Radioactive Decay

What is Radioactivity?

Radioactivity is the spontaneous emission of radiation from unstable nuclei. It is random and spontaneous — we cannot predict when any individual nucleus will decay, or control it by changing temperature, pressure or chemical state.

Radiation is emitted when an unstable nucleus decays to become more stable.

Types of Nuclear Radiation

Alpha (α) Radiation

• Particle: 2 protons + 2 neutrons (= helium nucleus, ⁴He)
• Charge: +2 (positive)
• Mass: Heavy (relatively)
• Ionising power: Very high — causes a lot of ionisation per cm of travel
• Penetrating power: Very low — stopped by a few cm of air or a thin sheet of paper
• Speed: ~5% of speed of light

Beta (β) Radiation

• Particle: A fast-moving electron emitted from the nucleus when a neutron changes to a proton
• Charge: −1 (negative)
• Mass: Very light
• Ionising power: Medium
• Penetrating power: Medium — stopped by a few mm of aluminium (or a thin sheet of plastic)
• Speed: Up to 90% of speed of light

Note: In beta emission, the nucleus GAINS a proton (because a neutron → proton + electron). Atomic number increases by 1; mass number unchanged.

Gamma (γ) Radiation

• Type: Electromagnetic radiation (very high-frequency wave, not a particle)
• Charge: 0 (no charge)
• Mass: 0
• Ionising power: Very low — least ionising per cm
• Penetrating power: Very high — several cm of lead or metres of concrete needed to significantly reduce intensity
• Speed: Speed of light (3 × 10⁸ m/s)

Gamma is not a particle — it is a high-energy photon emitted after alpha or beta decay when the nucleus still has excess energy. It does not change the atomic number or mass number.

Nuclear Equations

In radioactive decay, we write nuclear equations showing changes to the nucleus.

Alpha decay example: $${}^{238}{92} ext{U} ightarrow {}^{234}{90} ext{Th} + {}^{4}_{2} ext{He}$$ (Uranium-238 decays to Thorium-234 + alpha particle)

• Mass number: 238 = 234 + 4 ✓
• Atomic number: 92 = 90 + 2 ✓

Beta decay example: $${}^{14}{6} ext{C} ightarrow {}^{14}{7} ext{N} + {}^{0}_{-1}e$$ (Carbon-14 decays to Nitrogen-14 + beta particle/electron)

• Mass number: 14 = 14 + 0 ✓
• Atomic number: 6 = 7 + (−1) ✓

Half-life

Half-life: The time taken for half the nuclei in a radioactive sample to decay (or for the count rate to halve).

Half-life is constant for any given isotope — it does not change with temperature, pressure or chemical state.

Example: A sample has 800 undecayed nuclei. Its half-life is 30 minutes.

• After 30 min: 400 nuclei remain
• After 60 min: 200 remain
• After 90 min: 100 remain

Half-life calculation: N(t) = N₀ × (1/2)^(t/T½)

Or use the pattern — divide the number of nuclei by 2 for each half-life elapsed.

Uses of half-life:

• Carbon-14 (half-life 5730 years): radiocarbon dating of ancient organic material
• Iodine-131 (half-life 8 days): medical tracer/treatment (short enough to minimise damage)
• Technetium-99m (half-life 6 hours): medical imaging

Uses and Hazards

Uses: Smoke detectors (α source); sterilisation (γ); cancer treatment (γ/β); medical tracers (γ); industrial thickness testing (β) Hazards: Ionising radiation damages cells and DNA → cancer, radiation sickness; alpha most dangerous if inhaled/ingested; gamma can penetrate the body from outside.