6.3 - Radioactive Decay & Half-Life
Count-rate and activity
Radioactive substances emit radiation from the nuclei of their atoms.
Count-rate
- The count-rate is the number of radiation counts picked up by a detector each second.
- A common detector is a Geiger-Muller tube, connected to a counter that displays the number of counts.
- Photographic film can also detect radiation: it becomes darker the more radiation it's exposed to.
Activity
- The activity is the rate at which a source decays.
- It's measured in becquerels (Bq), where 1 Bq is 1 decay (one nuclear disintegration) per second.
- A larger radioactive sample has a higher activity, because it contains more radioactive nuclei that can decay.
Radioactive decay and half-life
Radioactive decay is random and spontaneous:
- Random - It's impossible to predict which nucleus will decay next, or exactly when any one nucleus will decay.
- Spontaneous - The rate of decay isn't affected by physical conditions like temperature, pressure or chemical bonding.
Why activity falls
- Each time a nucleus decays it becomes more stable, so the number of undecayed radioactive nuclei steadily falls.
- With fewer radioactive nuclei left, the activity (and count-rate) of the sample decreases over time.
Half-life
- The half-life is the time taken for the number of radioactive nuclei in a sample to halve.
- This is also the time taken for the activity (or count-rate) of a sample to halve.
- Each isotope has its own fixed, characteristic half-life.
Purple nuclei are still radioactive; grey nuclei have already decayed.
Half-life and hazard
- Short half-life - Activity falls quickly: high radiation at the start, but the source soon becomes safe.
- Long half-life - Activity falls slowly: smaller amounts of radiation released, but for a very long time, so nearby areas stay exposed.
Finding half-life from a decay graph
A graph of activity (or count-rate, or number of radioactive nuclei) against time curves downwards, becoming less steep as time goes on.
Reading the half-life off the curve
- Read the initial value off the vertical axis.
- Work out half of this value.
- Find the time on the horizontal axis at which the curve reaches that halved value - that time is one half-life.
- Check by halving again: each successive halving should take the same length of time.
Subtract the background count first
- Before plotting, subtract the background count from every reading.
- If it isn't removed, the calculated half-life will be incorrect.
Worked example - Half-life from an activity drop
The activity of a radioactive sample is measured as 1,200 Bq. Three hours later it has fallen to 75 Bq. Find its half-life.
Step 1 - Count the half-lives
1,200 Bq → 600 Bq → 300 Bq → 150 Bq → 75 Bq
That's four halvings, so four half-lives have passed.
Step 2 - Divide the elapsed time by the number of half-lives
half-life = 3 hours ÷ 4 = 45 minutes
The activity formula A = N/t
Where:
- = Activity, in becquerels (Bq)
- = Number of nuclear disintegrations (decays) counted
- = Time, in seconds (s)
Worked example - Activity from disintegrations and time
A radioactive isotope undergoes 96 nuclear disintegrations in 80 s. Calculate its activity.
Step 1 - Formula
Step 2 - Substitution and calculation
Measuring half-life by recording count-rate over time
The half-life of a source can be measured by tracking how its count-rate falls over time using a Geiger-Muller tube connected to a Geiger counter.
Method
- Record the count-rate over a fixed interval (e.g. 10 seconds).
- Repeat at regular intervals (e.g. every 30 seconds) as the source decays.
- Remove the source and measure the background count-rate with the same tube.
- Subtract the background count-rate from each reading to give the corrected count-rate.
- Plot the corrected count-rate against time and find the time taken for the corrected count-rate to halve.
TermDefinition
Count rateThe number of decays recorded by a detector in a given time, usually each second.
ActivityThe rate at which a source of unstable nuclei decays, measured in becquerels (Bq).
Half-lifeThe time taken for the number of radioactive nuclei in a sample to halve, or for the activity (count rate) of the sample to fall to half its original value.