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Radioactive decay and half-life
Radioactive decay is a random process at the atomic level, but with large numbers of atoms the statistical behavior is predictable: a fixed fraction decays per unit time. This gives exponential decay — the remaining amount falls by half in every half-life period, regardless of how much is present.
Half-life is a property of the isotope, not the amount. Whether you start with 1 gram or 1 kilogram of carbon-14, after 5,730 years half remains. This predictability is what makes half-life calculations reliable for dating and dosing.
Applications of half-life
Radiocarbon dating uses carbon-14 (half-life 5,730 years) to date organic materials up to 50,000 years old. Uranium-238 (half-life 4.47 billion years) is used for geological dating of rocks. Medical imaging uses technetium-99m (half-life 6 hours) — short enough to decay safely after the scan.
In nuclear medicine, drug dosing accounts for biological half-life (how quickly the body eliminates a drug) alongside physical half-life (radioactive decay). The effective half-life is shorter than either alone.
Frequently asked questions
- What is half-life?
- Half-life is the time required for half of a radioactive substance to decay. After one half-life, 50% remains. After two half-lives, 25%. After ten half-lives, less than 0.1% remains.
- What is the half-life formula?
- N(t) = N0 times (1/2)^(t/t_half), where N0 is initial amount, t is elapsed time, and t_half is the half-life. Equivalently: N(t) = N0 times e^(-0.693 times t/t_half).
- What is the half-life of carbon-14?
- Carbon-14 has a half-life of approximately 5,730 years. This predictable decay rate makes it useful for radiocarbon dating of organic materials up to about 50,000 years old.
- How many half-lives until a substance is essentially gone?
- After 7 half-lives, approximately 0.78% remains. After 10 half-lives, approximately 0.098% remains. A common rule of thumb: a substance is considered negligible after 10 half-lives.