Half-Life
Half-life is the time required for half of a sample of a radioactive substance to decay — a fixed, characteristic property of each radioactive isotope, independent of the sample's size, age, or surrounding conditions, and directly related to the isotope's decay constant.
Curious
Half-life is the most intuitive way to describe how quickly a radioactive substance decays. Start with any amount of a radioactive isotope, wait one half-life, and exactly half of it will have decayed into something else, leaving half remaining. Wait a second half-life, and half of what's left decays too, leaving a quarter of the original amount — and so on, indefinitely.
Half-lives vary enormously between different radioactive isotopes — from tiny fractions of a second for some highly unstable nuclei, to billions of years for others, like uranium-238's half-life of about 4.5 billion years, roughly the age of the Earth itself. This huge range reflects the sensitivity of the underlying quantum tunnelling process (for alpha decay in particular) to the exact height and width of the nuclear potential barrier each specific isotope's nucleons must tunnel through.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| t_½ | Half-life | second (s), or any convenient time unit |
| λ | Decay constant | s⁻¹ |
| ln(2) | Natural logarithm of 2 ≈ 0.6931 | dimensionless |
Worked example: A sample has a half-life of 8 days (approximately iodine-131's half-life). Its decay constant is λ = ln(2)/t_½ = 0.6931/8 ≈ 0.0866 per day. After 24 days (exactly 3 half-lives), the fraction remaining is (1/2)³ = 1/8 = 12.5% of the original amount.
Deep Dive
Willard Libby's development of radiocarbon dating in the late 1940s, building on the earlier discovery of carbon-14, provided archaeology and geology with an unprecedented, physics-based tool for absolute dating of organic material — a technique that transformed both fields and earned Libby the 1960 Nobel Prize in Chemistry. Modern radiocarbon dates are additionally calibrated against independent chronologies (tree-ring dating, ice cores) to correct for small historical variations in atmospheric carbon-14 production, refining the technique's accuracy considerably beyond Libby's original method.
Relationship to mean lifetime: Half-life is related to, but numerically distinct from, the mean lifetime τ = 1/λ (the average time a given unstable nucleus survives before decaying) — the two are related by t_½ = τ ln(2) ≈ 0.693τ, meaning the mean lifetime is always somewhat longer than the half-life. Both quantities describe exactly the same underlying exponential decay process; the choice between them is largely a matter of convention and convenience for different applications (half-life is more common in dating and medical contexts, while mean lifetime appears more often in particle physics).
Medical applications of radioactive isotopes (nuclear medicine imaging and radiation therapy) require careful selection of isotopes with half-lives matched to their intended use — short enough that radioactivity doesn't linger dangerously in a patient's body long after treatment, but long enough to remain useful for the required imaging or therapeutic window; technetium-99m, with a half-life of about 6 hours, is a widely used example specifically chosen for this balance.
Concept Relationship Map
Requires: radioactive decay
Enables: radiocarbon dating, nuclear medicine applications
Commonly confused with: assuming two half-lives means complete decay (it means one quarter remains, not zero)
Sources
- Libby, W.F. (1946). Physical Review, 69(11–12), 671–672.
- Krane, K.S. (1987). Introductory Nuclear Physics. Wiley, Ch. 6.