AQA A-Level Physics: Particles and radiation (7408) – Revision Notes

These notes condense section 3.2 Particles and radiation of the AQA AS and A-level Physics (7407/7408) specification, version 1.4 (AS and A-level exams June 2016 onwards): 3.2.1 Particles and 3.2.2 Electromagnetic radiation and quantum phenomena. It is AS and A-level content, examined in A-level Paper 1 and assumed in Paper 2. Sections 3.9-3.13 are options (you study one, assessed in Paper 3 Section B); this topic is compulsory. For full explanations and worked examples, use the Particles and radiation study guide.

Also see: practice questions, the AQA A-level Physics hub, the printable checklist and the free diagnostics.

Key equations

Equation	Use	Units
specific charge = Q/m	nuclei, ions, particles	C kg⁻¹
E = hf = hc/λ	photon energy	J
hf = ϕ + Ek(max)	photoelectric effect	J (or eV on both sides)
eVs = Ek(max)	stopping potential	Vs in V
hf = E1 − E2	photon emitted between levels	J
λ = h/mv	de Broglie wavelength	m
1 eV = 1.60 × 10⁻¹⁹ J	energy conversion	–

Constants used here: h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C, mₑ = 9.11 × 10⁻³¹ kg.

3.2.1.1 The atom in numbers

	Charge / C	Rel. charge	Mass / kg	Rel. mass
p	+1.60 × 10⁻¹⁹	+1	1.67 × 10⁻²⁷	1
n	0	0	1.67 × 10⁻²⁷	1
e⁻	−1.60 × 10⁻¹⁹	−1	9.11 × 10⁻³¹	≈ 0.0005

• Z = protons; A = nucleons; neutrons = A − Z. Nuclide notation: ᴬ_Z X.
• Isotopes: same Z, different number of neutrons.
• Specific charge = charge/mass (C kg⁻¹). For an ion use the net charge (number of electrons gained or lost × e) and mass ≈ A × 1.67 × 10⁻²⁷ kg.

3.2.1.2 Nuclear stability

• Strong nuclear force: attractive to about 3 fm, repulsive below about 0.5 fm, acts between nucleons.
• Alpha: ᴬ_Z X → ᴬ⁻⁴_(Z−2) Y + ⁴₂α.
• β⁻: ᴬ_Z X → ᴬ_(Z+1) Y + ⁰₋₁β + ν̄ₑ.
• Neutrino proposed because beta particles have a range of energies: energy conservation needed another particle.

3.2.1.3 Antiparticles and photons

Particle	Antiparticle	Rest energy / MeV
electron	positron	0.511
proton	antiproton	938.3
neutron	antineutron	939.6
neutrino	antineutrino	–

Same mass and rest energy; opposite charge.

• E = hf = hc/λ.
• Annihilation: particle + antiparticle → two photons (momentum). E_photon(min) = rest energy of one particle.
• Pair production: one photon → particle + antiparticle. E_photon(min) = 2 × rest energy.

Worked reminder. Minimum photon energy to make a neutron-antineutron pair = 2 × 939.6 = 1879.2 MeV. Any extra energy becomes kinetic energy of the pair.

3.2.1.4 Exchange particles

Force	Exchange particle	Acts on
Electromagnetic	virtual photon	charged particles
Weak	W⁺, W⁻	all particles
Strong (between nucleons)	pion	hadrons

Method: drawing a weak-interaction diagram

1. Write the equation. Put the incoming particles at the bottom.
2. Find which particle changes identity (for example p → n).
3. Choose W⁺ or W⁻ so charge balances at that vertex.
4. At the other vertex, the W turns into (or meets) the leptons; check charge again.

Covered: β⁻, β⁺, electron capture (p + e⁻ → n + νₑ), electron-proton collision (e⁻ + p → n + νₑ). Gluon, Z⁰ and graviton are not tested.

3.2.1.5–3.2.1.6 Classification and quarks

Quark	Q	B	S
u	+⅔	+⅓	0
d	−⅓	+⅓	0
s	−⅓	+⅓	−1

Antiquarks: reverse every sign.

Family	Members	B	Quarks
Baryons	p (uud), n (udd)	+1	qqq
Antibaryons	p̄ (ūūd̄), n̄ (ūd̄d̄)	−1	q̄q̄q̄
Mesons	π⁺ ud̄, π⁻ dū, π⁰ uū/dd̄, K⁺ us̄, K⁻ sū, K⁰ ds̄, K̄⁰ sd̄	0	qq̄
Leptons	e⁻, μ⁻, νₑ, ν_μ (+ antiparticles)	0	none

• Proton: the only stable baryon. Kaon: decays into pions. Muon: decays into an electron.
• Lepton numbers: Lₑ = +1 for e⁻ and νₑ, −1 for e⁺ and ν̄ₑ; L_μ = +1 for μ⁻ and ν_μ, −1 for μ⁺ and ν̄_μ.
• Strange particles: made in pairs by the strong interaction, decay by the weak interaction.
• Large international teams validate new particle results.

3.2.1.7 Conservation checklist

Quantity	Strong	Weak
Charge Q	conserved	conserved
Baryon number B	conserved	conserved
Lₑ and L_μ (separately)	conserved	conserved
Strangeness S	conserved	can change by 0, ±1
Energy, momentum	conserved	conserved

• β⁻: d → u. β⁺: u → d. Neutron decay: n → p + e⁻ + ν̄ₑ.
• Data will be given for particles outside the specified list.

Method: is this interaction possible?

