HookThe day a physicist fired bullets at gold and one bounced back
In 1909, in a basement laboratory at the University of Manchester, Hans Geiger and a 20-year-old undergraduate named Ernest Marsden aimed a beam of alpha particles at a sheet of gold foil just a few thousand atoms thick. Everyone expected the tiny, fast particles to punch straight through — the accepted 'plum pudding' picture had the atom's positive charge spread thinly across the whole thing, far too diffuse to deflect anything. Almost all the alphas did sail through. But roughly one in eight thousand came straight back. Ernest Rutherford, who set them the task, later said it was the most incredible event of his life: as if you had fired a 15-inch naval shell at a piece of tissue paper and it had bounced back and hit you.
The only way to explain the rebounds was to admit that almost all of an atom's mass, and all of its positive charge, is crammed into a minuscule central nucleus — about ten thousand times smaller than the atom itself. That single result overturned the model of matter and gave us the picture P4 is built on: a dense nucleus of protons and neutrons, with electrons occupying the vast empty space around it. This section takes you from the size of an atom through isotopes and nuclear notation, into radioactive decay, half-life and the maths that goes with it, and out to the two processes — fission and fusion — that power reactors and stars.
ModelInside the atom — a nucleus and a lot of empty space
An atom has a radius of about \(1 \times 10^{-10}\ \text{m}\). At its centre sits a nucleus roughly \(1 \times 10^{-14}\ \text{m}\) across — around ten thousand times smaller than the atom, yet holding more than 99.9 per cent of its mass. If the atom were the size of a football stadium, the nucleus would be a pea on the centre spot. The nucleus contains protons (positive) and neutrons (no charge); the negative electrons orbit at set distances called energy levels (or shells).
Electrons are not fixed there forever. If an electron absorbs electromagnetic radiation of the right energy it jumps to a higher energy level, further from the nucleus; when it falls back it emits electromagnetic radiation. This absorb-and-emit behaviour is why elements produce their own characteristic line spectra, and it is the reason the whole atom stays neutral: the number of electrons equals the number of protons, so the charges cancel exactly. Remove or add an electron and you have created a charged ion.
ModelMass number, atomic number and isotopes
Two numbers pin down any nucleus. The atomic number (proton number) is the number of protons — it is what makes an atom that element, so every carbon atom has 6 protons and nothing else does. The mass number (nucleon number) is the total of protons plus neutrons. We write a nucleus as \({}^{A}_{Z}\text{X}\), with the mass number \(A\) on top and the atomic number \(Z\) below, for example \({}^{12}_{6}\text{C}\). The number of neutrons is simply \(A - Z\).
Isotopes are atoms of the same element — same number of protons — with different numbers of neutrons, and therefore different mass numbers. Carbon-12 and carbon-14 are both carbon (6 protons each) but carbon-14 carries two extra neutrons. Because chemistry is decided by electrons, and electrons follow protons, isotopes behave identically in reactions; the difference shows up only in mass and, crucially, in nuclear stability. Isotopes with an unstable balance of protons and neutrons are the ones that decay and give out radiation.
CaseHow the model was built — and rebuilt
Science did not arrive at the nuclear atom in one leap; it corrected itself in stages, which is exactly why examiners like this story. Before the electron was even known, atoms were thought to be tiny indivisible spheres. After J. J. Thomson discovered the electron in 1897 he proposed the plum pudding model (1904): a ball of positive charge with electrons dotted through it like fruit in a pudding.
That model made a clear prediction — alpha particles should barely be deflected — and Geiger and Marsden's 1909 scattering experiment falsified it. Rutherford's 1911 interpretation replaced the pudding with a tiny, dense, positive nucleus. Niels Bohr then refined it in 1913, showing that electrons must occupy fixed energy levels at set distances, or atoms would collapse. Later experiments proved the positive charge came in whole units — protons — and in 1932 James Chadwick found the neutron, explaining the missing mass. The lesson AQA rewards: a scientific model is provisional, tested against evidence, and revised when an experiment refuses to agree with it.
