What you'll learn
This revision guide covers all aspects of radioactivity required for WJEC GCSE Physics examinations. You will understand atomic structure, the three types of nuclear radiation, how radioactive decay occurs, and how to perform half-life calculations. These topics frequently appear in both short-answer and calculation questions worth significant marks.
Key terms and definitions
Radioactive decay — the spontaneous and random emission of radiation from unstable atomic nuclei, which cannot be predicted for individual atoms or affected by external conditions.
Half-life — the time taken for half of the radioactive nuclei in a sample to decay, or for the activity of a sample to fall to half its original value.
Activity — the rate at which nuclei in a radioactive sample decay, measured in becquerels (Bq), where 1 Bq equals 1 decay per second.
Isotope — atoms of the same element with the same number of protons but different numbers of neutrons in their nuclei.
Ionisation — the process of adding or removing electrons from atoms to form charged particles called ions; caused when radiation collides with atoms.
Background radiation — the low-level nuclear radiation that is present everywhere in the environment from natural and artificial sources.
Alpha particle (α) — a type of nuclear radiation consisting of two protons and two neutrons (identical to a helium nucleus), with a relative charge of +2.
Beta particle (β) — a high-speed electron emitted from the nucleus when a neutron converts into a proton, with a relative charge of -1.
Core concepts
Atomic structure and nuclear notation
The atom consists of a small central nucleus containing protons and neutrons, surrounded by electrons in shells. The nucleus contains most of the atom's mass.
Nuclear notation shows the composition of an atom:
- Mass number (A) — the total number of protons and neutrons in the nucleus (top number)
- Atomic number (Z) — the number of protons in the nucleus (bottom number)
For example: ²³⁸₉₂U has 92 protons, 146 neutrons (238 - 92), and 92 electrons in a neutral atom.
Isotopes are atoms of the same element with different numbers of neutrons. Carbon-12 (¹²₆C) and carbon-14 (¹⁴₆C) both have 6 protons but different neutrons. Some isotopes are unstable and radioactive.
Types of nuclear radiation
Alpha radiation (α)
- Composition: 2 protons + 2 neutrons (helium nucleus)
- Charge: +2
- Mass: 4 atomic mass units
- Penetration: stopped by paper or a few centimetres of air
- Ionising power: highly ionising
- Range in air: approximately 5 cm
- Deflection in fields: deflected by electric and magnetic fields (small deflection due to large mass)
Beta radiation (β)
- Composition: high-speed electron from the nucleus
- Charge: -1
- Mass: 1/2000 atomic mass units (negligible)
- Penetration: stopped by a few millimetres of aluminium
- Ionising power: moderately ionising
- Range in air: approximately 1 metre
- Deflection in fields: deflected by electric and magnetic fields (large deflection due to small mass)
Gamma radiation (γ)
- Composition: electromagnetic wave/photon
- Charge: 0 (neutral)
- Mass: 0
- Penetration: reduced by thick lead or several metres of concrete; never completely stopped
- Ionising power: weakly ionising
- Range in air: follows inverse square law; effectively unlimited
- Deflection in fields: not deflected by electric or magnetic fields
Nuclear equations
When radioactive decay occurs, nuclear equations show the changes in the nucleus. The mass and atomic numbers must balance on both sides.
Alpha decay: The nucleus loses 2 protons and 2 neutrons. ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He (or ⁴₂α)
Mass number decreases by 4; atomic number decreases by 2.
Beta decay: A neutron converts to a proton, emitting a fast electron. ¹⁴₆C → ¹⁴₇N + ⁰₋₁e (or ⁰₋₁β)
Mass number stays the same; atomic number increases by 1.
Gamma emission: The nucleus releases excess energy without changing composition. No change to mass or atomic number; often accompanies alpha or beta decay.
Radioactive decay and half-life
Radioactive decay is:
- Random — impossible to predict which nucleus will decay next
- Spontaneous — not affected by temperature, pressure, chemical reactions, or any external conditions
The activity of a sample decreases over time as fewer radioactive nuclei remain. Half-life provides a measure of decay rate.
Calculating with half-life:
If the initial activity is 800 Bq and the half-life is 2 hours:
- After 1 half-life (2 hours): 400 Bq
- After 2 half-lives (4 hours): 200 Bq
- After 3 half-lives (6 hours): 100 Bq
- After 4 half-lives (8 hours): 50 Bq
Formula method: Activity remaining = Initial activity × (1/2)^n where n = number of half-lives = total time ÷ half-life
Different isotopes have vastly different half-lives, from fractions of a second to billions of years.
Background radiation
Background radiation exists everywhere at a low level from various sources:
Natural sources (approximately 87%):
- Radon gas (50%) — from uranium decay in rocks, seeps into buildings
- Rocks and soil (14%) — especially granite containing uranium
- Cosmic rays (12%) — from space, more intense at high altitude
- Food and drink (11%) — especially bananas (potassium-40) and brazil nuts
- Living organisms — carbon-14 in all organic matter
Artificial sources (approximately 13%):
- Medical procedures (mostly X-rays and CT scans)
- Nuclear weapons testing fallout (historical)
- Nuclear power plant discharges (very small contribution)
- Nuclear accidents (e.g., Chernobyl, Fukushima)
When measuring radiation, background radiation must be measured separately and subtracted from readings to find the true activity of a source.
