engineering

Half-Life

The time required for half of a radioactive substance to decay, or more generally, for a quantity to reduce to half its initial value.

Half-life (tΒ½) is the time for a quantity to decrease by 50%. It applies to radioactive decay, drug metabolism, and chemical reactions.

Decay Formula

N(t) = Nβ‚€ Γ— (1/2)^(t/tΒ½), where Nβ‚€ = 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.

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