What is radioactivity?
Radioactivity is the spontaneous emission of radiation from unstable nuclei. The decay is random (we cannot say when a particular nucleus will decay) and spontaneous (unaffected by temperature or pressure). There are three types of emission:
| Type | What it is | Charge | Penetrating power |
|---|---|---|---|
| Alpha (α) | helium nucleus | +2 | lowest (stopped by paper) |
| Beta (β) | fast electron | −1 | medium (stopped by aluminium) |
| Gamma (γ) | electromagnetic wave | 0 | highest (reduced by lead) |
Half-life
The half-life (T½) is the time taken for half of the radioactive nuclei in a sample to decay, or for the activity to fall to half its value.
Key formula / 关键公式
After n half-lives the number of undecayed nuclei is
N = N₀ × (½)ⁿ, where n = t ÷ T½.
Half-life: T½ = time for the number (or activity) to halve.
Worked example / 例题
A sample has 8.0 × 10⁶ undecayed nuclei and a half-life of 5 days. How many remain after 15 days?
n = 15 ÷ 5 = 3 half-lives, so N = 8.0 × 10⁶ × (½)³ = 8.0 × 10⁶ ÷ 8 = 1.0 × 10⁶ nuclei.
Remember / 记住
- Alpha is most ionising but least penetrating; gamma is the opposite.
- Decay is random and spontaneous.
- After n half-lives, N = N₀ × (½)ⁿ.