Define half-life without an individual decay deadline
Explain half-life as a halving of a large radioactive population or source activity.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Recognise a half fraction.
- Understand random nuclear decay.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which definition describes half-life?
What you will learn
- Explain half-life as a halving of a large radioactive population or source activity.
- Define population half-life and explain why it does not set a single-nucleus deadline.
Define the halving interval
Half-life is the time taken for half the radioactive nuclei in a sample to decay. Equivalently, it is the time for source activity to fall to half its initial value. Under unchanged detector conditions, a background-free count rate from that source also follows the halving pattern.
The fraction is applied to the radioactive nuclei still present at the start of each interval. Half of the remainder decays in the next half-life, not another fixed half of the original sample.
Keep individual randomness
A half-life is not a deadline at which every particular nucleus must decay. Individual events remain random. Large samples have a reliable average trend, while small samples and short detector observations can fluctuate around that trend.
Core examples here have no background contribution. If a measured record includes background, its total reading cannot automatically be treated as source activity. Background correction is developed in the Supplement sequence.
Sources for this lesson
Pause and explain
Must one particular nucleus decay before one half-life has passed?
Worked example
A large model population starts at 800 radioactive nuclei. What mean number remains after two half-lives?
Show the worked solution
- After one interval, 400 remain.
- Half of 400 is 200.
- The remaining fraction is one quarter.
Answer 200 on the mean model.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find the mean remaining fraction after two half-lives.
Give me a hint
Halve once per interval.
Compare my reasoning
- Start with fraction 1.
- First halving gives 1/2.
- Second gives 1/4.
1/4.
Look for these in your work
- Apply successive halving.
- Use the remainder.
A background-free mean count rate falls from 160 to 80 counts/s in 2 minutes. Find half-life.
Give me a hint
Identify a factor-of-two decrease.
Compare my reasoning
- The final rate is half the initial rate.
- The elapsed time is 2 minutes.
- This is one half-life.
2 minutes.
Look for these in your work
- Use matching conditions.
- State the unit.
A learner says every nucleus left at one half-life is faulty. Evaluate it.
Give me a hint
Compare individual randomness with sample halving.
Compare my reasoning
- About half remain in the mean model.
- Remaining nuclei have not reached an individual deadline.
- Their survival is consistent with random decay.
Remaining nuclei are expected; survival is not a fault.
Look for these in your work
- Use the population definition.
- Retain random individual timing.
Common mistakes
- Halve the remainder.
- Do not assign individual deadlines.
- Use background-free Core records.
What can you explain now?
What fraction remains after one half-life in the mean model?
Compare with the explanation
One half
The remaining radioactive population is halved over one half-life.
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Make it stick
Define population half-life and explain why it does not set a single-nucleus deadline.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.