1. Write Q, B, Lₑ, L_μ and S under every particle, on both sides.
2. Add each row. Any mismatch in Q, B, Lₑ or L_μ: impossible.
3. If only S changes, by 1: possible by the weak interaction only.
4. If S changes by 2 or more: impossible.

Worked reminder. K⁺ → π⁺ + π⁰. Q: +1 → +1 + 0. B: 0 → 0. S: +1 → 0 + 0, a change of 1. Allowed, weak decay – as expected, since strange particles decay by the weak interaction.

3.2.2.1 Photoelectric effect

• hf = ϕ + Ek(max); threshold f₀ = ϕ/h; stopping potential eVs = Ek(max).
• One photon frees at most one electron. Below f₀: no emission at any intensity.
• More intensity → more photoelectrons per second; same Ek(max).
• Higher frequency → larger Ek(max).

Worked reminder. Radiation of 1.5 × 10¹⁵ Hz on a metal with ϕ = 3.6 eV: hf = 9.95 × 10⁻¹⁹ J = 6.22 eV, so Ek(max) = 6.22 − 3.6 = 2.62 eV and Vs = 2.62 V. Working in eV throughout avoids converting back and forth.

3.2.2.2 Collisions of electrons with atoms

• 1 eV = 1.60 × 10⁻¹⁹ J. eV → J: multiply. J → eV: divide.
• Excitation: electron moves up a level. Ionisation: electron removed.
• An incoming electron can give part of its energy; a photon is absorbed only if its energy exactly matches a gap (or exceeds the ionisation energy).
• Fluorescent tube: electrons excite mercury atoms → UV photons → phosphor absorbs UV → emits visible light.

3.2.2.3 Energy levels

• Line spectra → discrete energy levels.
• hf = E1 − E2 (levels in J or eV; convert to J before using h).
• n levels give at most n(n − 1)/2 different emission lines.

3.2.2.4 Wave-particle duality

• Photoelectric effect → light behaves as particles. Electron diffraction → particles behave as waves.
• λ = h/mv. Greater momentum → shorter λ → less diffraction (smaller rings).

Must-know distinctions

• Hadron vs lepton: hadrons feel the strong interaction; leptons do not.
• Baryon vs meson: three quarks (B = ±1) vs quark-antiquark (B = 0).
• Annihilation vs pair production: two photons out, minimum energy each = one rest energy; versus one photon in, minimum energy = two rest energies.
• Excitation vs ionisation: moving up a level vs leaving the atom.
• Intensity vs frequency: intensity sets the number of photoelectrons; frequency sets Ek(max).

Quick self-test

1. Find the energy of a photon of frequency 5.0 × 10¹⁴ Hz, in J and in eV.
2. Convert 2.4 eV to joules.
3. A metal has work function 2.3 eV. Find its threshold frequency.
4. State the minimum photon energy, in MeV, to produce an electron-positron pair.
5. Find the de Broglie wavelength of a 0.20 kg ball moving at 30 m s⁻¹.
6. Calculate the specific charge of an alpha particle.
7. Find the wavelength emitted when hydrogen falls from −1.51 eV to −13.6 eV.
8. Find the de Broglie wavelength of an electron moving at 2.0 × 10⁶ m s⁻¹.
9. Give the quark make-up and strangeness of a K⁻.
10. Is p → n + e⁺ + ν̄ₑ allowed? Give a reason.
11. Which exchange particle is involved in electron capture?

Answers

1. E = hf = 6.63 × 10⁻³⁴ × 5.0 × 10¹⁴ = 3.3 × 10⁻¹⁹ J, which is 2.1 eV.
2. 2.4 × 1.60 × 10⁻¹⁹ = 3.84 × 10⁻¹⁹ J.
3. f₀ = (2.3 × 1.60 × 10⁻¹⁹)/6.63 × 10⁻³⁴ = 5.6 × 10¹⁴ Hz.
4. 2 × 0.511 = 1.022 MeV.
5. λ = 6.63 × 10⁻³⁴/(0.20 × 30) = 1.1 × 10⁻³⁴ m – far too small to diffract.
6. (2 × 1.60 × 10⁻¹⁹)/(4 × 1.67 × 10⁻²⁷) = 4.79 × 10⁷ C kg⁻¹.
7. ΔE = 12.09 eV = 1.934 × 10⁻¹⁸ J; λ = hc/ΔE = 1.03 × 10⁻⁷ m (ultraviolet).
8. λ = 6.63 × 10⁻³⁴/(9.11 × 10⁻³¹ × 2.0 × 10⁶) = 3.6 × 10⁻¹⁰ m.
9. sū, S = −1.
10. No: Lₑ goes from 0 to −2 (positron −1, antineutrino −1). It should be a neutrino.
11. W⁺ (from proton to electron), or equivalently W⁻ from electron to proton.

Where marks are usually lost

• Writing a neutrino in β⁻ decay or an antineutrino in β⁺ decay.
• Saying annihilation makes one photon; momentum needs two.
• Using the pion as the exchange particle for the weak interaction.
• Checking strangeness for a weak decay and calling it forbidden.
• Saying higher intensity gives faster photoelectrons.
• Leaving energy in eV when substituting into λ = hc/E.
• Calling a meson a baryon because it contains quarks; count the quarks.
• Giving the electron capture products as a neutron and an antineutrino.
• Forgetting the strong force is repulsive below about 0.5 fm when explaining why nuclei do not collapse.

Official syllabus

AQA AS and A-level Physics (7407/7408) specification, version 1.4, July 2026, AS and A-level exams June 2016 onwards, published by AQA. Section 3.2 Particles and radiation.