Fundamental Particles – Quarks, Leptons & Their Charges (Cambridge AS & A Level Physics 9702)
What you must know for 11.2 Fundamental particles
- There are two families of elementary particles:
- Quarks – six flavours (up, down, charm, strange, top, bottom).
- Leptons – electron (e⁻), muon (μ⁻), tau (τ⁻) and their associated neutrinos (νₑ, νμ, ντ).
- Each quark carries an electric charge of either + ⅔ e or – ⅓ e; the corresponding antiquark has the opposite sign.
- Quarks combine to form baryons (three quarks) or mesons (a quark + antiquark). The total charge of any hadron is the algebraic sum of the charges of its constituents.
- Only the electric charge of each (anti)quark is required for this objective; colour, spin and mass are optional and are mentioned only briefly.
1. The elementary charge
The symbol e denotes the magnitude of the elementary charge, e ≈ 1.60 × 10⁻¹⁹ C. All charges in the tables below are expressed as multiples of e.
2. Quark flavours and their electric charges
| Quark flavour | Symbol | Electric charge |
|---|
| Up | u | + ⅔ e |
| Down | d | – ⅓ e |
| Charm | c | + ⅔ e |
| Strange | s | – ⅓ e |
| Top | t | + ⅔ e |
| Bottom | b | – ⅓ e |
3. Corresponding antiquarks (opposite charge)
In the tables below the over‑bar denotes an antiquark, e.g. \(\bar{u}\) is the anti‑up quark.
| Antiquark flavour | Symbol | Electric charge |
|---|
| Anti‑up | \(\bar{u}\) | – ⅔ e |
| Anti‑down | \(\bar{d}\) | + ⅓ e |
| Anti‑charm | \(\bar{c}\) | – ⅔ e |
| Anti‑strange | \(\bar{s}\) | + ⅓ e |
| Anti‑top | \(\bar{t}\) | – ⅔ e |
| Anti‑bottom | \(\bar{b}\) | + ⅓ e |
4. Leptons (for completeness)
| Lepton | Symbol | Electric charge |
|---|
| Electron | e⁻ | – e |
| Electron neutrino | νₑ | 0 |
| Muon | μ⁻ | – e |
| Muon neutrino | ν_μ | 0 |
| Tau | τ⁻ | – e |
| Tau neutrino | ν_τ | 0 |
5. Baryons vs. mesons (colour‑neutrality note)
- Baryons are made of three quarks (e.g. uud). The three colours (red, green, blue) combine to give a colour‑neutral particle.
- Mesons are made of a quark + antiquark pair (e.g. u\(\bar{d}\)). The colour of the quark is cancelled by the corresponding anticolour of the antiquark, also producing a colour‑neutral state.
- These colour‑neutrality statements are not examined for this objective but help avoid the misconception that isolated quarks can exist.
6. Quark composition of the most common hadrons
- Proton = u u d
- Neutron = u d d
- Pion family
- π⁺ = u \(\bar{d}\)
- π⁻ = d \(\bar{u}\)
- π⁰ = \(\frac{1}{\sqrt{2}}\)( u \(\bar{u}\) + d \(\bar{d}\) ) – a quantum‑mechanical superposition of the two neutral combinations.
7. Charge‑conservation example: β⁻‑decay at quark level
In β⁻‑decay a down quark inside a neutron changes into an up quark, emitting a W⁻ boson which subsequently decays into an electron and an anti‑neutrino:
\[
d \;\longrightarrow\; u \;+\; W^{-}
\qquad
W^{-}\;\longrightarrow\; e^{-} \;+\; \bar{\nu}_{e}
\]
- Charge of the initial d‑quark: – ⅓ e
- Charge of the final u‑quark: + ⅔ e
- Charge of the W⁻ boson: – e (carried away by the electron‑anti‑neutrino system)
- Net charge before and after the decay: – ⅓ e + e = + ⅔ e, which equals the charge of the final u‑quark. Thus electric charge is conserved.
8. Worked examples
- Charge of a proton (uud)
- u = + ⅔ e (twice) → 2 × (+ ⅔ e) = + &frac43; e
- d = – ⅓ e
- Total = + &frac43; e – ⅓ e = + e
Result: a proton carries a net charge of + e.
- Charge of a neutron (udd)
- u = + ⅔ e
- d = – ⅓ e (twice) → 2 × (– ⅓ e) = – ⅔ e
- Total = + ⅔ e – ⅔ e = 0
Result: a neutron is electrically neutral.
- Charge of the meson π⁺ (u \(\bar{d}\))
- u = + ⅔ e
- \(\bar{d}\) = + ⅓ e (opposite of d)
- Total = + ⅔ e + ⅓ e = + e
Result: π⁺ carries a charge of + e.
- Charge of the combination c \(\bar{s}\) b
- c = + ⅔ e
- \(\bar{s}\) = + ⅓ e (opposite of s)
- b = – ⅓ e
- Total = + ⅔ e + ⅓ e – ⅓ e = + ⅔ e
Result: the system has a net charge of + 2⁄3 e.
9. Practice questions
- What is the electric charge of an anti‑charm quark?
- State the charges of the three quarks that make up a proton and verify that they sum to + e.
- Calculate the total charge of the particle c \(\bar{s}\) b.
- True or false: the anti‑top quark has a charge of + ⅔ e.
- Write the quark composition of a neutron and show that its net charge is zero.
- In β⁻‑decay a down quark transforms into an up quark, emitting an electron and an anti‑neutrino. Using quark charges, explain why the overall electric charge is conserved.
10. Suggested colour‑coded revision diagram
Draw a two‑column chart:
- Left column – the six quark flavours (u, d, c, s, t, b) coloured red, green and blue (any order). Write the charge (+ 2⁄3 e or – 1⁄3 e) beside each symbol.
- Right column – the corresponding antiquarks (\(\bar{u}\), \(\bar{d}\), …) coloured the anti‑colours (anti‑red, anti‑green, anti‑blue) with the opposite charge.
This visual aid helps you recall both the symbol and the sign of the charge at a glance.
11. Summary of key points
- Quarks: six flavours; charges + 2⁄3 e (up‑type) or – 1⁄3 e (down‑type).
- Antiquarks have the same magnitude but opposite sign.
- Leptons (e⁻, μ⁻, τ⁻) carry – e; their neutrinos are neutral.
- Hadrons are colour‑neutral combinations:
- Baryons = three quarks (red‑green‑blue).
- Mesons = quark + antiquark (colour‑anticolour).
- Charge of a hadron = sum of the charges of its constituent (anti)quarks.
- Proton = uud → + e
- Neutron = udd → 0
- π⁺ = u \(\bar{d}\) → + e
- Only electric charge is required for this objective; other quantum numbers are optional.