Radioactivity: Atoms and Nuclear Decay
Atomic Structure and Isotopes
Every atom has a nucleus made of protons (positive charge) and neutrons (no charge). Electrons (negative charge) occupy energy levels around the nucleus. The number of protons defines the element — carbon always has 6 protons, oxygen always has 8. In a neutral atom, the number of electrons equals the number of protons.
Isotopes are atoms of the same element with different numbers of neutrons. They have the same atomic number (protons) but different mass numbers (protons + neutrons). We write isotopes in nuclear notation: \(^A_Z X\) where \(A\) is the mass number and \(Z\) is the atomic number. For example, carbon-12 (\(^{12}_{6}\text{C}\)) has 6 protons and 6 neutrons, while carbon-14 (\(^{14}_{6}\text{C}\)) has 6 protons and 8 neutrons. Some isotopes have unstable nuclei that emit radiation spontaneously — these are radioactive isotopes.
Isotopes have the same atomic number (protons) but different mass numbers (protons + neutrons). Radioactive decay is a random, spontaneous process — individual decay events cannot be predicted.
Types of Radiation
Unstable nuclei emit three main types of radiation, each with different properties:
• Alpha (α) particles — 2 protons + 2 neutrons (equivalent to a helium-4 nucleus, \(^4_2\text{He}\)). Strongly ionising because of their large charge and mass. Weakly penetrating: stopped by a sheet of paper, a few centimetres of air, or skin.
• Beta (β) particles — a high-speed electron emitted when a neutron converts into a proton inside the nucleus. Moderately ionising and moderately penetrating: stopped by a few millimetres of aluminium.
• Gamma (γ) rays — electromagnetic radiation emitted when the nucleus releases excess energy. Weakly ionising but highly penetrating: only significantly reduced by thick lead or several metres of concrete. Often emitted alongside alpha or beta decay.
In nuclear equations, both mass numbers and atomic numbers must balance on each side of the arrow.
Alpha decay: the nucleus loses 2 protons and 2 neutrons. Mass number decreases by 4, atomic number decreases by 2. Example — uranium-238 decays to thorium-234:
$$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$$
Beta decay: a neutron converts to a proton, emitting an electron from the nucleus. Mass number stays the same, atomic number increases by 1. Example — carbon-14 decays to nitrogen-14:
$$^{14}_{6}\text{C} \rightarrow ^{14}_{7}\text{N} + ^{0}_{-1}\text{e}$$
Gamma emission: the nucleus releases excess energy as a gamma ray. No change to mass number or atomic number — it is not shown as a separate particle in the equation.
Alpha: −4 mass, −2 atomic. Beta: same mass, +1 atomic. Gamma: no change. Both mass numbers and atomic numbers must balance in every nuclear equation.
Ionisation and Detecting Radiation
Ionisation occurs when radiation knocks electrons from atoms, creating charged ions. Alpha particles are the most ionising — they transfer their energy quickly because of their large charge and mass. Gamma rays are the least ionising but travel the furthest. Ionisation in living cells can damage DNA, potentially causing mutations or cancer. The greater the ionising power, the lower the penetrating power — alpha radiation is stopped quickly because it transfers its energy so readily.
The activity of a radioactive source is measured in becquerels (Bq), where 1 Bq = 1 decay per second. In the laboratory, a Geiger–Müller (GM) tube detects ionising radiation and records a count rate in counts per second or per minute. When measuring a source, always account for background radiation — the low-level radiation always present in the environment from natural sources (radon gas, cosmic rays, food and building materials) and, to a much smaller extent, artificial sources.
Half-Life
Half-life is the time taken for half of the unstable nuclei in a sample to decay — equivalently, the time for the activity to halve. Radioactive decay is random: we cannot predict when any individual nucleus will decay, but statistical behaviour of large numbers of nuclei is reliable and predictable.
After one half-life, half the original unstable nuclei remain. After two half-lives, a quarter remain. After three, an eighth. For example, if a sample has an activity of 800 Bq and its half-life is 3 hours, after 9 hours (3 half-lives): \(800 \rightarrow 400 \rightarrow 200 \rightarrow 100\) Bq.
On a graph of activity against time, the curve falls steeply at first and then more gradually — this is an exponential decay curve. To read the half-life from the graph: identify the starting activity, find the time at which it has halved, and read across. Then check: does the activity halve again in the same time interval? It should — half-life is constant for a given isotope regardless of how much of the material is left.
In the laboratory, plotting count rate against time (after subtracting background count rate) gives the same exponential shape. The corrected count rate should be used — not the raw reading — to ensure you are measuring only the decay of the source.
Half-life is the time for activity (or number of unstable nuclei) to halve. It is constant for a given isotope. Radioactive decay cannot be sped up or slowed down by changing physical conditions such as temperature or pressure.