P13: Nuclear Radiation and Hazards
Properties of alpha, beta, and gamma radiation, half-life calculations, nuclear equations, and the uses and hazards of ionising radiation.
Types of Nuclear Radiation
Unstable nuclei decay by emitting radiation. The three main types are alpha (ฮฑ), beta (ฮฒ), and gamma (ฮณ). Each type has different penetration, ionisation, and range in air.
Alpha Radiation (ฮฑ)
An alpha particle is two protons and two neutrons โ identical to a helium nucleus. It is emitted from the nucleus during alpha decay.
- Strongly ionising โ it readily knocks electrons off atoms
- Low penetration โ stopped by a thin sheet of paper or a few cm of air
- Short range in air (3โ5 cm)
- Positively charged (+2) โ deflected by electric and magnetic fields
Beta Radiation (ฮฒ)
A beta particle is a high-speed electron emitted from the nucleus when a neutron changes into a proton and an electron.
- Moderately ionising
- Moderate penetration โ stopped by a few mm of aluminium
- Range in air up to about 1 metre
- Negatively charged (โ1) โ deflected by electric and magnetic fields (opposite direction to alpha)
Gamma Radiation (ฮณ)
Gamma radiation is electromagnetic radiation emitted from the nucleus. It has no mass and no charge.
- Weakly ionising
- Highly penetrating โ reduced by several cm of lead or metres of concrete (never fully stopped)
- Unlimited range in air (follows inverse square law)
- No charge โ not deflected by electric or magnetic fields
| Property | Alpha (ฮฑ) | Beta (ฮฒ) | Gamma (ฮณ) |
|---|---|---|---|
| What it is | Helium nucleus (2p + 2n) | High-speed electron | Electromagnetic wave |
| Charge | +2 | โ1 | 0 |
| Mass | 4 (relative) | Very small | 0 |
| Ionising power | Strong | Moderate | Weak |
| Penetrating power | Low | Moderate | High |
| Stopped by | Paper / 5 cm air | 3โ5 mm aluminium | Thick lead / concrete |
| Range in air | 3โ5 cm | ~1 m | Follows inverse square law |
| Deflected by fields? | Yes (towards negative) | Yes (towards positive) | No |
Remember the pattern: the more ionising, the less penetrating. Alpha is the most ionising but the least penetrating. Gamma is the least ionising but the most penetrating.
Nuclear Equations
Nuclear equations show the changes that take place in a nucleus during radioactive decay. Both atomic number and mass number must be conserved (balanced on both sides).
Alpha Decay
When a nucleus emits an alpha particle, its mass number decreases by 4 and its atomic number decreases by 2.
General equation: AZX โ Aโ4Zโ2Y + 42ฮฑ
Worked Example: Uranium-238 Alpha Decay
23892U โ 23490Th + 42ฮฑ
Mass number: 238 = 234 + 4 โ
Atomic number: 92 = 90 + 2 โ
The new element is thorium (Th) because the atomic number has changed from 92 to 90.
Beta Decay
When a nucleus emits a beta particle, a neutron turns into a proton. The mass number stays the same but the atomic number increases by 1.
General equation: AZX โ AZ+1Y + 0โ1ฮฒ
Worked Example: Carbon-14 Beta Decay
146C โ 147N + 0โ1ฮฒ
Mass number: 14 = 14 + 0 โ
Atomic number: 6 = 7 + (โ1) โ
The new element is nitrogen (N) because the atomic number has changed from 6 to 7.
Gamma Emission
Gamma emission does not change the atomic number or mass number of the nucleus. It releases excess energy from an excited nucleus.
AZX โ AZX + ฮณ
Half-Life
The half-life of a radioactive isotope is the time it takes for the number of nuclei of the isotope in a sample to halve, or the time it takes for the count rate (activity) from a sample containing the isotope to fall to half its initial value.
Half-life is different for each radioactive isotope. It can range from fractions of a second to billions of years. It is not affected by physical conditions.
After n half-lives, the fraction remaining = (1/2)n
After n half-lives, the count rate = initial count rate ร (1/2)n
Worked Example: Simple Half-Life
A radioactive isotope has a half-life of 8 days. The initial count rate is 800 counts per minute. What is the count rate after 24 days?
Number of half-lives = 24 รท 8 = 3
- After 1 half-life (8 days): 800 รท 2 = 400
- After 2 half-lives (16 days): 400 รท 2 = 200
- After 3 half-lives (24 days): 200 รท 2 = 100 counts per minute
Or using the formula: 800 ร (1/2)3 = 800 ร 1/8 = 100 counts per minute
Worked Example: Finding Half-Life from Data
A sample has a count rate of 640 counts/s. After 30 minutes, the count rate is 80 counts/s. What is the half-life?
Count rate drops: 640 โ 320 โ 160 โ 80
That is 3 half-lives.
3 half-lives = 30 minutes, so 1 half-life = 10 minutes
Worked Example: Fraction Remaining
Iodine-131 has a half-life of 8 days. What fraction of a sample remains after 32 days?