MechanismRadioactive decay and the four radiations
An unstable nucleus becomes stable by throwing out radiation, and it does so at random: you can never predict which nucleus will decay next or exactly when. What you can measure is the activity — the rate at which nuclei decay — measured in becquerel (Bq), where 1 Bq is one decay per second. A detector such as a Geiger–Müller tube records the count-rate, the decays reaching the detector each second.
There are four types to know. An alpha particle (\({}^{4}_{2}\text{He}\), two protons and two neutrons) is heavy and highly ionising but very weakly penetrating — stopped by a sheet of paper or a few centimetres of air. A beta particle (\({}^{0}_{-1}\text{e}\), a fast electron from the nucleus) is moderately ionising and stopped by a few millimetres of aluminium. A gamma ray is a high-energy electromagnetic wave, weakly ionising but very penetrating — needing thick lead or metres of concrete. Finally a nucleus can emit a neutron. The rule of thumb: the more strongly ionising a radiation is, the less far it penetrates, because it dumps its energy quickly.
ModelBalancing nuclear equations
When a nucleus decays it changes into a different nucleus, and the change follows two conservation rules: the mass numbers on each side must add up to the same total, and so must the atomic numbers. Alpha decay removes 2 protons and 2 neutrons, so the mass number drops by 4 and the atomic number by 2 — the atom becomes a different element. Beta decay is subtler: a neutron turns into a proton and the emitted electron, so the mass number is unchanged while the atomic number goes up by 1. Gamma emission carries away energy only and changes neither number.
The examiner's trick is to hand you the parent nucleus and the emitted particle and ask for the daughter, or vice versa. Balance the top row and the bottom row separately and the answer falls out.
Uranium-238 decays by alpha emission. Write the equation.
Start with the parent and the alpha particle: \[{}^{238}_{92}\text{U} \rightarrow {}^{A}_{Z}\text{X} + {}^{4}_{2}\text{He}\] Balance the mass numbers (top): \(238 = A + 4\), so \(A = 234\). Balance the atomic numbers (bottom): \(92 = Z + 2\), so \(Z = 90\). Element 90 is thorium, giving \[{}^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\text{He}\]
Now a beta example — carbon-14 decays by beta emission: \[{}^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{0}_{-1}\text{e}\] The mass number stays 14, the atomic number rises from 6 to 7 (carbon becomes nitrogen), and the electron's \(-1\) bottom number keeps the atomic numbers balanced: \(6 = 7 + (-1)\). That last check is the mark most students drop.
DataHalf-life — measuring the unpredictable
Decay is random for a single nucleus, but a sample holds billions, and averages become reliable. The half-life is the time for the number of unstable nuclei — and therefore the activity — to halve. It is fixed for a given isotope: carbon-14 is 5,730 years, iodine-131 is 8 days, uranium-238 is 4.5 billion years.
After one half-life, half the original nuclei remain; after two, a quarter; after three, an eighth. The fraction remaining after \(n\) half-lives is \(\left(\frac{1}{2}\right)^{n}\). Two exam skills come from this: reading a half-life off a graph (find where activity has dropped to half its start, then read the time), and calculating the net decline — the fraction or ratio that has decayed. The net decline as a ratio is often written as, for instance, 7:1 decayed-to-remaining after three half-lives, because 7 of the original 8 have gone.
A radioactive source has a count-rate of \(800\ \text{Bq}\). Thirty minutes later it reads \(100\ \text{Bq}\). Find the half-life, and state the net decline as a ratio.
Halve the count-rate step by step and count the steps: \[800 \rightarrow 400 \rightarrow 200 \rightarrow 100\] That is 3 halvings, so 3 half-lives have passed in 30 minutes. \[\text{half-life} = \frac{30}{3} = 10\ \text{minutes}\] Check with the fraction rule: after 3 half-lives the fraction remaining is \(\left(\frac{1}{2}\right)^{3} = \frac{1}{8}\), and \(\frac{100}{800} = \frac{1}{8}\) — consistent.
