Find half-life from background-free tables and curves
Identify equal halving intervals on a source-only mean decay record.
Section 5.2.4 · Half-life
Exam scope and assessment notes
Core and Extended · Physics 0972, 2026–2028. Use labelled nuclides, supplied count intervals and stated background conditions. Model drawings are not to scale. Written practice is self-checked. Human subject-teacher review, supervised practical competence and cumulative assessment remain pending. Cambridge states that IGCSE 0972 has the same subject content as IGCSE 0625, with 9–1 grading. This StudyForA pathway maps the 2026–2028 syllabus only. This 9–1 graded qualification is available only in a limited number of administrative zones. Confirm that your centre can enter you for this code and exam series with Cambridge International. Cambridge has published a separate syllabus for 2029. StudyForA has not reconciled that version yet; this page supports exams in 2026, 2027 and 2028 only.
Before you begin
- Read time-rate axes.
- Recognise successive halving.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which interval finds half-life from this table?
What you will learn
- Identify equal halving intervals on a source-only mean decay record.
- Read half-life from repeated halving pairs and a background-free mean decay curve.
Read a matched table
A supplied background-free mean record has rates 160, 80, 40 and 20 counts/s at 0, 2, 4 and 6 minutes. Each factor-of-two decrease takes 2 minutes, so the half-life is 2 minutes. Use two readings connected by a halving, not simply adjacent points of any spacing.
Different reference levels give the same interval: 80 → 40 takes 2 minutes just as 160 → 80 does. Equal time intervals give equal fractions, not equal absolute losses.
Read the curve shape
The mean curve falls quickly initially and more slowly later. Draw horizontal and vertical guides between one level and half that level to read the elapsed time. The ideal source-only curve approaches zero but is not a straight line reaching zero after two half-lives.
The plotted smooth curve is a mean teaching model. Real short counts scatter around it. All readings in this Core example have no background contribution; the next lesson treats records that include background.
Pause and explain
Does the mean source-only curve fall by the same absolute amount every 2 minutes?
Worked example
Rates are 160 at 0 min, 80 at 2 min, 40 at 4 min and 20 at 6 min. Find half-life.
Show the worked solution
- 160 → 80 takes 2 minutes.
- 80 → 40 also takes 2 minutes.
- The consistent halving interval is 2 minutes.
Answer 2 minutes.
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 half-life using the 160 and 80 counts/s points.
Give me a hint
Read the corresponding times.
Compare my reasoning
- 160 occurs at 0 min.
- 80 occurs at 2 min.
- The difference is 2 min.
2 minutes.
Look for these in your work
- Use source-only data.
- Subtract the times.
Use 80 and 40 counts/s to check the result.
Give me a hint
Choose another halving pair.
Compare my reasoning
- 80 occurs at 2 min.
- 40 occurs at 4 min.
- 4 − 2 = 2 min.
2 minutes, confirming the same half-life.
Look for these in your work
- Use a second pair.
- Compare the intervals.
A student joins 160 at 0 min to zero at 4 min with a straight line. Explain the error.
Give me a hint
Compare the line with successive halving.
Compare my reasoning
- At 2 min the mean is 80.
- At 4 min it is 40, not zero.
- A halving curve has a decreasing gradient magnitude.
The model remains 40 counts/s at 4 min and follows a curved decrease.
Look for these in your work
- Use the given table.
- Distinguish equal fractions and linear loss.
Common mistakes
- Use a factor of two.
- Equal fractions are not equal losses.
- A smooth curve is a mean model.
What can you explain now?
Is 40 half of 80?
Compare with the explanation
Yes
A halving comparison divides the first level by two.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Read half-life from repeated halving pairs and a background-free mean decay curve.
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.