AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
The half-life of a radioactive isotope is the time it takes for the number…
Full specification wording
Half-lives and the random nature of radioactive decay: The half-life of a radioactive isotope is the time it takes for the number of nuclei of the isotope in a sample to halve, or the time it takes for the count rate (or activity) from a sample containing the isotope to fall to half its initial level.
Half-life is the time for half the unstable nuclei in a sample to decay, so the number of nuclei of that isotope halves.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 2 of 5
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Half-life is the time for half the unstable nuclei in a sample to decay, so the number of nuclei of that isotope halves. Equivalently, it is the time for the count rate or activity from the sample to fall to half its initial level. For example, if a source gives 800 counts per minute, after one half-life it gives about 400, after two about 200, and after three about 100. Because decay is random, individual nuclei decay unpredictably, but large numbers give a smooth, predictable halving pattern. Half-life is fixed for a given isotope and is unaffected by temperature, pressure or chemical state. It allows dating and medical tracing.
What earns the marks
- State that half-life is the time for the number of nuclei of the isotope in a sample to halve.
- State the equivalent definition: the time for the count rate or activity from the sample to fall to half its initial level.
- Use the halving sequence correctly, for example 800 → 400 → 200 → 100 counts per minute over successive half-lives.
- Explain that random decay of individual nuclei produces a predictable halving pattern only because a sample contains very many nuclei.
- Recognise that half-life is constant for a given isotope and is not changed by temperature, pressure or chemical combination.
- Calculate the number of half-lives from total time divided by half-life, or find activity after a given time by repeated halving.
Common mistakes and how to put them right
Treating half-life as the time for all the nuclei to decay.
Put it right by stressing that half remain after each half-life, so the number never reaches zero in a simple halving model.
Halving the time rather than the count rate or number of nuclei.
Put it right by applying each half-life to the quantity, not to the time.
Assuming half-life changes with temperature or chemical state.
Put it right by stating that nuclear decay is unaffected by external conditions.
Exam tips
- Write the definition in terms of either nuclei or count rate, and make clear which quantity is halving.
- Show each halving step in a calculation so the examiner can follow the sequence.
- Check whether the question asks for activity remaining or time elapsed, and label units such as counts per minute or seconds.
Try the lesson
The start of the Half-lives and the random nature of radioactive decay: The half-life of a radioactive isotope is the time it takes for the number of nuclei of the isotope in a sample to halve, or the time it takes for the count rate (or activity) from a sample containing the isotope to fall to half its initial level. lesson, made from checked teaching notes for this specification point.
Have a go first
A sample of a radioactive isotope contains 40 million unstable nuclei. After 15 hours, the number of unstable nuclei has fallen to 20 million. What is the half-life of this isotope?
Listen
Half-life is the time for half the unstable nuclei in a sample to decay, so the number of nuclei of that isotope halves. Equivalently, it is the time for the count rate or activity from the sample to fall to half its initial level. For example, if a source gives 800 counts per minute, after one half-life it gives about 400, after two about 200, and after three about 100. Because decay is random, individual nuclei decay unpredictably, but large numbers give a smooth, predictable halving pattern. Half-life is fixed for a given isotope and is unaffected by temperature, pressure or chemical state. It allows dating and medical tracing. A strong answer earns marks for these points. State that half-life is the time for the number of nuclei of the isotope in a sample to halve. State the equivalent definition: the time for the count rate or activity from the sample to fall to half its initial level. Use the halving sequence correctly, for example 800 → 400 → 200 → 100 counts per minute over successive half-lives. Explain that random decay of individual nuclei produces a predictable halving pattern only because a sample contains very many nuclei. A common slip: Treating half-life as the time for all the nuclei to decay. Instead, stressing that half remain after each half-life, so the number never reaches zero in a simple halving model. Exam tip: Write the definition in terms of either nuclei or count rate, and make clear which quantity is halving.
See it
Put it in order
Put these steps in the order they happen.
- 1. After two half-lives: about 200
- 2. After three half-lives: about 100
- 3. After one half-life: about 400
- 4. Initial count rate: 800 counts per minute
Key words
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Half-life
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Random nature of radioactive decay
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Halving of nuclei number and count rate
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Uses of half-life in dating and medicine
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See every definition
- Half-life
- The time it takes for the number of nuclei of the isotope in a sample to halve, or for the count rate from a sample to fall to half its initial level.
- Random nature of radioactive decay
- Individual nuclei decay unpredictably, but large numbers give a smooth, predictable halving pattern.
- Halving of nuclei number and count rate
- After each half-life the number of nuclei of the isotope halves, and the count rate or activity falls to half its initial level.
- Uses of half-life in dating and medicine
- A fixed half-life for a given isotope allows dating and medical tracing.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
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Test your understanding of Half-lives and the random nature of radioactive decay: The half-life of a radioactive isotope is the time it takes for the number of nuclei of the isotope in a sample to halve, or the time it takes for the count rate (or activity) from a sample containing the isotope to fall to half its initial level.
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