Half-life is the time for a radioactive sample to fall to half its activity. To answer a question, count how many half-lives fit into the time given and halve once for each.
This lesson is part of nuclear energy. It builds on distinguishing radiation types.
How do I work out the amount remaining?
Follow three steps. They work on any question about decay time.
- Find the half-life, from the question or from the data.
- Divide the total time by the half-life to count the number of half-lives.
- Halve the starting amount once for each half-life.
Worked example: reading half-life from a table
A radioactive sample has an activity of 800 counts per minute. The activity is recorded every 4 hours.
| Time (h) | Activity (counts per minute) |
|---|---|
| 0 | 800 |
| 4 | 400 |
| 8 | 200 |
| 12 | 100 |
Find the half-life. The activity halves from 800 to 400 in 4 hours. It halves again from 400 to 200 in the next 4 hours. So the half-life is 4 hours.
Predict the activity at 20 hours. Divide 20 by 4 to get 5 half-lives. Halve 800 five times: 400, 200, 100, 50, 25. The activity is 25 counts per minute.
State the assumption. This assumes that background radiation has been subtracted from every reading. Without that, the real decay would be hidden by the background count.
The mistake that costs marks
The slip is to think that two half-lives remove all of the sample. The table shows 200 after two half-lives, which is a quarter of the start, not zero.
| Step | Wrong | Right |
|---|---|---|
| After 2 half-lives | Nothing remains | A quarter remains (200 of 800) |
| Counting halvings | 20 h at 4 h half-life is 20 halvings | 20 ÷ 4 = 5 halvings |
| Reading from a graph | Read time when the curve reaches zero | Read time when the activity is half the start |
Always say what you divided. Write “20 ÷ 4 = 5 half-lives” before you start halving.
Half-life from a graph
A decay graph is a smooth curve that falls steeply and then flattens. To read half-life from it, mark the starting activity on the vertical axis.
Halve that value, draw a line across to the curve, and read the time below it. A second halving should take the same time as the first, which is a good check.
Check yourself
A sample of activity 640 counts per minute has a half-life of 3 days. What is the activity after 12 days?
Answer
12 ÷ 3 = 4 half-lives.
Halve 640 four times: 320, 160, 80, 40. The activity is 40 counts per minute.
What to study next
Half-life also explains why radioactive waste stays a problem for a long time. Continue with comparing energy-generation principles. Use the graph evidence and fair-comparison lab for extra data practice.
To practise half-life questions with a teacher, see online one-to-one Science tuition.