P4.2 Atoms and Nuclear Radiation
Radioactive decay
Unstable nuclei decay spontaneously by emitting radiation to become more stable. This is a random process — it is impossible to predict when a particular nucleus will decay. It is also spontaneous — unaffected by temperature, pressure, chemical state or any external conditions.
Types of radiation
| Radiation | Symbol | Nature | Charge | Mass (u) | Range in air | Stopped by |
|---|---|---|---|---|---|---|
| Alpha | α | 2 protons + 2 neutrons (helium-4 nucleus) | +2 | 4 | ~5 cm | Paper / skin |
| Beta (−) | β⁻ | Fast-moving electron | −1 | ~0 | ~1 m | Aluminium (a few mm) |
| Gamma | γ | Electromagnetic wave (photon) | 0 | 0 | Infinite (intensity ∝ 1/r²) | Thick lead / concrete |
Ionising power: α > β > γ (alpha ionises most strongly; gamma least)
Penetrating power: γ > β > α (gamma penetrates most; alpha least)
Nuclear equations
Alpha decay: Atomic number decreases by 2; mass number decreases by 4.
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
Beta-minus decay: A neutron converts to a proton + electron + antineutrino. Atomic number increases by 1; mass number unchanged.
¹⁴₆C → ¹⁴₇N + ⁰₋₁e
Gamma emission: No change in proton or neutron number. Often follows alpha or beta decay as the nucleus loses excess energy.
Balancing nuclear equations: Atomic numbers and mass numbers must balance on both sides.
Half-life
Half-life (t½): The time for half of the radioactive nuclei in a sample to decay.
OR: The time for the count rate (activity) to fall to half its initial value.
Half-life is constant for a given isotope — it does not depend on the amount present.
| Time elapsed | Fraction remaining |
|---|---|
| 0 | 1 |
| 1 × t½ | 1/2 |
| 2 × t½ | 1/4 |
| 3 × t½ | 1/8 |
| n × t½ | (1/2)ⁿ |
Worked example: A sample has count rate 400 Bq. t½ = 30 minutes. What is the count rate after 2 hours?
2 hours = 120 minutes = 4 × 30 min = 4 half-lives
Count rate = 400 × (1/2)⁴ = 400 × 1/16 = 25 Bq
Contamination vs irradiation
Irradiation: Exposure to radiation from an external source. The source is outside the body. When removed from the source, exposure stops. Gamma and beta can irradiate from a distance.
Contamination: Radioactive material enters the body (ingested, inhaled, or through skin). Emits radiation from inside the body — particularly dangerous because the source cannot be removed. Alpha is most dangerous if ingested (high ionising power, close to tissues).
Uses of radioactive isotopes
- Medical imaging: Technetium-99m (gamma emitter, short t½ ~6 h) as tracer.
- Cancer treatment (radiotherapy): Gamma or beta to kill tumour cells.
- Carbon dating: ¹⁴C (t½ ~5,700 years) to date organic materials.
- Industrial tracers: Detect leaks in pipelines.
- Smoke alarms: Americium-241 (alpha emitter) ionises air between electrodes.
Common exam errors
- Saying alpha decay increases atomic number — it decreases by 2.
- Not balancing nuclear equations — check both totals.
- Confusing contamination and irradiation (contamination is inside the body).
- Saying half-life is when all radioactive material is gone — it's when half has decayed.
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