Net decline: of every 8 original nuclei, 1 remains and 7 have decayed, so the decayed-to-remaining ratio is \(7:1\). Quoting the ratio, not just the fraction remaining, is what turns a 2-mark answer into 3.
CaseContamination, dose and the risks we actually run
Two hazards get confused, and examiners test the difference every year. Irradiation is being exposed to radiation from a source outside you — it stops the moment you move away, and the object does not become radioactive. Contamination is getting radioactive atoms onto or into you; those atoms keep decaying wherever they are, which is far harder to deal with. Precautions follow the distinction: shielding, distance and short exposure times guard against irradiation, while gloves, sealed sources and protective suits stop contamination. Because the stakes are high, findings on radiation risk must be checked by other scientists — peer review — before they are accepted.
We all absorb some radiation all the time. Background radiation comes mostly from natural sources — radon gas seeping from the ground (the largest single source in much of the UK, notably Cornwall's granite), cosmic rays, rocks, food and drink — plus a smaller human-made slice, chiefly medical X-rays. Absorbed dose is measured in sieverts (Sv), which weigh both the amount and the harmfulness of the radiation. A single chest X-ray is a fraction of a millisievert; a transatlantic flight adds a little more cosmic exposure.
How dangerous an isotope is depends on its half-life and its radiation type. A short half-life means intense activity that fades fast; a long half-life means weak activity that lingers for generations. Alpha emitters are relatively harmless outside the body — skin stops them — but devastating if swallowed or inhaled, where they ionise living tissue directly. Those same properties are turned to use: gamma sources sterilise surgical instruments and treat tumours, tracers with short half-lives are injected for medical imaging, and radiation is used to check for flaws in engineering. Every use is a judgement of benefit against risk — the exact evaluation examiners ask you to make.
ModelFission and fusion — splitting apart, forcing together
Nuclear fission is the splitting of a large, unstable nucleus (uranium-235 or plutonium-239) into two smaller daughter nuclei, releasing energy and, usually, two or three neutrons. Those neutrons can strike further nuclei and trigger a chain reaction. Left unchecked the chain runs away — that is a bomb; in a reactor, control rods absorb spare neutrons and a moderator slows them, keeping the reaction steady so the heat can raise steam and drive turbines.
Nuclear fusion is the opposite: two light nuclei, such as isotopes of hydrogen, join to form a heavier nucleus, releasing far more energy per kilogram than fission. Fusion powers the Sun and every star. The catch is the conditions: the nuclei are both positive and repel fiercely, so only enormous temperatures and pressures push them close enough to fuse — which is why a self-sustaining fusion power station remains one of the hardest engineering problems on Earth, even though the fuel is effectively limitless. Keep the direction straight: fission breaks a big nucleus, fusion builds from small ones.
VocabularyKey terms the mark scheme pays for
TrapsMisconceptions that cost marks
ExamWhat examiners want
In nuclear-equation questions, balance the two rows separately and write the check: mass numbers on top must sum equally, atomic numbers on the bottom must sum equally. For beta decay remember the electron counts as \({}^{0}_{-1}\text{e}\), so the atomic number rises by 1 while the mass number is unchanged — the sign on that \(-1\) is the mark students most often lose.
For half-life, never estimate: halve the starting value repeatedly, count the halvings, and divide the time by that number. Quote the net decline as a ratio (7:1 after three half-lives, not just 'an eighth left') when the question asks how much has decayed, and state units on the half-life.
When you compare alpha, beta and gamma, always give both properties together — ionising power and penetration — because they trade off, and pin each to what stops it (paper, a few millimetres of aluminium, thick lead). On contamination-versus-irradiation and uses-of-radiation questions, structure the answer as a risk-versus-benefit judgement and name a real precaution (shielding, distance, limited time, sealed sources). Examiners reward the evaluation, not just the fact.