This mini-lesson covers AQA 3.8 — Nuclear physics: Rutherford scattering, the properties of α, β and γ radiation, the radioactive decay law (N = N0e−λt), half-life, nuclear radius, E = mc², binding energy per nucleon, and fission and fusion.
Section 3.8 is compulsory and appears on Paper 2.
Where this sits: AQA sections 3.1–3.8 are compulsory for every A-level Physics student. (Sections 3.9–3.13 are the five options — you study just one of those.)
Work through each screen, answer the questions as you go (many are full A-level calculations) and collect ⭐ stars. Press Start when you're ready.
3.8.1 · Rutherford
Rutherford scattering and the nuclear atom
Alpha particles were fired at a very thin gold foil. Three observations, three conclusions:
Most passed straight through → the atom is mostly empty space.
A few were deflected through large angles → there is a concentrated positive charge.
About 1 in 8000 came almost straight back → that charge is in a tiny, massive nucleus.
Experimental detail: the foil had to be very thin (so alphas scattered only once) and the whole apparatus was in a vacuum (alphas are absorbed by a few centimetres of air). This destroyed the plum-pudding model.
3.8.1 · radiation
Alpha, beta and gamma — and the inverse square law
Alpha (α): a helium nucleus (2p + 2n). Highly ionising, range a few cm in air, stopped by paper. Deflected by fields.
Beta-minus (β−): a fast electron from a neutron turning into a proton. Stopped by a few mm of aluminium. Deflected the opposite way to α.
Gamma (γ): a high-energy EM photon, no charge or mass. Weakly ionising, never fully stopped — only reduced by thick lead or concrete. Not deflected by fields.
I = k ÷ x²gamma intensity obeys an inverse square law with distance from a point source — double the distance, quarter the intensity
Safety and background: always subtract the background count before analysing data. Sources of background: radon gas, rocks and buildings, cosmic rays, food and drink, and medical procedures. Handle sources with tongs, keep them at arm’s length, and store them in a lead-lined box.
Sort it
Alpha, beta or gamma?
Tap a property, then tap the radiation it belongs to.
🔴 Alpha
🔵 Beta-minus
🟣 Gamma
3.8.2 · decay law
Radioactive decay, decay constant and half-life
Radioactive decay is random (you cannot say which nucleus decays next) and spontaneous (unaffected by temperature, pressure or chemical state). But with huge numbers of nuclei the behaviour is beautifully predictable:
A = λN · N = N0e−λt · A = A0e−λtλ = decay constant (probability of decay per nucleus per second, s−1) · A = activity in becquerels (Bq)
T½ = ln2 ÷ λ = 0.693 ÷ λhalf-life: the time for half the undecayed nuclei (or the activity) to halve
A large λ means a short half-life — the nuclide is very unstable.
Carbon dating uses carbon-14 (T½ = 5730 years); rock dating uses long-lived nuclides like uranium-238.
Plot ln A against t: a straight line of gradient −λ.
?Which statement about radioactive decay is correct?
3.8.3 · nuclear radius
Nuclear radius and nuclear density
Electron diffraction by nuclei gives the most accurate radii. The first minimum of the diffraction pattern gives the nuclear diameter.
R = R0A1/3R0 ≈ 1.05 fm = 1.05×10−15 m · A = nucleon number
Since R ∝ A1/3, the volume (∝ R³) is proportional to A — so nuclear density is constant for every nuclide (about 1017 kg m−3).
This means nucleons are packed together like incompressible spheres, and the nuclear force is short-range.
Worked example
For A = 125: A1/3 = 5. R = 1.05 × 5 = 5.25 fm.
Calculate
Your turn — calculation 3
3Calculate the radius of a nucleus with nucleon number A = 125, in fm. (R0 = 1.05 fm)
fm
Hint: R = R0A1/3. The cube root of 125 is 5.
Quick check
Think it through
?Because R = R0A1/3, what can you deduce about nuclear density?
3.8.4 · mass & energy
Mass–energy, binding energy and the BE/nucleon curve
E = mc²1 u = 1.661×10−27 kg · 1 u is equivalent to 931.5 MeV
A nucleus has less mass than its separated nucleons. That mass defect Δm corresponds to the binding energy: the energy you would need to pull the nucleus apart.
The key graph is binding energy per nucleon against nucleon number. It rises steeply, peaks at iron-56 (about 8.8 MeV per nucleon — the most stable nuclide), then falls slowly.
Energy is released in any change that moves nuclei towards the peak: fusion of light nuclei (left of the peak) and fission of heavy nuclei (right of it).
Worked example — helium-4
The mass defect of a helium-4 nucleus is about 5.0×10−29 kg.
E = Δmc² = 5.0×10−29 × (3.0×108)² = 4.5×10−12 J.
In MeV: 4.5×10−12 ÷ 1.60×10−13 = 28.1 MeV. Per nucleon: 28.1 ÷ 4 = 7.0 MeV. ✓
Calculate
Your turn — calculation 4
4A helium-4 nucleus has a mass defect of 5.0 × 10−29 kg. Calculate its binding energy in MeV. (c = 3.0×108 m s−1; 1 MeV = 1.60×10−13 J)
MeV
Hint: E = Δmc² = 5.0×10−29 × 9.0×1016 = 4.5×10−12 J. Then divide by 1.60×10−13.
Calculate
Your turn — calculation 5
5Using that binding energy, calculate the binding energy per nucleon of helium-4, in MeV.
MeV
Hint: Helium-4 has 4 nucleons: 28.1 ÷ 4.
3.8.5 · fission & fusion
Induced fission, fusion and the reactor
Induced fission: a slow (thermal) neutron is absorbed by uranium-235, which splits into two roughly equal daughter nuclei plus 2 or 3 neutrons and about 200 MeV of energy. Those neutrons can trigger a chain reaction.
Moderator (water, graphite): slows the neutrons down by elastic collisions, because U-235 captures slow neutrons far more readily.
Control rods (boron, cadmium): absorb neutrons to keep the reaction just critical.
Coolant: carries the thermal energy to the heat exchanger to raise steam.
Fusion needs very high temperature and pressure so nuclei have enough kinetic energy to overcome the electrostatic repulsion and get close enough for the strong nuclear force to bind them. This is why fusion is so hard on Earth.
Waste: spent fuel is highly radioactive with long half-lives — it is stored under water, then vitrified and buried deep underground.
Why both release energy: both push the nucleons towards the peak of the binding-energy-per-nucleon curve, so the products are more tightly bound. The lost mass appears as energy via E = mc².
Match it
Match each observation to its conclusion
Tap a card on the left, then its partner on the right.
Statement
Answer
Quick check
Think it through
?Why does the fusion of two light nuclei release energy?
Quick check
Think it through
?What is the role of the moderator in a thermal nuclear reactor?
Recap
The big ideas to know
Rutherford: mostly empty space · tiny, massive, positive nucleus
Radiation: α = paper, most ionising · β = few mm Al · γ = thick lead, inverse square law
Decay law: A = λN · N = N0e−λt · T½ = ln2/λ · random and spontaneous
Nuclear radius: R = R0A1/3 → nuclear density is constant
Mass–energy: E = mc² · mass defect → binding energy · 1 u = 931.5 MeV
BE/nucleon: peaks at iron-56 · fusion (light) and fission (heavy) both move towards the peak
Reactor: moderator slows neutrons · control rods absorb them · coolant removes heat
You have covered the whole of AQA 3.8 — from Rutherford’s foil to the physics of a power station. Press Finish to see your score.
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