Number of half-lives = 32 รท 8 = 4
Fraction remaining = (1/2)4 = 1/16
So 1/16 (6.25%) of the original sample remains after 32 days.
If asked to find the half-life from a graph, find the time it takes for the count rate (or number of nuclei) to halve from any starting value on the curve. The half-life should be the same no matter which point you start from โ this is a good check.
Decay Curves
A decay curve is a graph of count rate (or number of undecayed nuclei) against time. It is an exponential decay curve โ it starts steep and gradually flattens out.
The decay curve never reaches zero. In theory, there is always some remaining activity, but it becomes too small to measure above background radiation.
Key features of a decay curve:
- Every half-life interval, the count rate drops by half
- The curve is steepest at the start (most nuclei decaying per unit time)
- The curve becomes less steep over time (fewer undecayed nuclei remaining)
Contamination vs Irradiation
Irradiation is when a person is exposed to radiation from an external source. Contamination is when radioactive material gets onto or into a person's body.
| Feature | Irradiation | Contamination |
|---|---|---|
| Definition | Exposure to radiation from outside the body | Radioactive material on or inside the body |
| Duration | Stops when the source is removed or shielded | Continues until the material is removed or decays |
| Risk | Generally lower risk (limited exposure time) | Higher risk (the source is inside/on you, constantly irradiating nearby tissue) |
| Prevention | Shielding, distance, limiting time | Protective clothing, washing, avoiding inhalation/ingestion |
Contamination is generally more dangerous than irradiation because the radioactive source is inside or on the body, meaning tissues are irradiated continuously and from very close range. However, irradiation from a very strong external source can also be extremely dangerous.
Uses of Radiation
Medical Uses
- Alpha: Radiotherapy (less common), smoke detectors (americium-241)
- Beta: Tracers in medicine (e.g. iodine-131 for thyroid), monitoring thickness of paper or sheet metal
- Gamma: Sterilising surgical equipment, radiotherapy (cobalt-60), tracers in medicine
Worked Example: Thickness Monitoring
A beta source is placed on one side of rolled sheet metal and a detector on the other. If the metal is too thick, fewer beta particles get through and the count rate drops. If the metal is too thin, more beta particles get through and the count rate rises. The rollers are adjusted to keep the thickness constant.
Beta is used (not alpha or gamma) because alpha would be stopped by the metal, and gamma would pass straight through without being affected enough.
Industrial and Other Uses
- Smoke detectors: Alpha source (americium-241) ionises air, creating a current. Smoke particles disrupt the current, triggering the alarm.
- Sterilisation: Gamma rays kill bacteria on medical equipment and food without making them radioactive.
- Radiocarbon dating: Carbon-14 beta decay used to date organic materials up to ~50,000 years old.
Dangers of Ionising Radiation
Ionising radiation can damage cells and DNA. The effects depend on the dose and type of radiation. Damage can be stochastic (random, probability increases with dose) or deterministic (certain above a threshold dose).
Health Effects
- Low doses: May cause cancer (stochastic) โ increased probability with dose. Mutations in DNA may lead to uncontrolled cell division.
- High doses: Cause radiation sickness, tissue damage, and death (deterministic). Kills large numbers of cells rapidly.
- Genetic mutations: Radiation can damage DNA in reproductive cells, potentially causing mutations passed to offspring.
Safety Precautions
- Keep radioactive sources in lead-lined containers when not in use
- Hold sources at arm's length using tongs
- Keep sources as far from the body as possible (inverse square law)
- Limit the time of exposure
- Use shielding appropriate to the radiation type
- Wear protective clothing to prevent contamination
- Monitor exposure with dosimeter badges
When answering questions about radiation safety, think about the three principles of radiation protection: time (minimise exposure time), distance (maximise distance from source), and shielding (use appropriate material between you and the source).
Background Radiation and Safe Handling
Background radiation must always be measured and subtracted from readings to get accurate results. Different locations have different background levels due to variations in radon gas, altitude (cosmic rays), and local geology.
When working with radioactive sources in the lab, always measure the background count first with no source present, then subtract it from all readings taken with the source.
Worked Example: Background Subtraction
A student measures the following count rates with a GM tube:
- Background (no source): 20 counts/min
- With a beta source at 5 cm: 320 counts/min
Corrected count rate = 320 โ 20 = 300 counts/min
Practice Questions
1. Compare alpha, beta, and gamma radiation in terms of ionising power and penetrating power. [4 marks]
Alpha radiation is the most strongly ionising but has the lowest penetrating power (stopped by paper). Beta radiation is moderately ionising and moderately penetrating (stopped by a few mm of aluminium). Gamma radiation is the weakest at ionising but has the highest penetrating power (reduced by thick lead or concrete). The more ionising a radiation type is, the less penetrating it tends to be.
