Radioactivity and Nuclear Decay: GCSE Physics Guide

Predict first: when an unstable nucleus ejects a particle, what happens? The nucleus transforms into a different element. Radioactivity is a spontaneous, random property of certain atomic nuclei — it cannot be triggered or stopped by any chemical or physical process — and understanding it is essential for GCSE physics and nuclear medicine.

What is radioactivity?

Radioactivity is the spontaneous emission of radiation from an unstable atomic nucleus. Some nuclei are unstable because they have too many neutrons, too many protons, or simply too much energy. To become more stable, these nuclei undergo nuclear decay, emitting particles or electromagnetic radiation (or both) in the process.

Key features of radioactive decay:

It is spontaneous — it cannot be started, stopped, or accelerated by chemical or physical means (temperature, pressure, light)

It is random — you cannot predict exactly when any individual nucleus will decay, only the probability

It is independent of the chemical environment — whether the atom is in a compound or not makes no difference

The activity of a radioactive source is measured in becquerels (Bq) — one becquerel equals one nuclear decay per second.

What are the three types of nuclear radiation?

Type | Particle / wave | Charge | Relative mass | Penetrating power | Stopped by | Ionising ability
Alpha (α) | Helium-4 nucleus (2 protons + 2 neutrons) | +2 | 4 | Low | Paper or a few cm of air | Highest
Beta (β) | Fast-moving electron (from neutron → proton + electron) | −1 | ~1/2000 | Medium | A few mm of aluminium | Medium
Gamma (γ) | Electromagnetic wave (very short wavelength) | 0 | 0 | High | Several cm of lead or metres of concrete | Lowest

Key relationships:

Greater ionising ability → more energy transferred to matter per unit path → less penetrating

Alpha is the most ionising (strips electrons from many atoms per mm of travel) but cannot penetrate skin

Gamma is the least ionising but travels through the body, making external exposure more dangerous

What is nuclear decay and how does it change the nucleus?

Nuclear decay changes the composition of the nucleus, often transforming one element into another (transmutation).

Alpha decay: The nucleus loses 2 protons and 2 neutrons (a helium-4 nucleus):

Mass number decreases by 4

Atomic number decreases by 2

Example: Radium-226 → Radon-222 + alpha particle

²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

Beta decay: A neutron converts to a proton, emitting a fast electron (beta particle):

Mass number stays the same

Atomic number increases by 1

Example: Carbon-14 → Nitrogen-14 + beta particle

¹⁴₆C → ¹⁴₇N + ⁰₋₁e

Gamma emission: Gamma rays are often emitted alongside alpha or beta decay as the nucleus releases excess energy. Gamma emission does not change the mass number or atomic number — only the energy of the nucleus changes.

What is half-life and how do you calculate it?

The half-life of a radioactive isotope is the time taken for half the radioactive nuclei in a sample to decay. Because decay is random, it is a statistical property — after one half-life, approximately half the original nuclei remain undecayed.

Worked example:

A sample initially contains 80 g of a radioactive isotope with a half-life of 30 minutes. How long will it take for the activity to fall to 10 g of undecayed isotope?

Number of half-lives | Time elapsed | Mass remaining
0 | 0 min | 80 g
1 | 30 min | 40 g
2 | 60 min | 20 g
3 | 90 min | 10 g

After 3 half-lives (3 × 30 = 90 minutes), 10 g of the original isotope remains undecayed.

General formula: N = N₀ × (½)ⁿ, where N is the remaining amount, N₀ is the initial amount, and n is the number of half-lives elapsed.

Half-lives range from microseconds (highly unstable isotopes) to billions of years (very stable isotopes like uranium-238, half-life ~4.5 billion years).

What are the uses of radioactivity?

Radioactivity has many important applications:

Application | Type of radiation used | Why
Medical imaging (PET scans) | Gamma (via positron-emitting tracers) | Gamma penetrates the body so detectors outside can locate the source
Cancer radiotherapy | Gamma | Focused gamma beams kill tumour cells
Sterilisation of medical equipment | Gamma | Gamma kills bacteria without heating the equipment
Smoke detectors | Alpha (americium-241) | Alpha ionises air between electrodes; smoke particles absorb ions, reducing current and triggering the alarm
Thickness gauges (paper, metal) | Beta | Beta penetration is sensitive to small changes in thickness
Carbon-14 dating | Beta (carbon-14 decay) | The known half-life of ¹⁴C (5,730 years) lets scientists date organic materials up to ~50,000 years old

What are the dangers of ionising radiation and how do we protect ourselves?

Ionising radiation damages living cells by stripping electrons from atoms, breaking chemical bonds. The biological effects depend on:

Type of radiation (alpha most dangerous if inhaled or ingested; gamma most dangerous externally)

Dose received (measured in sieverts, Sv)

Duration of exposure

Health risks:

DNA damage leading to mutations, which may cause cancer (stochastic effect)

At very high doses: acute radiation syndrome (radiation sickness), organ failure, death (deterministic effect)

Protection methods:

Method | Effect
Increase distance | Intensity falls with distance squared (inverse square law)
Reduce exposure time | Less time = less dose received
Shielding | Lead aprons for gamma; aluminium for beta; paper/clothing for alpha
Containment | Radioactive materials handled in sealed glove boxes; nuclear waste stored in lead-lined containers

Workers who handle radioactive materials wear dosimeters (radiation badges) to monitor cumulative dose.

Frequently asked questions

What is the difference between alpha, beta, and gamma radiation?

Alpha radiation consists of helium-4 nuclei (2 protons + 2 neutrons), is positively charged (+2), and is stopped by paper or skin — but is the most ionising type. Beta radiation consists of fast electrons emitted from the nucleus when a neutron converts to a proton, is negatively charged (−1), and is stopped by a few millimetres of aluminium. Gamma radiation is high-energy electromagnetic waves with no charge and no mass, requiring centimetres of lead or metres of concrete to absorb, but it is the least ionising per unit path length.

What is half-life in simple terms?

Half-life is the time it takes for half the radioactive atoms in a sample to decay. If you start with 1,000 radioactive atoms and the half-life is 10 minutes, after 10 minutes you will have approximately 500 undecayed atoms; after 20 minutes approximately 250; after 30 minutes approximately 125, and so on. The activity (rate of decay) halves with every half-life. The half-life is a fixed property of each radioactive isotope and cannot be changed by physical or chemical means.

Why is alpha radiation the most dangerous inside the body but least dangerous outside?

Alpha particles are the most heavily ionising form of radiation — they transfer large amounts of energy to surrounding atoms within a very short distance, causing extensive DNA damage. However, they are stopped by a sheet of paper or the outer dead layer of skin, so external alpha sources pose little risk. The danger arises when alpha-emitting material is inhaled, ingested, or injected — for example, the polonium-210 used to poison Alexander Litvinenko in 2006 was an alpha emitter that caused lethal damage to his internal organs from inside.

What is the difference between background radiation and radiation from a source?

Background radiation is low-level ionising radiation present everywhere in the environment from natural and artificial sources. Natural sources include radon gas (from rocks, especially granite), cosmic rays from space, radiation from naturally occurring radioactive isotopes in food and building materials, and radiation from the Earth's rocks and soil. Artificial background radiation comes from medical procedures, nuclear power plants, and nuclear weapons testing. Background radiation must always be subtracted from measurements of a radioactive source to get accurate results in experiments.

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