link points forward to electric current and resistivity (course 5): the fractional charges of quarks were first inferred indirectly from how charge is distributed and conducted in matter, and the modern definition of the coulomb is grounded in the elementary charge e that quarks carry in multiples of ⅓.

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Quarks

Quarks are fundamental particles — they have no known internal structure. At A-Level, you need to know three flavours (types) of quark:

Quark	Symbol	Charge (e)	Baryon number (B)	Strangeness (S)
Up	u	+⅔	+⅓	0
Down	d	−⅓	+⅓	0
Strange	s	−⅓	+⅓	−1

Key Points About Quarks

• Quark charges are fractional: +⅔e or −⅓e. These are the only particles with fractional charges — all observable particles have integer charge.
• Quarks have baryon number +⅓ each (so three quarks make a baryon with baryon number +1).
• The strange quark has strangeness −1 (by convention — this is a historically assigned quantum number).
• Quarks are never observed in isolation — they are always confined within hadrons. This is called colour confinement (related to the strong force carried by gluons).

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Antiquarks

Every quark has a corresponding antiquark with the opposite charge, opposite baryon number, and opposite strangeness:

Antiquark	Symbol	Charge (e)	Baryon number (B)	Strangeness (S)
Anti-up	ū	−⅔	−⅓	0
Anti-down	d̄	+⅓	−⅓	0
Anti-strange	s̄	+⅓	−⅓	+1

Key Point: Every quantum number of an antiquark is the exact negative of the corresponding quark. So if the strange quark has strangeness −1, the anti-strange quark has strangeness +1.

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Hadrons

Hadrons are particles made of quarks. They feel the strong nuclear force. Hadrons are divided into two families:

Baryons (Three Quarks)

Baryons are made of three quarks (qqq). They have baryon number B = +1 (since each quark contributes +⅓).

Baryon	Quark composition	Charge (e)	Strangeness
Proton (p)	uud	+⅔ +⅔ −⅓ = +1	0
Neutron (n)	udd	+⅔ −⅓ −⅓ = 0	0
Sigma-plus (Σ⁺)	uus	+⅔ +⅔ −⅓ = +1	−1
Sigma-zero (Σ⁰)	uds	+⅔ −⅓ −⅓ = 0	−1
Sigma-minus (Σ⁻)	dds	−⅓ −⅓ −⅓ = −1	−1
Xi-minus (Ξ⁻)	dss	−⅓ −⅓ −⅓ = −1	−2
Omega-minus (Ω⁻)	sss	−⅓ −⅓ −⅓ = −1	−3

Antibaryons (Three Antiquarks)

Antibaryons are made of three antiquarks (q̄q̄q̄). They have baryon number B = −1.

• Antiproton (p̄): ūūd̄ — charge = −⅔ −⅔ +⅓ = −1
• Antineutron (n̄): ūd̄d̄ — charge = −⅔ +⅓ +⅓ = 0

Mesons (Quark-Antiquark Pair)

Mesons are made of one quark and one antiquark (qq̄). They have baryon number B = 0 (since +⅓ and −⅓ cancel).

Meson	Quark composition	Charge (e)	Strangeness
Pion-plus (π⁺)	ud̄	+⅔ +⅓ = +1	0
Pion-minus (π⁻)	ūd	−⅔ −⅓ = −1	0
Pion-zero (π⁰)	uū or dd̄	0	0
Kaon-plus (K⁺)	us̄	+⅔ +⅓ = +1	+1
Kaon-minus (K⁻)	ūs	−⅔ −⅓ = −1	−1
Kaon-zero (K⁰)	ds̄	−⅓ +⅓ = 0	+1
Anti-kaon-zero (K̄⁰)	d̄s	+⅓ −⅓ = 0	−1

Exam Tip: Learn the quark compositions of the proton (uud), neutron (udd), pions, and kaons. These are frequently examined. To verify the quark composition, add up the charges: for the proton, +⅔ + ⅔ + (−⅓) = +1 ✓. For the neutron, +⅔ + (−⅓) + (−⅓) = 0 ✓.

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Verifying Quark Compositions

Worked Example 1 — Verify the quark composition of the proton

The proton is stated to be uud.

• Charge: +⅔ + ⅔ + (−⅓) = +⅔ + ⅔ − ⅓ = +3/3 = +1e ✓ (proton has charge +1e)
• Baryon number: +⅓ + ⅓ + ⅓ = +1 ✓ (proton is a baryon)
• Strangeness: 0 + 0 + 0 = 0 ✓ (proton has no strangeness)

Worked Example 2 — Verify the quark composition of K⁺

The K⁺ (kaon-plus) is stated to be us̄.

• Charge: +⅔ + ⅓ = +1e ✓ (K⁺ has charge +1e)
• Baryon number: +⅓ + (−⅓) = 0 ✓ (kaons are mesons, B = 0)
• Strangeness: 0 + (+1) = +1 ✓ (K⁺ has strangeness +1)

Worked Example 3 — Determine the quark composition of a particle

A particle has charge −1e, baryon number +1, and strangeness −2. What is its quark composition?

