⏳ Think of an hourglass
At the start, lots of sand falls each second. Near the end, there is little sand left to fall, so less falls each second. A radioactive source behaves in the same way.
Radioactivity » Activity and Half-Life
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 7.1, 7.11, 7.12
- What the activity of a radioactive source is, and why it is measured in becquerels
- Why the activity of a source goes down over time
- The definition of half-life
- Why different isotopes have very different half-lives
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Unlock This CourseActivity of a radioactive source
In Alpha, Beta and Gamma Radiation you learnt that an unstable nucleus decays at random. A radioactive source contains a huge number of unstable nuclei, and some of them decay every second. The activity of a source is the number of nuclei that decay each second.
Activity is measured in becquerels (Bq). One becquerel is one decay per second. A source with an activity of 500 Bq has 500 nuclei decaying every second.
Key terms:
- Activity: the number of nuclei in a radioactive source that decay each second.
- Becquerel (Bq): the unit of activity. 1 Bq is 1 decay per second.
Do not mix activity up with count rate. Activity is what the source itself is doing. Count rate is the number of counts a detector records. It is usually lower than the activity because the detector catches only some of the radiation.
Why the activity goes down
Each time a nucleus decays, it changes into a different nucleus. So the number of the original unstable nuclei in the source gets smaller and smaller.
With fewer unstable nuclei left, fewer decays happen each second. So the activity of a radioactive source decreases over a period of time.
🎲 Still random
Each decay is still random, but we can predict how the activity of a large number of nuclei falls.
Half-life
The activity falls quickly at first and then more slowly. To describe how fast a source fades, scientists use the half-life.
Learn this
The half-life of an isotope is the time taken for half of the unstable nuclei in a sample to decay, or the time taken for the activity of the sample to halve.
Both versions of the definition are correct, because the activity is proportional to the number of unstable nuclei left. You can use either in the exam.
Key terms:
- Half-life: the time taken for half of the unstable nuclei in a sample to decay, or for the activity to halve.
Worked example
A source has an activity of 800 Bq. Its half-life is 2 hours.
After 2 hours, the activity has halved.
800 ÷ 2 = 400 Bq.
So after one half-life the activity is 400 Bq. (Working out the activity after several half-lives is in Half-Life Calculations and Graphs.)
Different isotopes, different half-lives
Every radioactive isotope has its own half-life. The half-life of an isotope is constant: it is the same for every sample of that isotope, however big or small the sample is.
Half-lives can be very different, from a fraction of a second to billions of years.
| Isotope | Approximate half-life |
|---|---|
| Polonium-214 | about 0.0002 seconds |
| Iodine-131 | about 8 days |
| Cobalt-60 | about 5 years |
| Carbon-14 | about 5700 years |
| Uranium-238 | about 4.5 billion years |
An isotope with a short half-life has an activity that falls away quickly. An isotope with a long half-life stays active for a very long time. You do not need to learn these values.
Each decay is random, yet the half-life is fixed. This is because there are so many nuclei in a sample that the random decays average out. We cannot say which nucleus will decay next, but we can say how long it takes for half of them to go.
Units used in this topic
| Unit | Symbol | Used for |
|---|---|---|
| becquerel | Bq | activity of a source |
| centimetre | cm | distance, such as source to detector |
| hour | h | time, for half-lives of hours or days |
| minute | min | time, such as a counting period |
| second | s | time, and the unit in "decays per second" |
Common mistakes
Common mistakes
- Saying the source is "used up" after one half-life. Only half of the unstable nuclei have decayed. The other half is still there.
- Saying that after two half-lives all the nuclei have decayed. The half-life is a time for half of what is left to decay, not a fixed number of nuclei.
- Thinking a hot or cold sample changes the half-life. It does not. The half-life of an isotope is constant.
- Writing the unit as bq or BQ. The unit is Bq.
Exam-style question
A radioactive source contains the isotope iodine-131. Its activity is measured over several days.
(a) State the unit used to measure the activity of a source. [1 mark]
(b) Explain why the activity of the source decreases over time. [2 marks]
(c) The half-life of iodine-131 is 8 days. State what is meant by half-life. [1 mark]
(d) Another isotope has a half-life of 5700 years. Explain how the activity of a sample of this isotope changes over one day, compared with a sample of iodine-131 with the same number of unstable nuclei. [2 marks]
Model answer
(a) becquerel (Bq) (1)
(b) The unstable nuclei decay and change into other nuclei (1). So there are fewer unstable nuclei left, so fewer decays each second (1).
(c) The time taken for half of the unstable nuclei in a sample to decay (or for the activity to halve) (1).
(d) The isotope with the 5700 year half-life has a much longer half-life, so its activity falls much more slowly (1). Over one day its activity falls by a much smaller fraction than the iodine-131 (1).
Exam tip
In "explain why" questions on activity, link the ideas in order: nuclei decay, so fewer unstable nuclei are left, so fewer decays each second.