Physics • Year 12 • Module 8 • Lesson 17
Quarks and the Standard Model
Apply your understanding of quark composition, charge conservation, and the Standard Model structure to real data, comparative analysis, and prediction tasks.
1. Interpret particle data — quark composition and charge
The table below lists six hadrons detected at the Large Hadron Collider (LHC). Use the quark charge rules (u, c, t = +2/3; d, s, b = −1/3; antiquarks have opposite sign) to complete the empty columns. 10 marks
| Particle | Symbol | Quark content | Calculated total charge | Baryon (B) or Meson (M)? |
|---|---|---|---|---|
| Proton | p | uud | ||
| Neutron | n | udd | ||
| Pi-plus | π+ | u&dbar; | ||
| Pi-minus | π− | d&ubar; | ||
| Kaon-plus | K+ | u&sbar; | ||
| Lambda | Λ0 | uds |
1.1 Complete the “Calculated total charge” and “Baryon or Meson?” columns above. Show working for the K+ charge calculation. 6 marks (1 per row)
1.2 A new particle Δ++ has quark content uuu. Calculate its electric charge and state what this confirms about the up quark. 2 marks
1.3 Explain why there is no hadron with the quark content “uu” (two quarks only). 2 marks
2. Interpret data — quark mass across generations
The bar chart below shows the approximate masses of the six quarks on a log scale, grouped by generation. 7 marks
Figure 1. Approximate quark masses by flavour on a log10 scale. Data: Particle Data Group (2022). Illustrative bar heights.
2.1 Describe the trend in quark mass from Generation 1 to Generation 3 as shown by the graph. 2 marks
2.2 By approximately how many orders of magnitude does the top quark mass exceed the up quark mass? Use the graph to estimate. 2 marks
2.3 Explain why the top quark is never found inside stable hadrons such as protons or neutrons, using information from the graph. 3 marks
3. Compare the four fundamental forces
Complete the two-column table below. For each feature, write a concise description that contrasts the electromagnetic force and the weak force. 8 marks (1 per cell)
| Feature | Electromagnetic force | Weak force |
|---|---|---|
| Force carrier(s) | ||
| Mass of carrier | ||
| Range | ||
| Particles affected |
4. Predict and justify — deep inelastic scattering at SLAC
In the 1960s, physicists at the Stanford Linear Accelerator Centre (SLAC) fired high-energy electrons at protons. Instead of scattering smoothly, many electrons bounced back at large angles — more than expected if the proton were a uniform sphere of charge.
5 marks
4.1 Explain what the large-angle scattering results indicated about the internal structure of the proton. In your answer, use the word point-like. 3 marks
4.2 Predict whether a free quark was ever detected in these experiments. Justify your prediction using the concept of quark confinement. 2 marks
Q1.1 — Quark composition and charge table
Proton (uud): +2/3 + 2/3 − 1/3 = +1; Baryon. Neutron (udd): +2/3 − 1/3 − 1/3 = 0; Baryon. π+ (u&dbar;): +2/3 + 1/3 = +1; Meson. π− (d&ubar;): −1/3 + (−2/3) = −1; Meson. K+ (u&sbar;): +2/3 + 1/3 = +1 (s has charge −1/3 → &sbar; has +1/3); Meson. Λ0 (uds): +2/3 − 1/3 − 1/3 = 0; Baryon.
K+ working: q(u) = +2/3; q(&sbar;) = +1/3 (antiparticle of s, which is −1/3); total = +2/3 + 1/3 = +1.
Q1.2 — Delta-plus-plus (uuu)
Charge = 3 × (+2/3) = +2. This confirms that the up quark carries a charge of +2/3 (not a whole-number charge), because three identical up quarks produce a total charge of +2 — a result only explainable with fractional charges.
Q1.3 — Why “uu” does not exist
Hadrons must be colour-neutral. A two-quark combination (uu) cannot be colour-neutral because colour neutrality for quarks requires either three quarks carrying red, green, and blue respectively, or a quark–antiquark pair carrying a colour and its anticolour. Two quarks carry two colours that cannot sum to white.
Q2.1 — Quark mass trend
Quark mass increases significantly with each successive generation [1]. The up and down quarks of Generation 1 are the lightest (<5 MeV/c²), while the top quark of Generation 3 is the heaviest (~173,000 MeV/c²) [1].
Q2.2 — Orders of magnitude, top vs up
log10(173,000) ≈ 5.24; log10(2.2) ≈ 0.34. Difference ≈ 4.9 orders of magnitude [1] — approximately 5 orders of magnitude [1].
Q2.3 — Top quark not in stable hadrons
The top quark has a mass of ~173,000 MeV/c² [1], which means it requires an enormous amount of energy to create (equivalent to nearly the mass of a gold atom) [1]. At ordinary energies inside protons and neutrons, only the lightest quarks (u and d) exist; the top quark’s large mass means it decays via the weak force in ~5 × 10−25 s, far too fast to form a bound hadron [1].
Q3 — Electromagnetic vs weak force
Force carrier(s): EM: photon (γ); Weak: W+, W−, Z0. Mass of carrier: EM: massless (m = 0); Weak: massive (~80 GeV/c² for W, ~91 GeV/c² for Z). Range: EM: infinite; Weak: very short (~10−18 m). Particles affected: EM: all electrically charged particles; Weak: all quarks and leptons (including electrically neutral particles such as neutrinos).
Q4.1 — SLAC deep inelastic scattering
The large-angle scattering indicated that the proton contains point-like hard scattering centres rather than being a uniform, smeared-out charge distribution [1]. Just as Rutherford’s gold-foil experiment revealed a point-like nucleus, SLAC’s results revealed point-like constituents (quarks) inside the proton [1]. The high fraction of large-angle scatters was inconsistent with a “soft” proton but matched the expected signature of scattering off discrete, concentrated charges [1].
Q4.2 — Free quarks not detected
No free quark was detected [1]. Quark confinement means that when sufficient energy is injected to separate a quark from the proton, the strong force creates a new quark–antiquark pair from the energy rather than producing an isolated quark; only colour-neutral hadrons emerge from the collision [1].