P7: Radioactivity

What you'll learn

This topic covers the structure of atoms, radioactive decay processes, and how we detect and use nuclear radiation safely. You'll learn to perform half-life calculations, interpret decay graphs, and understand real-world applications from medical imaging to nuclear power. This module accounts for approximately 10% of your OCR GCSE Physics examination.

Key terms and definitions

Isotope — atoms of the same element with the same number of protons but different numbers of neutrons, resulting in different mass numbers.

Radioactive decay — the random, spontaneous process by which unstable nuclei emit radiation to become more stable.

Half-life — the time taken for half the nuclei in a radioactive sample to decay, or for the activity to fall to half its initial value.

Activity — the rate at which nuclei in a radioactive source decay, measured in becquerels (Bq), where 1 Bq = 1 decay per second.

Ionisation — the process of adding or removing electrons from atoms to create charged particles (ions).

Background radiation — low-level ionising radiation that is always present in the environment from natural and artificial sources.

Alpha particle (α) — a type of nuclear radiation consisting of two protons and two neutrons (helium nucleus), with a charge of +2.

Beta particle (β) — a high-energy electron emitted from the nucleus when a neutron converts to a proton.

Core concepts

Atomic structure and isotopes

The atom consists of a small, dense nucleus containing protons and neutrons, surrounded by electrons in shells. The atomic number (Z) indicates the number of protons, while the mass number (A) indicates the total number of protons and neutrons.

Isotopes are represented using notation: ᴬ₂X, where X is the element symbol. For example:

• Carbon-12: ¹²₆C (6 protons, 6 neutrons)
• Carbon-14: ¹⁴₆C (6 protons, 8 neutrons)

Both are carbon isotopes because they have 6 protons, but carbon-14 is radioactive due to its unstable nucleus. The neutron-to-proton ratio determines nuclear stability — isotopes with too many or too few neutrons are unstable and undergo radioactive decay.

Types of nuclear radiation

There are three main types of ionising radiation you must know for OCR GCSE:

Alpha radiation (α)

• Composition: 2 protons + 2 neutrons (helium nucleus)
• Symbol: ⁴₂He or α
• Charge: +2
• Penetration: stopped by paper or a few centimetres of air
• Ionising power: highly ionising
• Range in air: approximately 3–5 cm
• Deflection in fields: deflected by electric and magnetic fields

Beta radiation (β)

• Composition: high-energy electron from nucleus
• Symbol: ⁰₋₁e or β
• Charge: –1
• Penetration: stopped by thin aluminium (3–5 mm)
• Ionising power: moderately ionising
• Range in air: up to 1 metre
• Deflection in fields: deflected by electric and magnetic fields (opposite direction to alpha)

Gamma radiation (γ)

• Composition: electromagnetic wave/photon
• Symbol: γ
• Charge: 0 (neutral)
• Penetration: reduced by thick lead or several metres of concrete
• Ionising power: weakly ionising
• Range in air: unlimited (follows inverse square law)
• Deflection in fields: not deflected by electric or magnetic fields

Nuclear decay equations

You must be able to write and balance nuclear equations for alpha and beta decay.

Alpha decay: When a nucleus emits an alpha particle, the mass number decreases by 4 and the atomic number decreases by 2.

Example: Radium-226 decaying to radon-222 ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

Beta decay: When a nucleus emits a beta particle, a neutron converts to a proton. The mass number stays the same and the atomic number increases by 1.

Example: Carbon-14 decaying to nitrogen-14 ¹⁴₆C → ¹⁴₇N + ⁰₋₁e

The total mass number and total atomic number must be equal on both sides of the equation.

Radioactive decay and half-life

Radioactive decay is random — you cannot predict which nucleus will decay next or when. However, it is also spontaneous — not affected by external conditions like temperature, pressure, or chemical bonding.

The half-life is constant for a given isotope. Different isotopes have vastly different half-lives:

• Polonium-214: 0.00016 seconds
• Iodine-131: 8 days
• Carbon-14: 5,730 years
• Uranium-238: 4.5 billion years

Calculating remaining amount after decay:

After n half-lives:

• Remaining nuclei = original amount × (1/2)ⁿ
• Activity = original activity × (1/2)ⁿ

You can also use the formula: Number of half-lives (n) = total time elapsed ÷ half-life

Activity and count rate

Activity is measured in becquerels (Bq), where 1 Bq = 1 decay per second. A detector measures count rate (counts per second or counts per minute), which is related to but not identical to activity because:

• Not all radiation reaches the detector
• Not all radiation entering the detector is detected

Count rate decreases over time following the same half-life pattern as activity. When measuring count rate, you must subtract background radiation to find the corrected count rate:

Corrected count rate = measured count rate – background count rate

Background radiation

Background radiation comes from natural and artificial sources:

Natural sources (approximately 85%):

• Radon gas from rocks (mainly granite) — largest contributor in UK (around 50%)
• Cosmic rays from space
• Rocks and soil containing radioactive materials
• Food and drink (e.g., potassium-40 in bananas)
• Living organisms

Artificial sources (approximately 15%):

• Medical procedures (X-rays, radiotherapy)
• Nuclear weapons testing (fallout)
• Nuclear power stations
• Nuclear accidents (e.g., Chernobyl, Fukushima)

Background radiation varies by location — higher in Cornwall and parts of Scotland due to granite rocks, and higher at altitude due to cosmic rays.