2. Write the nuclear equation for the alpha decay of radium-226 (atomic number 88). [3 marks]
22688Ra โ 22286Rn + 42ฮฑ
Mass number: 226 = 222 + 4. Atomic number: 88 = 86 + 2. The daughter nucleus is radon-222.
3. A radioactive sample has an initial count rate of 5120 counts/s. Its half-life is 6 hours. Calculate the count rate after 30 hours. [3 marks]
Number of half-lives = 30 รท 6 = 5. Count rate = 5120 ร (1/2)5 = 5120 ร 1/32 = 160 counts/s.
4. Explain the difference between irradiation and contamination, and state which is generally more dangerous. [3 marks]
Irradiation is exposure to radiation from an external source โ it stops when the source is removed or shielded. Contamination is when radioactive material gets onto or into the body โ it continues to irradiate tissues until the material is removed or decays. Contamination is generally more dangerous because the source remains in or on the body, continuously irradiating nearby tissue from close range.
5. A sample of a radioactive isotope has a count rate of 4800 counts/min. After 45 minutes, the count rate is 300 counts/min. Calculate the half-life of the isotope. [3 marks]
4800 โ 2400 โ 1200 โ 600 โ 300. That is 4 half-lives. 4 half-lives = 45 minutes, so half-life = 45 รท 4 = 11.25 minutes.
Maths Skills
Half-Life Calculations
After n half-lives, the fraction of remaining nuclei or count rate = (1/2)n. To find the number of half-lives: n = total time / half-life. For whole number half-lives, simply halve repeatedly. For non-integer values, use the formula: N = N0 × (1/2)n.
Worked Example
Iodine-131 has a half-life of 8 days. A sample has an initial activity of 6400 counts/s. What is the activity after 20 days?
n = 20 / 8 = 2.5 half-lives
Activity = 6400 × (1/2)2.5 = 6400 × 0.1768 = 1131 counts/s
Interpreting Decay Curves
A decay curve is an exponential graph of count rate (or number of undecayed nuclei) against time. To find the half-life from a graph, read the initial count rate, find the time at which the count rate has halved, and repeat from different starting points to check consistency. The curve never reaches zero — it approaches it asymptotically.
Logarithmic Decay (Higher)
When the count rate data is plotted on a logarithmic scale, an exponential decay appears as a straight line. The gradient of this line is related to the decay constant. This makes it easier to determine the half-life from noisy experimental data, as the straight-line fit smooths out random fluctuations.
Common Misconceptions
What Half-Life Measures
Half-life is the time for all the radiation to halve. Half-life is the time for the count rate (activity) OR the number of unstable nuclei in a sample to halve. It does not mean the radiation itself halves — each remaining nucleus still emits radiation at the same rate. It is the number of active nuclei that decreases by half over each half-life period.
Irradiation vs Contamination
Irradiation and contamination are the same thing. Irradiation is exposure to radiation from an external source — it stops as soon as you move away or shield the source. Contamination is when radioactive material gets on or into your body — it continues to irradiate you from close range until the material is removed or decays. Contamination is generally more dangerous because the source remains in contact with your body.
6-Mark Extended Question
Compare the properties of alpha, beta and gamma radiation and explain why different types are used for different applications. [6 marks]
Alpha radiation consists of two protons and two neutrons (a helium nucleus). It is strongly ionising but has low penetration — stopped by paper or a few cm of air (1). This makes alpha suitable for smoke detectors, where it ionises air in a chamber; smoke absorbs the alpha particles, breaking the circuit and triggering the alarm (1). Beta radiation is a high-speed electron, moderately ionising and moderately penetrating — stopped by a few mm of aluminium (1). This makes beta ideal for monitoring sheet metal thickness, as it partially penetrates thin materials, giving a count rate sensitive to small changes in thickness (1). Gamma radiation is an electromagnetic wave, weakly ionising but highly penetrating — reduced by thick lead or metres of concrete (1). This makes gamma suitable for sterilising medical equipment and for cancer radiotherapy, where deep penetration into the body is needed to reach tumours without surgery (1).
AO3: Analyse and Evaluate
A student measures the count rate of a radioactive sample every 10 seconds and records the following data (background already subtracted):
| Time (s) | Count rate (counts/s) |
|---|---|
| 0 | 800 |
| 10 | 565 |
| 20 | 400 |
| 30 | 283 |
| 40 | 200 |
| 50 | 142 |
| 60 | 100 |
(a) Determine the half-life of the isotope. (b) Predict the count rate at 90 seconds. (c) Explain why the student should subtract the background count before performing these calculations.
Evaluation
(a) The count rate halves from 800 to 400 in 20 s, and from 400 to 200 in another 20 s. The half-life is 20 seconds.
(b) At 90 s, n = 90/20 = 4.5 half-lives. Count rate = 800 × (1/2)4.5 = 800 × 0.0442 = 35.4 counts/s.
(c) Background radiation adds a constant offset to every reading. Without subtracting it, the apparent half-life would be incorrect because the count rate would not halve truly — at low activities, the background would make the count rate appear higher than it really is, falsely increasing the measured half-life.
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