recall that electrons and neutrinos are fundamental particles called leptons

1. Atoms, Nuclei & Radiation

The Cambridge AS & A Level Physics syllabus (Section 11.1) requires students to understand the basic properties of atoms and nuclei, the types of nuclear radiation and the notation used for isotopes and nuclear reactions.

1.1 Nuclear notation

• For a nucleus the standard notation is ^A_ZX, where:
  • A = mass number (total number of nucleons)
  • Z = atomic number (number of protons)
  • X = chemical symbol of the element
• Example: ²³⁸₉₂U represents a uranium‑238 nucleus (92 protons, 146 neutrons).

1.2 Types of nuclear radiation

Radiation	Particle emitted	Charge	Mass (≈ u)	Typical decay equation
α‑decay	α particle (He nucleus)	+2 e	4	AZX → A‑4Z‑2Y + 42He
β⁻‑decay	electron	‑1 e	≈ 0	AZX → AZ+1Y + e⁻ + \(\bar{u}_{e}\)
β⁺‑decay (positron emission)	positron	+1 e	≈ 0	AZX → AZ‑1Y + e⁺ + \(u_{e}\)
γ‑radiation	photon	0	≈ 0	AZX* → AZX + γ

1.3 Conservation laws in nuclear processes

• Charge conservation: total electric charge before and after a reaction is the same.
• Mass‑number (nucleon) conservation: the sum of A values is unchanged (γ‑emission does not change A).
• Lepton‑number conservation: leptons (e⁻, μ⁻, τ⁻, and their neutrinos) carry L = +1; antileptons carry L = ‑1.
• Baryon‑number conservation: quarks have B = +1⁄3, antiquarks B = ‑1⁄3; the total B is unchanged.

2. Fundamental Particles

Section 11.2 of the syllabus introduces the two families of fundamental fermions: leptons and quarks. All have spin ½ and no known sub‑structure.

2.1 Leptons

Leptons do not carry colour charge, so they do not feel the strong nuclear force. Each of the three generations contains a charged lepton and a neutral neutrino.

Lepton	Symbol	Electric charge (e)	Lepton number (L)	Mass (MeV c⁻²)
Electron	e⁻	‑1	+1	0.511
Electron neutrino	νe	0	+1	< 1 eV (extremely small)
Muon	μ⁻	‑1	+1	105.7
Muon neutrino	νμ	0	+1	< 1 eV (extremely small)
Tau	τ⁻	‑1	+1	1776.9
Tau neutrino	ντ	0	+1	< 1 eV (extremely small)

2.1.1 Antileptons

Every lepton has an antiparticle with opposite electric charge and opposite lepton number (L = ‑1).

Antilepton	Symbol	Electric charge (e)	Lepton number (L)
Positron	e⁺	+1	‑1
Electron antineutrino	\(\bar{u}_{e}\)	0	‑1
Anti‑muon	μ⁺	+1	‑1
Muon antineutrino	\(\bar{u}_{\mu}\)	0	‑1
Anti‑tau	τ⁺	+1	‑1
Tau antineutrino	\(\bar{u}_{\tau}\)	0	‑1

2.2 Quarks

Quarks are the building blocks of hadrons. They carry a colour charge (red, green or blue) and therefore experience the strong nuclear force.

Quark	Symbol	Electric charge (e)	Baryon number (B)	Mass (MeV c⁻²)
Up	u	+2⁄3	+1⁄3	≈ 2.2
Down	d	‑1⁄3	+1⁄3	≈ 4.7
Charm	c	+2⁄3	+1⁄3	≈ 1270
Strange	s	‑1⁄3	+1⁄3	≈ 96
Top	t	+2⁄3	+1⁄3	≈ 173 000
Bottom	b	‑1⁄3	+1⁄3	≈ 4180

2.2.1 Antiquarks

Antiquarks have opposite electric charge, opposite baryon number (‑1⁄3) and carry the complementary colour charge (anti‑red, anti‑green, anti‑blue). The standard notation uses an over‑bar.