• Baryon number +1 → it is a baryon → three quarks
• Strangeness −2 → two strange quarks (each contributing −1)
• Third quark: total charge must be −1e. Two strange quarks contribute 2 × (−⅓) = −⅔. So the third quark must have charge −1 − (−⅔) = −⅓. This is a down quark.
• Composition: dss — this is the Xi-minus (Ξ⁻) particle.

Check: Charge = −⅓ + (−⅓) + (−⅓) = −1 ✓. Baryon number = ⅓ + ⅓ + ⅓ = +1 ✓. Strangeness = 0 + (−1) + (−1) = −2 ✓.

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Classification Summary

Category	Composition	Baryon Number	Examples
Baryon	qqq	+1	Proton (uud), Neutron (udd)
Antibaryon	q̄q̄q̄	−1	Antiproton (ūūd̄)
Meson	qq̄	0	Pion (π), Kaon (K)
Lepton	Fundamental	0	Electron, Neutrino

Common Misconception: Students sometimes think mesons contain two quarks. They don't — a meson contains one quark and one antiquark. The antiquark has a bar over its symbol. The baryon number of a meson is always zero because the +⅓ from the quark and the −⅓ from the antiquark cancel.

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The Discovery of Quarks — Deep Inelastic Scattering

Evidence for quarks came from deep inelastic scattering experiments at SLAC (Stanford Linear Accelerator Center) in the late 1960s. High-energy electrons were fired at protons:

• If the proton were a uniform sphere of charge, the electrons would scatter smoothly.
• Instead, the electrons sometimes scattered through very large angles — just like Rutherford's alpha particles scattering off nuclei.
• This showed that the proton's charge is concentrated in three point-like constituents — quarks.

The parallels with Rutherford scattering are striking: in both cases, high-energy projectile scattering revealed internal structure that was previously hidden.

Worked Example 4 — Identifying a Meson from Quantum Numbers

A meson has charge +1e, strangeness 0, and baryon number 0. What is its quark composition? Could it be a pion? Could it be a kaon?

• Baryon number 0 confirms it is a meson (one quark + one antiquark, since +⅓ and −⅓ cancel).
• Strangeness 0 means no strange or anti-strange quark involved.
• Charge +1: need one quark of charge +⅔ and one antiquark of charge +⅓ (= −1/3 × (−1)). So one up quark (u, +⅔) and one anti-down quark (d̄, +⅓).

Composition: ud̄ — this is the π⁺ (pion-plus).

A K⁺ has composition us̄ and strangeness +1, so it does not match (strangeness is 0 in this question). Pion-plus is the unique meson with the stated quantum numbers.

Worked Example 5 — Distinguishing Particle from Antiparticle

Particle A has quark composition uud; particle B has composition ūūd̄. Compute the charge, baryon number, and strangeness of each. What are these particles?

Particle A (uud):

• Charge: +⅔ + ⅔ + (−⅓) = +1
• Baryon number: +⅓ + ⅓ + ⅓ = +1
• Strangeness: 0
• This is the proton.

Particle B (ūūd̄):

• Charge: −⅔ + (−⅔) + (+⅓) = −1
• Baryon number: −⅓ + (−⅓) + (−⅓) = −1
• Strangeness: 0
• This is the antiproton (p̄).

The antiproton has the same magnitude of charge as the proton but opposite sign, and opposite baryon number. Antiprotons are produced in high-energy collisions at accelerators (the first was observed at the Bevatron in Berkeley in 1955; Owen Chamberlain and Emilio Segrè received the 1959 Nobel Prize for the discovery).

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Specimen Exam Question

Specimen question modelled on the AQA paper format (9 marks).

A particle X has charge −1e, baryon number +1 and strangeness −1.

(a) Determine the quark composition of X and identify the particle. [3 marks]

(b) X is produced in a strong-interaction collision between a high-energy negative pion (π⁻) and a proton. Write a balanced interaction equation that produces X together with one other strange particle, and justify, using conservation laws, why your proposed interaction is permitted. [4 marks]

(c) X is observed to decay with a lifetime of approximately 10⁻¹⁰ s rather than 10⁻²³ s. Explain what this tells you about the decay mechanism and which conservation law is no longer respected in the decay. [2 marks]

AO Breakdown

The question is constructed against the AQA AO weighting for a 9-mark structured item: AO1 (knowledge and understanding) carries roughly 3 marks for recalling quark properties and the quantum-number table; AO2 (application) carries roughly 4 marks for working out a specific quark composition from constraints and constructing a balanced interaction; AO3 (analysis and evaluation) carries roughly 2 marks for interpreting the lifetime evidence and identifying the responsible force. Examiners look for explicit conservation arithmetic and for the named conservation law that selects between strong, electromagnetic and weak mechanisms. Generic phrases such as "it is conserved" without a numerical line earn no credit at A-Level standard.

Grade-band Model Answers

Grade C response (4–5 marks out of 9).