Uses and hazards of radiation

Medical uses:

• Radiotherapy: gamma rays target and destroy cancer cells
• Medical tracers: gamma-emitting isotopes (e.g., technetium-99m, half-life 6 hours) injected to image organs
• Sterilisation: gamma rays kill bacteria on medical equipment

Industrial uses:

• Thickness monitoring: beta sources control paper/metal thickness during manufacturing
• Smoke detectors: alpha sources (americium-241) ionise air to detect smoke
• Carbon dating: measuring carbon-14 (half-life 5,730 years) in organic materials to determine age

Safety precautions:

• Keep distance from sources (inverse square law)
• Minimise exposure time
• Use shielding appropriate to radiation type
• Handle with tongs or robots
• Store in lead-lined containers
• Wear dosimeters to monitor exposure
• Never point sources at people

Hazards depend on exposure type:

Outside the body (irradiation):

• Alpha: minimal risk (stopped by skin)
• Beta: moderate risk (skin burns)
• Gamma: high risk (penetrates body, damages cells)

Inside the body (contamination):

• Alpha: very high risk (highly ionising, damages local tissue)
• Beta: high risk
• Gamma: moderate risk (mostly passes through)

Ionising radiation damages living cells by ionising atoms in DNA, causing mutations that may lead to cancer.

Nuclear fission and chain reactions

Nuclear fission is the splitting of a large, unstable nucleus (usually uranium-235 or plutonium-239) into two smaller nuclei, releasing energy and neutrons.

The process in a nuclear reactor:

1. A neutron is absorbed by a uranium-235 nucleus
2. The nucleus becomes unstable and splits
3. Two or three neutrons are released plus energy
4. These neutrons can cause further fission — a chain reaction

Control in nuclear reactors:

• Moderator (water or graphite): slows neutrons to increase fission probability
• Control rods (boron): absorb excess neutrons to control reaction rate
• Lowering control rods: more neutron absorption, slower reaction
• Raising control rods: fewer neutrons absorbed, faster reaction

The energy released heats water to produce steam, driving turbines to generate electricity. Nuclear power produces no greenhouse gases during operation but creates radioactive waste requiring long-term storage.

Worked examples

Example 1: Half-life calculation

Question: A radioactive sample has an initial activity of 800 Bq. After 60 days, its activity is 100 Bq. Calculate the half-life of this isotope. [3 marks]

Solution:

• Initial activity = 800 Bq
• Final activity = 100 Bq
• After 1 half-life: 800 → 400 Bq [1 mark]
• After 2 half-lives: 400 → 200 Bq
• After 3 half-lives: 200 → 100 Bq [1 mark]
• Number of half-lives = 3
• Half-life = 60 days ÷ 3 = 20 days [1 mark]

Example 2: Nuclear equation

Question: Complete the nuclear equation for the alpha decay of polonium-210: ²¹⁰₈₄Po → ____ + ⁴₂He [2 marks]

Solution:

• Mass number: 210 = ? + 4, so ? = 206 [1 mark]
• Atomic number: 84 = ? + 2, so ? = 82
• Element with atomic number 82 is lead (Pb)
• Answer: ²⁰⁶₈₂Pb [1 mark]

Example 3: Count rate with background radiation

Question: A student measures a count rate of 250 counts per minute from a radioactive source. The background count rate is 30 counts per minute. After 24 hours, the measured count rate is 140 counts per minute. Calculate the half-life of the source. [4 marks]

Solution:

• Initial corrected count rate = 250 – 30 = 220 counts per minute [1 mark]
• Final corrected count rate = 140 – 30 = 110 counts per minute [1 mark]
• 220 → 110 is one half-life [1 mark]
• Half-life = 24 hours [1 mark]

Common mistakes and how to avoid them

• Forgetting to subtract background radiation — always subtract the background count before performing half-life calculations. The background is constant and doesn't decay.

• Confusing mass number and atomic number — mass number (A) is the top number (protons + neutrons); atomic number (Z) is the bottom number (protons only). Remember: mass is more, so it's on top.

• Saying decay is affected by conditions — radioactive decay is random and spontaneous. Never state that temperature, pressure, or chemical bonding affects the decay rate.

• Mixing up penetration and ionisation — alpha has high ionising power but low penetration; gamma has low ionising power but high penetration. They are inversely related.

• Incorrect use of half-life formula — when using (1/2)ⁿ, n is the number of half-lives, not the time. Calculate n first by dividing total time by the half-life.

• Wrong safety precautions for different radiations — match shielding to radiation type: paper for alpha, aluminium for beta, lead for gamma. Don't suggest lead gloves for alpha sources.

Exam technique for "P7: Radioactivity"

• "Describe" versus "Explain" — Describe means state what happens; Explain means give reasons why. For example: Describe: "The count rate decreases." Explain: "The count rate decreases because nuclei decay, reducing the number of radioactive atoms remaining."

• Nuclear equations require balanced answers — check both mass numbers and atomic numbers balance on both sides. Show your working by writing the numbers above and below the element symbol clearly.

• Half-life questions often need multiple steps — show each halving clearly in your working (e.g., 800 → 400 → 200 → 100). This earns method marks even if your final answer is incorrect.

• Extended response questions on safety — include specific points about distance, time, shielding, and handling. Generic statements like "be careful" score zero marks. Relate precautions to the type of radiation involved.

Quick revision summary

Radioactive decay is random and spontaneous, producing alpha, beta, or gamma radiation. Alpha particles are helium nuclei (low penetration, high ionisation); beta particles are electrons (moderate properties); gamma rays are electromagnetic waves (high penetration, low ionisation). Half-life is the time for activity to halve. Always subtract background radiation before calculations. Nuclear equations must balance mass and atomic numbers. Radiation has medical and industrial uses but requires safety precautions. Nuclear fission releases energy when heavy nuclei split, controlled by moderators and control rods in reactors.