What you'll learn
This revision guide covers everything you need to know about half-life and the activity of radioactive sources for your AQA GCSE Physics exam. You'll learn how to calculate half-life, interpret decay curves, understand what affects radioactive decay, and apply these concepts to real-world contexts including medical applications and nuclear waste management.
Key terms and definitions
Radioactive decay — the spontaneous and random process by which an unstable atomic nucleus loses energy by emitting radiation (alpha, beta, or gamma).
Half-life — the time taken for half of the radioactive nuclei in a sample to decay, or the time taken for the activity or count rate to fall to half its original value.
Activity — the rate at which unstable nuclei decay in a radioactive source, measured in becquerels (Bq), where 1 Bq equals 1 decay per second.
Count rate — the number of radioactive emissions detected per unit time, typically measured in counts per second or counts per minute using a Geiger-Muller tube.
Random decay — the fact that it is impossible to predict exactly when a particular nucleus will decay, though the overall pattern for large numbers of nuclei is predictable.
Unstable nucleus — an atomic nucleus with an imbalance of protons and neutrons that will undergo radioactive decay to become more stable.
Background radiation — the low-level radiation that is always present in the environment from natural and artificial sources, which must be subtracted from measurements.
Becquerel (Bq) — the SI unit of activity, representing one nuclear decay per second.
Core concepts
Radioactive decay is random and spontaneous
Radioactive decay has specific characteristics that you must understand:
Spontaneous means the decay happens by itself without any external influence. You cannot make a nucleus decay by heating it, putting it under pressure, or using chemical reactions.
Random means we cannot predict which particular nucleus will decay next, or exactly when it will decay. However, with large numbers of nuclei, we can predict the overall pattern very accurately.
The rate of decay is unaffected by:
- Temperature
- Pressure
- Chemical bonding
- Physical state (solid, liquid, or gas)
This randomness is fundamental to nuclear physics and distinguishes radioactive decay from chemical reactions, which can be controlled by changing conditions.
Activity and count rate
Activity measures how many nuclei in a sample decay each second. The activity of a source decreases over time as there are fewer unstable nuclei remaining to decay.
Key points about activity:
- Measured in becquerels (Bq)
- 1 Bq = 1 decay per second
- A sample with activity of 500 Bq has 500 nuclei decaying every second
- Activity is directly proportional to the number of undecayed nuclei present
Count rate is what we actually measure using a detector like a Geiger-Muller tube. It's the number of radioactive emissions detected per second or per minute.
Important distinction:
- Count rate is usually lower than activity because detectors don't detect every single emission
- Not all radiation reaches the detector (some is absorbed or goes in different directions)
- Count rate follows the same decay pattern as activity
When taking measurements, you must account for background radiation:
Corrected count rate = measured count rate - background count rate
Background radiation comes from:
- Cosmic rays from space
- Rocks and soil (especially granite)
- Radioactive gases (radon) in the air
- Medical and industrial sources
- Nuclear weapons testing (historical)
- Nuclear accidents (e.g., Chernobyl, Fukushima)
Understanding half-life
The half-life is constant for a particular isotope and doesn't change regardless of:
- How much of the substance you have
- The age of the sample
- External conditions
Different radioactive isotopes have vastly different half-lives:
- Polonium-214: 0.00016 seconds
- Iodine-131: 8 days (used in medicine)
- Cobalt-60: 5.3 years (used in radiotherapy)
- Carbon-14: 5,730 years (used in radiocarbon dating)
- Uranium-238: 4.5 billion years
After each half-life period:
- Half of the remaining undecayed nuclei will have decayed
- The activity falls to half its previous value
- The count rate falls to half its previous value
For example, if you start with 1000 undecayed nuclei:
- After 1 half-life: 500 nuclei remain
- After 2 half-lives: 250 nuclei remain
- After 3 half-lives: 125 nuclei remain
- After 4 half-lives: approximately 63 nuclei remain
Calculating with half-life
You need to be able to perform calculations involving half-life using different approaches.
Method 1: Step-by-step halving
This works well when the time is a simple multiple of the half-life.
