Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. Think of it like a leaking balloon: the balloon (nucleus) slowly lets out air (particles) until it stabilises. In the same way, an unstable atom releases particles or energy until it becomes stable.
The half‑life of a radioactive isotope is the time taken for half of the atoms in a sample to decay. It is a constant for each isotope and gives a convenient way to describe how quickly a substance decays.
Mathematically, if N₀ is the initial number of atoms, then after time t the remaining number N(t) is:
\$N(t) = N_0 \, e^{-\lambda t}\$
where λ is the decay constant. The half‑life t_{1/2} is related to λ by:
\$t_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{\lambda}.\$
Analogy: Imagine a pile of 100 candies that magically disappears over time. If the pile halves every 3 days, then after 3 days you have 50 candies, after 6 days 25, and so on. That 3‑day period is the half‑life of the candy pile.
| Isotope | Half‑Life |
|---|---|
| Carbon‑14 | ≈ 5,730 years |
| Uranium‑238 | ≈ 4.5 × 10⁹ years |
| Iodine‑131 | ≈ 8 days |
Exam Tip: When given a decay equation, remember to:
Practice converting between λ and t_{1/2}—this is a common question type.