IGCSE Physics / Radiation and half-life
Half-life calculations revision notes
Edexcel International GCSE Physics (4PH1), chapter 23: Radiation and half-life, specification point 7.13. Free lesson.
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Half-life is the time taken for the activity or number of unstable nuclei in a sample to halve. You can use repeated halving to calculate what remains, find a half-life, or correct a count for background radiation.
How to build a halving table
Each half-life halves the amount that is left at that point. A halving table gives one row for each half-life, so you can track the activity without subtracting. For a half-life of 5 days, a starting activity of 800 Bq becomes 400 Bq after 5 days, 200 Bq after 10 days, 100 Bq after 15 days and 50 Bq after 20 days. The fractions of the starting activity left are 1/2, 1/4, 1/8 and 1/16.
How to find activity after a given time
First work out how many half-lives fit into the total time. Then halve the activity once for each half-life. The number of half-lives is time ÷ half-life. For example, 12 hours with a half-life of 3 hours gives 4 half-lives. You can also divide the starting activity by 2 raised to the number of half-lives.
How to find a half-life from two activities
Start with the first activity and halve it repeatedly until you reach the later activity. Count the halvings, then divide the total time by that number. This works because each halving represents one half-life. The half-life is time ÷ number of halvings.
Why you halve, not subtract
A common mistake is to subtract the same amount each time, as if the activity falls by a fixed amount. Instead, halve what is left now. The activity gets smaller but does not reach zero. Starting at 800 Bq, the correct sequence is 800 → 400 → 200 Bq, not 800 − 400 − 400 = 0 Bq.
How to correct a count for background
A GM tube measures radiation from the source and background radiation together. Find the source's count rate by subtracting the background first. After calculating the later source count, add the background back to find the tube's reading.