Radioactivity: Emissions, Half-Life and Equations

Atomic Structure and Isotopes

Every atom has a nucleus made of protons (positive charge) and neutrons (no charge). Electrons, which carry negative charge, occupy energy levels around the nucleus. The number of protons is the atomic number and defines which element the atom is. 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. Nuclear notation is written as $^A_Z X$, where $A$ is the mass number (protons + neutrons) and $Z$ is the atomic number. For example, carbon-12 ($^{12}_{6}\text{C}$) has 6 protons and 6 neutrons; carbon-14 ($^{14}_{6}\text{C}$) has 6 protons and 8 neutrons.

Key Fact

Isotopes have the same number of protons (same element) but different numbers of neutrons. Unstable isotopes have nuclei that decay spontaneously, emitting ionising radiation. Radioactive decay is random and cannot be predicted for any individual nucleus.

Types of Ionising Radiation

Unstable nuclei emit three main types of ionising radiation (some also emit neutrons):

• Alpha ($\alpha$) particles — a helium nucleus ($^4_2\text{He}$): 2 protons + 2 neutrons. Strongly ionising because of their large charge and mass. Weakly penetrating: stopped by a single sheet of paper or a few centimetres of air.
• Beta ($\beta$) particles — a high-speed electron produced when a neutron converts into a proton inside the nucleus. Moderately ionising and penetrating. Stopped by a few millimetres of aluminium.
• Gamma ($\gamma$) rays — high-energy electromagnetic radiation emitted from the nucleus. Weakly ionising but highly penetrating: only significantly reduced by several centimetres of lead or metres of concrete.

Increasing ionising power: $\gamma$ < $\beta$ < $\alpha$. Increasing penetrating power: $\alpha$ < $\beta$ < $\gamma$. There is a trade-off — the more ionising a particle is, the more energy it deposits quickly and the less it penetrates.

In any nuclear equation, the mass numbers and atomic numbers must balance on both sides.

Alpha decay: nucleus loses 2 protons and 2 neutrons. Mass number decreases by 4; atomic number decreases by 2.

$$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$$

Beta decay: a neutron converts to a proton. Mass number unchanged; atomic number increases by 1.

$$^{14}_{6}\text{C} \rightarrow ^{14}_{7}\text{N} + ^{0}_{-1}\text{e}$$

Gamma emission: no change to mass number or atomic number. Gamma is often emitted alongside alpha or beta decay as the nucleus releases excess energy.

Key Fact

Alpha decay: mass number −4, atomic number −2. Beta decay: mass number unchanged, atomic number +1. Gamma emission: no change to either. Numbers must balance on both sides of a nuclear equation.

Ionisation and Detecting Radiation

Ionising radiation knocks electrons from atoms, creating ions. This damages living cells by breaking chemical bonds and can mutate DNA, potentially causing cancer. Alpha particles are the most ionising, which is why swallowed or inhaled alpha sources are the most biologically dangerous, even though they are stopped by skin externally.

In the laboratory, a Geiger–Müller (GM) tube connected to a counter detects ionising radiation by measuring the electrical pulses produced when radiation enters the tube. The activity of a radioactive source is measured in becquerels (Bq), where 1 Bq = 1 nuclear decay per second. Always measure and subtract the background count rate (radiation present without the source) before recording results.

Half-Life

Half-life is the time taken for the number of unstable (undecayed) nuclei in a sample to halve — or equivalently for the activity to halve. Radioactive decay is random and spontaneous: you cannot predict when any individual nucleus will decay, but you can predict the average rate of decay for a large sample.

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 initial 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 is given by: $$\text{fraction remaining} = \left(\frac{1}{2}\right)^n$$ For example, after 5 half-lives: $\left(\frac{1}{2}\right)^5 = \frac{1}{32}$. If the original count rate was 6400 Bq, after 5 half-lives it would be $6400 \times \frac{1}{32} = 200$ Bq.

Background radiation is always present in the environment. Natural sources include radon gas from rocks (the largest source of exposure in the UK), cosmic rays from space, and radioactive materials in food and building materials. Artificial sources include medical procedures (such as X-rays) and discharges from the nuclear industry, though these contribute a much smaller proportion of the total.

Because background radiation varies from place to place and over time, you must take a background count before any laboratory measurement of a radioactive source, then subtract it from your readings to get the corrected count rate from the source alone.

Contamination and Irradiation

It is essential to distinguish between two different hazards:

Contamination occurs when radioactive material is deposited on or inside a person or object. The source continues to emit radiation in close contact with tissues. This is generally considered more dangerous than irradiation because the exposure is continuous and cannot be stopped by simply moving away. It is removed by washing or decontamination procedures.

Irradiation occurs when a person is exposed to radiation from an external source. The person does not themselves become radioactive. Once the source is removed, the irradiation stops. The risk depends on the type of radiation, dose received and duration of exposure.