- Determine how many half-lives have passed by dividing the total time by the half-life
- Halve the starting value that many times
Method 2: Using the equation
For GCSE, you may need to use:
Final amount = Initial amount × (1/2)^n
Where n = number of half-lives
Or you may see it written as:
Final activity = Initial activity × (1/2)^(time ÷ half-life)
Method 3: Reading from graphs
Decay curves show activity (or count rate) on the y-axis versus time on the x-axis. These curves have a characteristic exponential decay shape.
To find half-life from a graph:
- Choose a point on the curve and note its activity value
- Calculate half of that activity value
- Draw a horizontal line from half the activity to the curve
- Draw a vertical line down to the time axis
- The time difference is one half-life
You can verify by repeating this process from different starting points — you should get the same half-life value.
Practical applications of half-life
Understanding half-life is essential for many real-world applications:
Medical uses:
- Diagnosis: Isotopes like technetium-99m (half-life 6 hours) are used as tracers. The short half-life means high initial activity for clear images but rapid decay so minimal long-term radiation exposure
- Treatment: Cobalt-60 (half-life 5.3 years) produces gamma rays for cancer treatment. The longer half-life means the source doesn't need frequent replacement
Radiocarbon dating:
- Carbon-14 (half-life 5,730 years) is used to date organic materials up to about 50,000 years old
- Living organisms maintain constant C-14 levels by exchanging carbon with the atmosphere
- After death, no new C-14 is absorbed and existing C-14 decays
- By measuring remaining C-14, archaeologists can determine when the organism died
Nuclear waste management:
- Waste containing isotopes with short half-lives (days to years) can be stored until safe
- Isotopes with very long half-lives (thousands of years) require long-term storage solutions
- Storage facilities must contain radioactive material for multiple half-lives until activity is acceptably low
Smoke detectors:
- Americium-241 (half-life 432 years) is used in ionisation smoke detectors
- Long half-life ensures the detector works reliably for its entire operational life without the source weakening significantly
Net decline in radioactive emissions
As a radioactive source decays, there is a net decline in the emissions it produces. This happens because:
- Each decay reduces the number of undecayed radioactive nuclei
- Fewer undecayed nuclei means lower activity
- Lower activity means fewer emissions per second
The decline follows a predictable pattern:
- The rate of decline is steepest at the start when activity is highest
- The curve becomes less steep over time as fewer nuclei remain
- The curve never reaches zero — it approaches zero asymptotically
- After about 10 half-lives, the activity has fallen to roughly 0.1% of its original value
This net decline is why:
- Radioactive sources used in schools eventually need replacing
- Medical tracers are chosen with appropriate half-lives so they decay quickly after use
- Nuclear waste becomes less dangerous over time (though this may take thousands of years)
Worked examples
Example 1: Basic half-life calculation
Question: A radioactive isotope has a half-life of 30 minutes. A sample initially has an activity of 8000 Bq. Calculate the activity after 90 minutes. [3 marks]
Solution:
Step 1: Calculate the number of half-lives Number of half-lives = 90 ÷ 30 = 3 half-lives [1 mark]
Step 2: Halve the activity three times After 1 half-life (30 min): 8000 ÷ 2 = 4000 Bq After 2 half-lives (60 min): 4000 ÷ 2 = 2000 Bq After 3 half-lives (90 min): 2000 ÷ 2 = 1000 Bq [1 mark]
Answer: 1000 Bq [1 mark]
Alternative method using the equation: Activity = 8000 × (1/2)³ = 8000 × 1/8 = 1000 Bq
Example 2: Finding half-life from data
Question: The table shows how the count rate from a radioactive source changes over time. Background radiation has already been subtracted.
| Time (days) | Count rate (counts/min) |
|---|---|
| 0 | 240 |
| 10 | 120 |
| 20 | 60 |
| 30 | 30 |
(a) Determine the half-life of the source. [2 marks] (b) Predict the count rate after 40 days. [1 mark]
Solution:
(a) From 0 to 10 days: count rate falls from 240 to 120 (halves) [1 mark] Therefore, half-life = 10 days [1 mark]
You can verify: 10-20 days also shows halving (120→60), as does 20-30 days (60→30)
(b) After 40 days = 4 half-lives 30 ÷ 2 = 15 counts/min [1 mark]
Example 3: Medical application
Question: Technetium-99m is used as a medical tracer. It has a half-life of 6 hours and emits gamma radiation.
