Half-life (t½) is the time for a quantity to decrease by 50%. It applies to radioactive decay, drug metabolism, and chemical reactions.
Decay Formula
N(t) = N₀ × (1/2)^(t/t½), where N₀ = initial quantity, t = elapsed time.
Examples
- Carbon-14: 5,730 years (used in radiocarbon dating)
- Uranium-238: 4.47 billion years
- Ibuprofen: ~2 hours (pharmacology)
- Caffeine: ~5 hours
After 10 half-lives, only 0.1% of the original quantity remains.
Half-Life in Medicine
A drug's half-life determines dosing frequency — short half-life drugs (like some pain medications) need frequent redosing to maintain effect, while long half-life drugs (like some antidepressants) stay in the system for days after the last dose, which is why abruptly stopping certain medications can cause withdrawal effects over an extended period.
Radiocarbon Dating in Practice
Because carbon-14 has a 5,730-year half-life, it's useful for dating organic material up to about 50,000 years old (beyond ~10 half-lives, too little C-14 remains to measure reliably). Older materials require isotopes with much longer half-lives, like potassium-40 (1.25 billion years) for dating ancient rock.