Corrected count rate = measured count rate - background count rate
Uses and hazards of radioactivity
Medical applications:
- Tracers — beta or gamma emitters injected or swallowed to diagnose organ function (e.g., iodine-131 for thyroid, technetium-99m)
- Radiotherapy — gamma rays or beta particles kill cancer cells
- Sterilisation — gamma rays sterilise surgical equipment
Industrial applications:
- Thickness monitoring — beta sources measure paper, foil or plastic thickness automatically
- Smoke detectors — alpha emitters (americium-241) ionise air; smoke particles reduce current
- Radioactive dating — carbon-14 dating for organic materials up to 50,000 years old; uranium-lead dating for rocks
Safety precautions:
Ionising radiation damages living cells by ionisation, potentially causing cancer or cell death.
- Use tongs or remote handling to maximise distance
- Store sources in lead-lined containers when not in use
- Minimise exposure time
- Never point sources at people
- Wear protective clothing and dosimeter badges (for occupational exposure)
- Ensure adequate shielding (appropriate material for radiation type)
Investigating half-life
Practical method using dice simulation:
Dice represent nuclei; rolling a specific number (e.g., six) represents decay. Count remaining dice after each roll to model exponential decay.
Practical method using a radioactive source:
- Measure and record background radiation count for several minutes
- Calculate average background count rate
- Place radioactive source near Geiger-Müller tube
- Record count rate at regular time intervals
- Subtract background count rate from each reading
- Plot corrected count rate against time
- Read half-life from graph where count rate halves
The graph shows exponential decay. The half-life is constant — the time to halve is the same regardless of starting activity.
Worked examples
Example 1: Nuclear equations
Complete the nuclear equation for alpha decay of polonium-210: ²¹⁰₈₄Po → _____ + ⁴₂He
Solution: Mass number: 210 - 4 = 206 Atomic number: 84 - 2 = 82
Element with atomic number 82 is lead (Pb).
Answer: ²⁰⁶₈₂Pb [2 marks: 1 mark for correct numbers, 1 mark for correct element]
Example 2: Half-life calculation
A radioactive sample has an activity of 1200 Bq. Its half-life is 5 days. Calculate the activity after 15 days.
Solution: Number of half-lives = 15 days ÷ 5 days = 3 half-lives [1 mark]
After 1 half-life: 1200 ÷ 2 = 600 Bq After 2 half-lives: 600 ÷ 2 = 300 Bq After 3 half-lives: 300 ÷ 2 = 150 Bq [1 mark]
OR using formula: Activity = 1200 × (1/2)³ = 1200 × 1/8 = 150 Bq [1 mark]
Answer: 150 Bq [1 mark for correct answer with unit]
Example 3: Correcting for background radiation
A student measures background radiation as 25 counts per minute. With a radioactive source present, the count rate is 185 counts per minute. What is the corrected count rate from the source alone?
Solution: Corrected count rate = measured count rate - background count rate [1 mark] = 185 - 25 = 160 counts per minute [1 mark]
Answer: 160 counts per minute
Example 4: Choosing appropriate radiation
A factory needs to monitor the thickness of aluminium foil during production. Explain which type of radiation would be most suitable and why.
Solution: Beta radiation would be most suitable [1 mark]. Alpha radiation would be completely stopped by any foil, providing no information about thickness changes [1 mark]. Gamma radiation would mostly pass through thin foil regardless of small thickness variations [1 mark]. Beta radiation is partially absorbed by aluminium, so thickness changes alter the count rate detected, allowing automatic thickness monitoring [1 mark].
[Total: 4 marks for complete explanation with comparison]
Common mistakes and how to avoid them
Confusing mass number with atomic number — Remember mass number is always larger (top) and atomic number is smaller (bottom). Mass = protons + neutrons; atomic number = protons only.
Thinking radioactive decay can be affected by external conditions — Decay is spontaneous and random. Temperature, pressure, and chemical reactions have no effect on nuclear stability.
Forgetting to subtract background radiation — Always subtract background count rate from measurements when calculating the activity of a specific source. Examiners frequently test this.
Mixing up penetrating power and ionising power — These are inversely related. Alpha is highly ionising but poorly penetrating; gamma is weakly ionising but highly penetrating.
Incorrect half-life calculations — Divide the total time by the half-life to find the number of half-lives first. Then halve the activity that many times. Don't divide by the number of half-lives.
Wrong nuclear equation balancing — Both mass numbers (top) and atomic numbers (bottom) must balance separately on both sides of the equation. Check each independently.
Exam technique for "Radioactivity"
Command word awareness — "Describe" requires you to state features or characteristics; "Explain" requires reasons. For "Explain why beta radiation is suitable...", stating reasons earns marks, just naming beta does not.
Nuclear equations — Show your working clearly. Write the mass numbers and atomic numbers separately, then identify the element from the periodic table. Even if you get the element wrong, you can still earn marks for correct number balancing.
Half-life graph questions — Use a ruler to draw horizontal and vertical lines on decay curves. Show clearly where you read half of the original value and project down to the time axis. Examiners award method marks even if the final answer is slightly off.
Calculations with units — Always include correct units (Bq, seconds, minutes, years). In WJEC marking, final answers without units often lose the final mark even when numerically correct. State units consistently throughout multi-step calculations.
Quick revision summary
Radioactivity involves spontaneous, random decay of unstable nuclei, emitting alpha, beta or gamma radiation. Alpha particles (helium nuclei) are stopped by paper, highly ionising but short range. Beta particles (fast electrons) are stopped by aluminium, moderately ionising. Gamma rays (electromagnetic radiation) are reduced by lead, weakly ionising but highly penetrating. Half-life is the time for activity to halve. Always subtract background radiation from measurements. Nuclear equations must balance mass and atomic numbers. Uses include medical tracers, radiotherapy, and thickness monitoring. Safety requires distance, shielding, and minimising exposure time.