Antiquark	Symbol	Electric charge (e)	Baryon number (B)
Anti‑up	\(\bar{u}\)	‑2⁄3	‑1⁄3
Anti‑down	\(\bar{d}\)	+1⁄3	‑1⁄3
Anti‑charm	\(\bar{c}\)	‑2⁄3	‑1⁄3
Anti‑strange	\(\bar{s}\)	+1⁄3	‑1⁄3
Anti‑top	\(\bar{t}\)	‑2⁄3	‑1⁄3
Anti‑bottom	\(\bar{b}\)	+1⁄3	‑1⁄3

3. Hadrons – How Quarks Form Observable Particles

• Baryons – three quarks (qqq). The three colour charges combine to a colour‑neutral (white) state.
  • Proton: ^uud – charge +1 e, mass ≈ 938 MeV c⁻².
  • Neutron: ^udd – charge 0, mass ≈ 940 MeV c⁻².
• Mesons – a quark and an antiquark (q \(\bar{q}\)). Colour‑anticolour also gives a neutral colour state.
  • Pion family:
    • π⁺ = u \(\bar{d}\)
    • π⁻ = \(\bar{u}\) d
    • π⁰ = (u \(\bar{u}\) − d \(\bar{d}\))/√2
    Mass ≈ 140 MeV c⁻².

4. Why Electrons and Neutrinos Are Classified as Leptons

1. No colour charge – they do not participate in the strong interaction.
2. Spin ½ – all leptons are fermions.
3. Lepton‑number conservation – each carries L = +1 (antileptons L = ‑1).
4. Family grouping – the electron is paired with the electron neutrino; the muon with the muon neutrino; the tau with the tau neutrino.
5. Interaction pattern – the electron feels the electromagnetic and weak forces, whereas the neutrino interacts only via the weak force (and gravity).

5. β‑Decay at the Quark Level (Syllabus Requirement)

Neutron β⁻‑decay is a classic example that links the quark and lepton families.

\[ d \;\longrightarrow\; u \;+\; e^{-} \;+\; \bar{u}_{e} \]

• A down‑quark (charge ‑1⁄3) transforms into an up‑quark (charge +2⁄3) by emitting a virtual W⁻ boson.
• The W⁻ boson quickly decays into an electron and an electron‑antineutrino.
• At the nuclear level this appears as ¹₀n → ¹₁p + e⁻ + \(\bar{u}_{e}\).

6. Key Points to Remember

• Fundamental fermions = leptons + quarks; all have spin ½ and no known sub‑structure.
• Leptons: no colour charge, L = +1 (‑1 for antiparticles), interact electromagnetically (charged) or only weakly (neutrinos).
• Quarks: carry colour charge, B = +1⁄3 (‑1⁄3 for antiquarks), combine to form colour‑neutral hadrons.
• Three generations exist; each higher generation is heavier but otherwise identical.
• Antiparticles have opposite electric charge, opposite lepton/baryon number and opposite colour charge.
• Hadrons are colour‑neutral combinations: baryons (qqq) and mesons (q \(\bar{q}\)).
• In nuclear reactions charge, mass number, lepton number and baryon number are all conserved.

7. Typical Exam Question

Question: Explain why the electron and the electron neutrino are both considered fundamental particles, and describe one key difference in the way they interact with other particles.

Answer outline:

• Both have been shown by scattering experiments to be point‑like down to at least 10⁻¹⁸ m, so they have no known sub‑structure – they are fundamental.
• Both belong to the lepton family and each carries lepton number L = +1.
• Key difference in interactions: The electron carries electric charge (‑1 e) and therefore participates in electromagnetic interactions (e.g., it is deflected by electric or magnetic fields). The electron neutrino is electrically neutral and interacts only via the weak nuclear force (and gravity), making it extremely difficult to detect.