Radioactivity
Atomic Structure and Isotopes
Every atom has a nucleus made of protons (positive charge) and neutrons (no charge). Electrons (negative charge) orbit the nucleus at different energy levels. The number of protons defines the element (its atomic number). 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 but different mass numbers. We write isotopes using nuclear notation: \(^A_Z X\) where \(A\) is the mass number (protons + neutrons) and \(Z\) is the atomic number (protons). 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.
Isotopes are atoms of the same element with different numbers of neutrons. Some isotopes have unstable nuclei that emit radiation — this is radioactive decay. The process is random and spontaneous.
Types of Radiation
Unstable nuclei can emit three main types of radiation (P4.3d):
• Alpha (\(\alpha\)) particles — 2 protons + 2 neutrons (a helium nucleus, \(^4_2\text{He}\)). Strongly ionising because of their large charge and mass. Weakly penetrating: stopped by paper, skin or a few centimetres of air.
• Beta (\(\beta\)) particles — a high-speed electron emitted when a neutron converts into a proton. Moderately ionising and moderately penetrating. Stopped by a few millimetres of aluminium.
• Gamma (\(\gamma\)) rays — electromagnetic radiation from the nucleus. Weakly ionising but highly penetrating. Only significantly reduced by thick lead or several metres of concrete.
Alpha decay: the nucleus loses 2 protons and 2 neutrons. Mass number decreases by 4, atomic number decreases by 2. Example:
$$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$$
Beta decay: a neutron converts to a proton, emitting a high-speed electron. Mass number stays the same, atomic number increases by 1. Example:
$$^{14}_{6}\text{C} \rightarrow ^{14}_{7}\text{N} + ^{0}_{-1}\text{e}$$
Gamma emission: the nucleus releases excess energy as a gamma ray. No change to mass number or atomic number. Gamma is often emitted alongside alpha or beta decay.
In all nuclear equations, the mass numbers and atomic numbers must balance on both sides.
Alpha: mass number −4, atomic number −2. Beta: mass number unchanged, atomic number +1. Gamma: no change to either. Mass and atomic numbers must balance in decay equations.
Ionisation
Ionisation occurs when radiation knocks electrons from atoms, creating ions. Alpha particles are the most ionising (because of their large charge and mass), followed by beta, then gamma. Ionisation in living cells can damage DNA, potentially causing mutations or cancer. The greater the ionising power, the more damage to cells — but higher ionising power also means lower penetrating power, because the radiation transfers its energy quickly.
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 connected to a counter measures the count rate (counts per second or per minute), which is proportional to the activity of the source.
When investigating radioactivity, you must account for background radiation. Take a background count (with no source present), then subtract it from all measurements. This corrected count rate represents radiation from the source alone. Radioactive decay is random, so repeating measurements and calculating averages improves reliability.
The nuclear model of the atom developed over time. Thomson proposed the ‘plum pudding’ model (positive charge spread throughout with embedded electrons). Rutherford’s gold foil experiment (1909) disproved this: most alpha particles passed straight through the foil, but some were deflected and a few bounced back. This showed the atom is mostly empty space with a tiny, dense, positive nucleus. Bohr later refined the model with electrons in fixed energy levels (orbits) around the nucleus.
Half-Life
Half-life is the time taken for the number of radioactive nuclei (or the activity) of a sample to halve. Radioactive decay is random and unpredictable — we cannot predict when an individual nucleus will decay, but we can predict the average behaviour of a large number of nuclei (P4.3j).
After one half-life, half the original 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.
The fraction of radioactive nuclei remaining after \(n\) half-lives can be calculated using the formula: $$\text{fraction remaining} = \left(\frac{1}{2}\right)^n$$ For example, after 5 half-lives the fraction remaining is \(\left(\frac{1}{2}\right)^5 = \frac{1}{32}\). If the original activity was 6400 Bq, the activity after 5 half-lives would be \(6400 \times \frac{1}{32} = 200\) Bq.
Half-life is the time for half the unstable nuclei to decay. Decay is random — you can’t predict individual atoms, only the average behaviour of many atoms.
After \(n\) half-lives, the fraction remaining is \(\left(\frac{1}{2}\right)^n\). This formula lets you calculate the remaining activity or mass without repeated halving.
Background radiation is the low-level radiation that exists all around us. Natural sources include radon gas from rocks (the largest source in the UK), cosmic rays from space, and radioactive isotopes in food and building materials. Artificial sources include medical X-rays and the nuclear industry, but these contribute only a small fraction of total exposure.
When measuring the count rate of a radioactive source in the lab, you must subtract the background count rate first to get the corrected count rate. This ensures your measurement reflects only the source, not the environment.