Half-Life and Radioactive Contamination

This lesson covers the concept of half-life, how to interpret decay curves, the randomness of radioactive decay, and the crucial distinction between contamination and irradiation. This is part of the AQA GCSE Combined Science Trilogy specification (8464, sections 6.4.2 and 6.4.3).

---

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 activity (count rate) of a source to fall to half its original value.

Key Points

• Half-life is constant for any given isotope — it does not change over time.
• After one half-life, half the original unstable nuclei remain. After two half-lives, one quarter remain. After three half-lives, one eighth remain, and so on.
• Radioactive decay is random — you cannot predict which individual nucleus will decay next, but you can predict how many will decay in a given time (statistically).

---

Activity and Count Rate

Term	Definition	Unit
Activity	The rate at which unstable nuclei decay (number of decays per second)	Becquerel (Bq) — 1 Bq = 1 decay per second
Count rate	The number of decays detected per second by a detector (e.g. GM tube)	Counts per second or counts per minute

Exam Tip: Count rate is always less than the true activity because not all emitted radiation reaches the detector (some is absorbed or misses the detector). However, count rate is proportional to activity and can be used to determine half-life.

---

Calculating Half-Life from Data

Example Table

Time (minutes)	Activity (Bq)
0	800
2	400
4	200
6	100
8	50

The activity halves every 2 minutes, so the half-life is 2 minutes.

---

Half-Life on a Decay Curve

A decay curve (activity or count rate vs time) is an exponential decay curve that never reaches zero.

graph TD
    A["Plot activity vs time"] --> B["Curve starts high<br/>and decreases"]
    B --> C["Find the activity at time 0"]
    C --> D["Halve that value"]
    D --> E["Read across to the curve<br/>then down to the time axis"]
    E --> F["This time interval = half-life"]

How to Find Half-Life from a Graph

1. Read the initial activity from the y-axis (e.g. 600 Bq).
2. Halve it (e.g. 300 Bq).
3. Draw a horizontal line from 300 Bq to the curve.
4. Draw a vertical line down from the curve to the time axis.
5. Read the time — this is the half-life.
6. Check by halving again (150 Bq) and confirming the same time interval.

---

Worked Example

A radioactive source has an initial activity of 1200 Bq. Its half-life is 3 hours. What is its activity after 9 hours?

After 3 hours: $1200 \div 2 = 600$1200÷2=600 Bq

After 6 hours: $600 \div 2 = 300$600÷2=300 Bq

After 9 hours: $300 \div 2 = 150$300÷2=150 Bq

(9 hours = 3 half-lives: $1200 \times (\frac{1}{2})^3 = 1200 \times \frac{1}{8} = 150$1200×(21​)3=1200×81​=150 Bq)

---

Background Radiation

Background radiation is the low-level nuclear radiation that is present everywhere, all the time. It comes from:

Source	Contribution
Radon gas (from rocks, especially granite)	Largest source (~50% in the UK)
Medical (X-rays, scans)	Significant
Cosmic rays (from space)	Small
Food and drink (naturally occurring radioactive isotopes)	Small
Ground and buildings	Small
Nuclear industry	Very small

When measuring the activity of a radioactive source, you must subtract the background count rate to get the true activity of the source.

---

Contamination vs Irradiation

This is a key distinction that AQA frequently tests.

Feature	Irradiation	Contamination
Definition	Exposure to radiation from a source outside the body	Radioactive material deposited on or inside the body
Does the person become radioactive?	No	Yes (temporarily — the material on/in them emits radiation)
Most dangerous type	Gamma (most penetrating, hardest to shield from externally)	Alpha (most ionising, causes most damage to tissue when inside the body)
How to reduce risk	Minimise time, maximise distance, use shielding	Wear protective clothing, use sealed sources, follow decontamination procedures
Can it be stopped?	Yes — remove the source or use shielding	Difficult, especially internal contamination

graph TD
    A["Radiation exposure"] --> B["Irradiation<br/>(external source)"]
    A --> C["Contamination<br/>(radioactive material<br/>on/in the body)"]
    B --> D["Person does NOT<br/>become radioactive"]
    C --> E["Person IS a source<br/>of radiation until<br/>material removed/decayed"]

---

Safety Precautions

In the Laboratory

Precaution	Reason
Handle sources with long-handled tongs	Increases distance between the source and the body
Point source away from people	Reduces irradiation of others
Keep exposure time short	Reduces total dose
Store sources in lead-lined containers	Shielding reduces irradiation when not in use
Do not eat or drink near sources	Prevents ingestion (contamination)
Wash hands after handling	Removes contaminating material

In Industry and Medicine

Precaution	Detail
Workers wear dosimeters (film badges)	Monitor cumulative radiation dose
Radiation areas marked with warning signs	Alert people to the hazard
Lead screens and concrete walls	Shield workers from repeated exposure

---

Common Misconceptions

Misconception	Correction
Half-life means the time for all the radioactive atoms to decay	Half-life is the time for half of them to decay — the number never reaches exactly zero
After two half-lives, all the radioactive atoms have decayed	After two half-lives, one quarter of the original atoms remain
Irradiated objects become radioactive	No — irradiation does not make an object radioactive
Alpha radiation is always the most dangerous	Alpha is most dangerous when the source is inside the body; externally, gamma is more hazardous because it is more penetrating
Background radiation is dangerous	Background radiation is at very low levels and poses negligible risk in normal circumstances

---

Summary

• Half-life = the time for the activity (or number of unstable nuclei) to halve.
• Half-life is constant for a given isotope and decay is random.
• A decay curve is an exponential decay shape.
• Background radiation must be subtracted from count rate measurements.
• Irradiation = exposure to external radiation; the person does NOT become radioactive.
• Contamination = radioactive material on or inside the body; the person IS a source of radiation.
• Alpha is most dangerous for contamination; gamma is most hazardous for irradiation.
• Safety: time, distance, shielding (irradiation); protective clothing, sealed sources (contamination).

---

The Fraction Remaining After $n$n Half-Lives

A simple but powerful rule:

$\text{Fraction remaining} = \left(\frac{1}{2}\right)^n$Fraction remaining=(21​)n

Where $n$n is the number of half-lives elapsed.