Half-Life and ActivityAQA GCSE Physics: Revision notes
Section 1
What Is Half-Life?
Radioactive decay is a random process — you cannot predict when any single unstable nucleus will decay. However, for a large sample, the overall pattern of decay is predictable and follows a fixed decay curve.
Half-life is the time taken for either:
- the number of undecayed nuclei in a sample to halve, or
- the count rate (or activity) from a sample to halve.
Half-life is a constant for a given isotope — it does not depend on how much of the isotope you start with.
Think of half-life like a coin-flipping crowd: you can't say which person will flip heads next, but you can predict that roughly half the crowd will have flipped heads after enough time — the individual events are random, but the overall pattern is not.
Section 2
How Do You Find Half-Life From Data or a Graph?
To determine the half-life of an isotope from a decay graph (activity or count rate against time):
- Read the starting activity (or count rate) from the graph.
- Find the time taken for this value to fall to half of the starting value.
- That time is one half-life. Repeating this from the halved value to check it takes the same time confirms the half-life is constant.
The same method applies to a table of activity/time data: look for the time interval over which the activity consistently halves.
If a source starts at 800 Bq and falls to 400 Bq after 6 hours, then to 200 Bq after a further 6 hours, the half-life is 6 hours.
Section 3
How Do You Calculate the Decline After Several Half-Lives? (HT)
After each half-life, the activity (or number of undecayed nuclei) is halved again. This gives a repeating pattern:
| Number of half-lives | Fraction remaining |
|---|---|
| 1 | 1/2 |
| 2 | 1/4 |
| 3 | 1/8 |
| 4 | 1/16 |
To find the activity remaining after n half-lives, multiply the starting activity by (1/2)ⁿ, or express the decline as a ratio (e.g. 'reduced to 1/8 of the original after 3 half-lives').
A common error is thinking activity falls to zero after a fixed number of half-lives — it never reaches exactly zero, it just keeps halving.
Section 4
Why Does Half-Life Affect How Dangerous a Source Is?
The hazard from a radioactive source depends on its half-life as well as the type of radiation it emits:
- A short half-life means the activity is initially high (lots of decays per second) but falls quickly — dangerous for a short period.
- A long half-life means the activity is lower at any moment but the source remains radioactive, and therefore hazardous, for a very long time (sometimes thousands of years).
This is why the choice of isotope for a particular use (e.g. medical tracer vs nuclear waste storage) depends heavily on its half-life.
A medical tracer with a half-life of a few hours is chosen so it is active long enough for a scan but decays away quickly, minimising the patient's long-term radiation dose.
Must Know
- Half-life is the time for the number of undecayed nuclei, or the activity/count rate, to halve.
- Half-life is a constant for a given isotope, regardless of sample size.
- Find half-life from a graph by reading the time taken for activity to fall to half its starting value.
- After n half-lives, the fraction remaining is (1/2)ⁿ.
- A short half-life means high but short-lived activity; a long half-life means lower but long-lasting activity.
- The choice of isotope for medical or industrial use depends on matching its half-life to the job.
That's the notes covered.
Carry on to the next subtopic.