Half-life is the time for the activity of a radioactive sample to halve. On a decay graph, it is the time taken to go from any value to half of that value.
This lesson is part of SPM Physics nuclear physics. It follows distinguishing types of radiation, which explains what the detector is counting.
How do I read half-life from a graph?
Pick a value on the vertical axis, find half of it, and read across the horizontal axis to see how long the fall took. That time is the half-life.
Repeat from a different starting height to check. On a true decay curve, the answer is the same every time.
Worked example: one curve, two readings
An original graph shows the net activity of a sample. It starts at 640 Bq at 0 days, reaches 320 Bq at 4 days and reaches 160 Bq at 8 days.
From 640 to 320 took 4 days. From 320 to 160 took another 4 days. The half-life is 4 days, and the matching answers from two starting points confirm it.
To predict the remainder after 12 days, count the half-lives: 12 ÷ 4 = 3. The activity is 640 × ½ × ½ × ½ = 80 Bq.
How does the background count change the reading?
A detector also counts radiation from its surroundings. An original experiment records these raw counts per minute, with a background count of 20.
| Time (min) | Measured count | Net count (measured − 20) |
|---|---|---|
| 0 | 260 | 240 |
| 10 | 140 | 120 |
| 20 | 80 | 60 |
The net count halves from 240 to 120 in 10 minutes, and from 120 to 60 in the next 10 minutes. The half-life is 10 minutes.
The mistake that costs marks
There are two common slips. One is to read half-life from the raw counts. The other is to divide the time by the fraction remaining instead of counting halvings.
| Step | Wrong | Right |
|---|---|---|
| Raw counts used | 260 to 140 treated as a halving | Correct to 240, then 120: 10 min |
| 640 to 160 in 8 days | 8 ÷ 4 = 2 days | 640 to 160 is two halvings: 8 ÷ 2 = 4 days |
A quarter means two half-lives, an eighth means three, and a sixteenth means four. Count the halvings, then divide the time.
How much of a sample remains?
The fraction left after n half-lives is (½)ⁿ. An original 40 g sample of a substance with half-life 5.0 years has 40 ÷ 2 = 20 g after 5.0 years, 10 g after 10 years and 5.0 g after 15 years.
The same steps work for activity, count rate or number of nuclei. They do not work for the time at which the last nucleus decays, which cannot be predicted.
Check yourself
The net activity of a sample falls from 480 Bq to 60 Bq in 15 hours. Find the half-life, then find the activity after a further 10 hours.
Answer
480 to 60 is three halvings (480 to 240 to 120 to 60).
Half-life = 15 ÷ 3 = 5 hours.
10 more hours is two more half-lives: 60 ÷ 4 = 15 Bq.
What to study next
Half-life tells you how fast a substance decays; the next skill is to write what it decays into. Continue with balancing simple nuclear equations, then try the nuclear physics practice set.
For guided practice on decay graphs, see online one-to-one Physics tuition.