Radioactivity and Half-Life
How Our Understanding of the Atom Developed
The model of the atom has changed several times as new evidence became available — a classic example of how scientific explanations develop with evidence (IaS3). Early in the 19th century, John Dalton proposed that matter is made of tiny, indivisible solid spheres. This explained chemical reactions but had no internal structure.
In the late 19th century, J.J. Thomson discovered the electron and replaced Dalton's model with the plum pudding model — a positive sphere with electrons dotted through it like plums in a pudding. This was overturned in 1910–1911 when Rutherford, Geiger and Marsden fired alpha particles at thin gold foil. Most particles passed straight through, but some deflected sharply and a small fraction bounced back. The only explanation was a tiny, dense, positively charged nucleus surrounded by mostly empty space.
The Rutherford-Geiger-Marsden alpha particle scattering experiment (published 1911) provided evidence for the nuclear model. Bohr later refined this by proposing electrons occupy fixed energy levels (shells) around the nucleus. James Chadwick discovered the neutron in 1932, completing the modern picture.
Atomic Structure
Every atom has a nucleus containing protons and neutrons, surrounded by electrons in energy levels. Atoms are extremely small — on the order of \(10^{-10}\) m across — and the nucleus is about a hundred-thousandth of the diameter of the whole atom.
An element is defined by its number of protons (atomic number). Different forms of the same element that have different numbers of neutrons are called isotopes. We write isotopes in nuclear notation as \(^A_Z X\), where \(A\) is the mass number (protons + neutrons) and \(Z\) is the atomic number (protons).
Types of Radioactive Decay
Some atomic nuclei are unstable and emit radiation to become more stable — they are radioactive. Radioactive decay is a random process: you cannot predict when any particular nucleus will decay. There are four types of emission:
Alpha (\(\alpha\)) — two protons and two neutrons (a helium-4 nucleus: \(^4_2\text{He}\)). Strongly ionising; stopped by a few centimetres of air or a sheet of paper. In decay, mass number decreases by 4 and atomic number decreases by 2.
Beta (\(\beta\)) — a high-speed electron emitted when a neutron in the nucleus converts to a proton. Moderately ionising; stopped by a few millimetres of aluminium. Atomic number increases by 1; mass number unchanged.
Gamma (\(\gamma\)) — high-frequency electromagnetic radiation emitted from the nucleus after other decay. Weakly ionising; only significantly reduced by several centimetres of lead or metres of concrete. No change in mass number or atomic number.
Neutron emission — occasionally an unstable nucleus emits a neutron. Mass number decreases by 1; atomic number unchanged.
Example nuclear equation for alpha decay of radium-226: \(^{226}_{88}\text{Ra} \rightarrow ^{222}_{86}\text{Rn} + ^4_2\text{He}\). Check: top numbers balance (226 = 222 + 4) ✓; bottom numbers balance (88 = 86 + 2) ✓.
Ionising power and penetrating power are inversely related: alpha is most ionising, least penetrating (stopped by paper); gamma is least ionising, most penetrating (requires lead or thick concrete to reduce significantly).
Half-Life
As a radioactive sample decays, the number of unstable nuclei decreases over time, so the activity (number of decays per second) also decreases. The half-life of a radioactive isotope is the time it takes for either the number of undecayed nuclei, or the activity (measured in becquerels, Bq), to halve.
After one half-life: half the original nuclei remain. After two half-lives: a quarter remain. After three half-lives: one eighth remain. The net decline can be expressed as a ratio: after \(n\) half-lives, the fraction remaining is \(\frac{1}{2^n}\). This pattern can be used to read off half-life from an activity-time graph, or to calculate the fraction remaining after a given number of half-lives.
A radioactive sample has an initial activity of 3200 Bq. After 60 days the activity is 200 Bq. Calculate the half-life.
Count the halvings: 3200 → 1600 → 800 → 400 → 200. That is 4 halvings.
4 half-lives = 60 days, so one half-life = \(\frac{60}{4} = 15\) days.
You can also calculate from an activity-time graph by reading off the time it takes for activity to halve at any point on the decay curve — the half-life is the same throughout (a property of exponential decay). The ratio of activity after \(n\) half-lives to the original activity is \(\frac{1}{2^n}\).
Contamination and Irradiation
Contamination means radioactive material has been deposited on or inside the body (e.g. ingested or inhaled). This is particularly dangerous because the source continues to irradiate nearby cells indefinitely until it decays or is removed. Irradiation is exposure to an external radiation source — once the source is removed, exposure stops. Alpha particles are especially dangerous if a source is inside the body (high ionising power), but outside the body they are stopped by skin and pose less risk.