Half-Life and Radioactive Contamination vs Irradiation
Half-Life and Radioactive Contamination vs Irradiation
Radioactive decay is random — you cannot predict when a particular nucleus will decay. However, for a large number of nuclei, the overall rate of decay follows a predictable pattern described by half-life.
What is Half-Life?
The half-life of a radioactive isotope is the time it takes for:
- The number of unstable nuclei in a sample to halve, OR
- The count rate (activity) from a sample to fall to half its original value
Both definitions are equivalent and either can be used in the exam.
Activity is the rate at which unstable nuclei decay. It is measured in becquerels (Bq), where 1 Bq = 1 decay per second.
Calculating with Half-Life
After each half-life, the activity (or number of undecayed nuclei) halves:
| Number of half-lives | Fraction remaining | Percentage remaining |
|---|---|---|
| 0 | 1 | 100% |
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
| 5 | 1/32 | 3.125% |
Example 1: A source has an activity of 800 Bq and a half-life of 3 hours. What is the activity after 9 hours?
9 hours = 3 half-lives
800 then 400 then 200 then 100
Activity = 100 Bq
Example 2: A sample initially contains 10,000 undecayed atoms. After 20 minutes, 1,250 remain. What is the half-life?
10,000 then 5,000 then 2,500 then 1,250 = 3 half-lives
Half-life = 20 / 3 = 6.67 minutes
The Decay Curve
Plotting activity against time gives a characteristic decay curve — a smooth curve that never quite reaches zero. The graph shows exponential decay.
To find the half-life from a graph:
1. Read the initial activity from the y-axis
2. Find half of this value
3. Draw a horizontal line across to the curve
4. Draw a vertical line down to the x-axis
5. Read the time — this is one half-life
6. Check by repeating for the next halving — the time interval should be the same
Half-Lives of Different Isotopes
Half-lives vary enormously:
| Isotope | Half-life | Use |
|---|---|---|
| Fluorine-18 | ~110 minutes | PET scans (medical imaging) |
| Iodine-131 | ~8 days | Treating thyroid cancer |
| Cobalt-60 | ~5.3 years | Sterilising medical equipment |
| Carbon-14 | ~5,730 years | Carbon dating |
| Uranium-238 | ~4.5 billion years | Dating rocks |
Short half-life sources decay quickly and become safe sooner, but are intensely active while they last. Long half-life sources remain hazardous for a very long time.
Contamination vs Irradiation
This distinction is critical for safety and is a common exam question.
Irradiation is when a person or object is exposed to radiation from an external source. The person does NOT become radioactive. Once the source is removed, the irradiation stops.
- Example: Having an X-ray at the hospital — you are exposed to radiation, but you do not become radioactive afterwards
- Controlled by: shielding (lead aprons), distance, limiting exposure time
Contamination is when radioactive material is deposited on or inside a person, object, or area. The contaminating material continues to emit radiation as it decays. The person or object IS now a source of radiation.
- Example: Radioactive dust landing on skin or being inhaled
- Much harder to deal with because the source cannot simply be "switched off"
- Controlled by: protective clothing, sealed sources, decontamination procedures
| Irradiation | Contamination | |
|---|---|---|
| Radioactive material on/in you? | No | Yes |
| You become radioactive? | No | Effectively, yes |
| Stops when source removed? | Yes | No (source is on/in you) |
| Protection | Shielding, distance, time | Containment, protective clothing |
Safety Precautions
When working with radioactive sources:
- Use tongs or remote handling (maximise distance)
- Point the source away from people
- Minimise exposure time
- Store sources in lead-lined containers
- Wear protective equipment if there is a contamination risk
- Monitor exposure with a film badge dosimeter
Exam Tips
- Always state BOTH definitions of half-life — examiners accept either, but the six-mark answers should use both
- When reading half-life from a graph, clearly show your working with lines drawn on the graph
- In contamination vs irradiation questions, the key distinction is whether the radioactive material is ON or IN the person (contamination) or just nearby (irradiation)