Topic 11 is about unstable nuclei: what they emit, how fast they decay, and where the energy comes from.
A = λN · N = N₀e^(−λt) · t½ = ln2 / λ · ΔE = Δm c²radioactive decay is random and spontaneous — yet perfectly predictable in bulk
The two-word definition examiners want: radioactive decay is random (you cannot say which nucleus will decay next, or when) and spontaneous (it is unaffected by temperature, pressure or chemical state). Randomness at the level of one nucleus becomes an exact exponential law over 10²³ of them.
Work through each screen, answer the questions as you go (several are full A-level calculations) and collect ⭐ stars. Press Start when you're ready.
Topic 11 · radiation types
Alpha, beta and gamma
Alpha (α) — a helium nucleus, ⁴₂He. Charge +2e, relatively massive and slow. Most ionising, least penetrating — stopped by a sheet of paper or a few cm of air.
Beta-minus (β⁻) — a fast electron produced when a neutron turns into a proton (n → p + e⁻ + ν̄ₑ). Charge −e. Stopped by a few mm of aluminium.
Gamma (γ) — a high-energy photon, no charge and no mass. Least ionising, most penetrating — only reduced (never fully stopped) by thick lead or concrete. It follows an inverse-square law in air.
α decay: ᴬZX → ᴬ⁻⁴Z−2Y + ⁴₂Heβ⁻ decay: ᴬZX → ᴬZ+1Y + ⁰₋₁e + ν̄ₑ — mass number AND atomic number must balance
Background radiation (radon gas, rocks, food, cosmic rays, medical sources) must be measured and subtracted from every count-rate reading before you analyse the data. Miss this and your half-life will come out wrong.
Sort it
Alpha, beta or gamma?
Tap a statement, then tap the type of radiation it describes.
🔴 Alpha
🔵 Beta-minus
🟣 Gamma
Topic 11 · decay law
Activity, the decay constant and half-life
A = λN · N = N₀ e^(−λt) · A = A₀ e^(−λt)A = activity in becquerel (1 Bq = 1 decay per second) · λ = decay constant in s⁻¹ · N = number of undecayed nuclei
The decay constant λ is the probability per unit time that a given nucleus decays. A big λ means a fast decay and a short half-life.
t½ = ln 2 / λ = 0.693 / λhalf-life: the mean time for HALF the undecayed nuclei to decay — or for the activity to halve
Both N and A fall off with exactly the same exponential, because A = λN.
Take logs to straighten the graph: ln A = ln A₀ − λt, so a plot of ln A against t has gradient −λ.
Whatever you start with, after n half-lives the fraction remaining is (½)ⁿ.
2A wooden artefact contains 25% of the carbon-14 found in living wood. Given a half-life of 5730 years, calculate its age. Give your answer in years.
years
Hint: 25% = ½ × ½, which is exactly two half-lives. Age = 2 × 5730.
Calculate
Your turn — activity
3A sample contains 6.0 × 10²⁰ undecayed nuclei of an isotope whose half-life is 9.46 × 10⁸ s. Calculate its activity. Give your answer as a multiple of 10¹¹ Bq to 2 significant figures.
4A source has an activity of 800 Bq and a half-life of 8.0 days. Calculate its activity after 24 days. Give your answer in Bq.
Bq
Hint: 24 ÷ 8.0 = 3 half-lives. Each one halves the activity: 800 → 400 → 200 → ?
Quick check
What decay is
?Which statement about radioactive decay is correct?
Topic 11 · binding energy
Mass defect and binding energy
Weigh a nucleus and it comes out lighter than the sum of its separate nucleons. That missing mass is the mass defect, and by E = mc² it is the energy that was released when the nucleus formed.
ΔE = Δm c² · 1 u = 931.5 MeVbinding energy = the energy needed to PULL a nucleus completely apart into free nucleons
The number that matters is binding energy per nucleon — the fairest measure of nuclear stability.
The curve rises steeply for light nuclei, peaks at iron-56 (about 8.8 MeV per nucleon), and then falls slowly.
Iron-56 is the most stable nucleus. Everything wants to move towards it.
Fusion of light nuclei moves up the curve on the left → energy released.
Fission of heavy nuclei moves up the curve from the right → energy released.
Worked example — helium-4
Mass defect Δm = 2(1.00783) + 2(1.00867) − 4.00260 = 0.03040 u
Binding energy = 0.03040 × 931.5 = 28.3 MeV
Binding energy per nucleon = 28.3 ÷ 4 = 7.08 MeV
Calculate
Your turn — binding energy per nucleon
5A helium-4 nucleus has a mass defect of 0.03040 u. Calculate its binding energy per nucleon. Give your answer in MeV to 3 significant figures. (1 u = 931.5 MeV)
MeV
Hint: Total binding energy = 0.03040 × 931.5 = 28.3 MeV. Helium-4 has 4 nucleons, so divide by 4.
Topic 11 · fission & fusion
Fission and fusion
Nuclear fission: a heavy nucleus such as uranium-235 absorbs a slow (thermal) neutron, becomes unstable and splits into two lighter daughter nuclei plus 2 or 3 free neutrons and around 200 MeV of energy.
Those neutrons can trigger further fissions — a chain reaction. Controlled in a reactor by:
Moderator (graphite or water): slows the fast neutrons down by elastic collisions so that U-235 can absorb them.
Control rods (boron or cadmium): absorb neutrons to keep the reaction just critical.
Coolant: carries the thermal energy away to raise steam.
Nuclear fusion: two light nuclei join. It releases far more energy per nucleon than fission — but the nuclei must overcome their mutual electrostatic repulsion, which requires temperatures of order 10⁸ K and enormous pressure. That is why stars can do it easily and we still struggle.
The link back to Topic 10: fusion in stellar cores builds elements up to iron. Everything heavier than iron in your body was forged in a supernova.
Quick check
Why does fission release energy?
?Uranium-235 fissions into two lighter nuclei. Why is energy released?
Quick check
The moderator
?What is the role of the moderator in a nuclear fission reactor?
Quick check
Why fusion is hard
?Why does nuclear fusion require temperatures of the order of 10⁸ K?
Match it
Match the term to its meaning
Tap an item on the left, then its partner on the right.
Term
Meaning
Recap
The big ideas to know
Radiation: α = ⁴₂He, most ionising, stopped by paper · β⁻ = fast electron (n → p + e⁻ + ν̄ₑ), stopped by mm of aluminium · γ = photon, most penetrating
Decay is random and spontaneous — subtract background before analysing any count rate
Decay law: A = λN · N = N₀e^(−λt) · t½ = ln2/λ · ln A against t gives gradient −λ
After n half-lives the fraction remaining is (½)ⁿ
Mass defect: ΔE = Δmc²; 1 u = 931.5 MeV; binding energy per nucleon peaks at iron-56 (≈8.8 MeV)
Fission: heavy nucleus + slow neutron → two daughters + 2–3 neutrons + ≈200 MeV; moderator slows, control rods absorb
Fusion: light nuclei join; needs ≈10⁸ K to beat electrostatic repulsion; releases more energy per nucleon than fission
That is Edexcel Topic 11 — the topic that powers both the reactor and the star. Press Finish to see your score.
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