(a) Explain why gamma radiation is suitable for this use. [2 marks] (b) A patient is injected with a tracer that has an initial activity of 400 MBq. Calculate the activity remaining after 18 hours. [3 marks] (c) Explain why a short half-life is important for medical tracers. [2 marks]
Solution:
(a) Gamma radiation passes through the body without being absorbed significantly / can be detected outside the body [1 mark] Gamma is the least ionising / causes least damage to tissue [1 mark]
(b) Number of half-lives = 18 ÷ 6 = 3 half-lives [1 mark] After 1 half-life: 400 ÷ 2 = 200 MBq After 2 half-lives: 200 ÷ 2 = 100 MBq After 3 half-lives: 100 ÷ 2 = 50 MBq [1 mark] Answer: 50 MBq [1 mark]
(c) The tracer decays quickly so the patient is not exposed to radiation for long [1 mark] Reduces the risk of long-term damage to healthy cells / reduces total radiation dose [1 mark]
Common mistakes and how to avoid them
Confusing activity and count rate: Remember that activity is the actual decay rate of the source, while count rate is what the detector measures. Count rate is usually lower because detectors aren't 100% efficient. However, both decrease following the same half-life pattern.
Forgetting to subtract background radiation: Always subtract background count rate from your measured count rate before doing half-life calculations. The exam question will usually tell you the background radiation value or state that it has already been subtracted.
Thinking radioactive decay can be stopped or slowed: Radioactive decay cannot be affected by temperature, pressure, chemical reactions, or any physical process. This is a fundamental property that distinguishes nuclear processes from chemical ones.
Calculating the wrong number of half-lives: When dividing time by half-life, make sure the units match. If half-life is in days and time is in hours, convert first. Also, remember that after n half-lives, the amount remaining is (1/2)^n times the original, not 1/n.
Misreading decay graphs: When finding half-life from a graph, you can start from any point on the curve — not just the beginning. Find where the count rate halves from your chosen starting point. Drawing the lines clearly in pencil will help you read accurate values and gain method marks even if your final answer isn't perfect.
Assuming the source becomes "safe" after one half-life: After one half-life, half the radioactive nuclei remain, so the source is still significantly radioactive. Typically, a source needs to decay for 10 or more half-lives before it's considered relatively safe, as activity drops to about 0.1% of the original value.
Exam technique for "Half-life and activity of radioactive sources"
Command word "calculate": Show your working clearly. For half-life problems, write out each halving step separately even if you can do it in your head. This ensures you get method marks if you make an arithmetic error. State your final answer clearly with the correct unit (usually Bq, counts per second, or counts per minute).
Graph questions: When asked to determine half-life from a graph, draw construction lines clearly using a ruler and pencil. Mark the points you're using and show both the horizontal line (at half the activity) and vertical line (to the time axis). Label your time interval clearly. Examiners award marks for clear method even if you misread the graph slightly.
Extended response questions (6 marks): For questions asking you to explain the choice of radioactive isotope for a particular application, structure your answer in a logical sequence. Address: (1) the type of radiation emitted and why it's suitable, (2) the half-life and why that duration is appropriate, and (3) any safety or practical considerations. Use scientific terminology correctly — words like "ionising", "penetrating", "contamination", and "exposure" should be used precisely.
Units and significant figures: Activity is measured in becquerels (Bq), though you may see kilobecquerels (kBq) or megabecquerels (MBq). Time can be in seconds, minutes, hours, days, or years — pay attention to which unit the question uses. Give your answer to the same number of significant figures as the data provided, typically 2 or 3 significant figures.
Quick revision summary
Radioactive decay is random and spontaneous, unaffected by external conditions. Half-life is the time for activity or count rate to halve. Different isotopes have different fixed half-lives ranging from fractions of a second to billions of years. Activity, measured in becquerels, decreases exponentially following a predictable pattern. To calculate remaining activity, determine how many half-lives have passed and halve the original value that many times. Always subtract background radiation from measurements. Half-life knowledge is essential for medical applications, dating techniques, and nuclear waste management.