What is half-life, and how do we use it to work out how a radioactive source decays over time?
Half-life: the meaning of half-life, how activity and the number of undecayed nuclei fall by half each half-life, finding half-life from data or a graph, and uses such as dating and medical tracers.
An SQA National 5 Physics answer on half-life, covering what half-life means, how the activity and number of undecayed nuclei halve each half-life, how to find a half-life from a table or a decay graph, how to work out the activity after a number of half-lives, and uses such as carbon dating and medical tracers.
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What this key area is asking
The SQA wants you to define half-life, explain how the activity and number of undecayed nuclei fall by half each half-life, find a half-life from data or a decay graph, calculate the activity after a number of half-lives, and know uses such as dating and medical tracers.
What half-life means
Radioactive decay is a random process: you cannot say when any one nucleus will decay, only that, on average, half of a large number will decay in one half-life. This randomness is why a real count rate jumps about and why repeating measurements and subtracting the background count improves the result.
Halving each half-life
Finding half-life from a graph or table
To find a half-life from a decay graph (activity against time), read off the time at which the activity has dropped to half its starting value; you can check by finding the time for it to halve again, which should be the same, since the half-life is constant. From a table, count how many times the activity halves over a known total time and divide the total time by that number of half-lives. Always subtract the background count first if it is given, so that you use the true activity of the source and not the count boosted by background radiation.
Uses of half-life
The half-life of an isotope decides what it can be used for:
- Carbon dating: carbon-14 has a half-life of about , so measuring how much remains in old organic material (wood, bone) gives its age.
- Dating rocks: very long-lived isotopes such as uranium are used to date rocks that are millions of years old.
- Medical tracers: isotopes with a short half-life are used so that the radioactivity disappears quickly from the patient's body, limiting the dose.
Try this
Q1. State what is meant by the half-life of a radioactive source. [1 mark]
- Cue. The time for its activity (or number of undecayed nuclei) to fall to half.
Q2. A source of activity has a half-life of . Find its activity after . [2 marks]
- Cue. half-lives: .
Q3. State why an isotope used as a medical tracer usually has a short half-life. [1 mark]
- Cue. So the radioactivity disappears quickly and limits the patient's dose.
Exam-style practice questions
Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
SQA N5 style3 marksA radioactive source has an activity of 800 Bq. Its half-life is 5 years. Calculate its activity after 15 years.Show worked answer →
Work out how many half-lives have passed: half-lives.
Halve the activity once for each half-life: (1), (2), (3).
So after the activity is .
Markers reward finding the number of half-lives, halving the activity that many times, and the correct final activity in becquerels.
SQA N5 style4 marksThe activity of a source falls from 2400 Bq to 300 Bq in 12 hours. Calculate the half-life of the source.Show worked answer →
Count how many halvings take the activity from to : (1) (2) (3). That is half-lives.
The total time is for half-lives, so one half-life is .
Markers reward counting the number of halvings (3), dividing the total time by the number of half-lives, and a final answer of .
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Sources & how we know this
- SQA National 5 Physics Course Specification — SQA (2019)