halflife

The half-life is the time required for a quantity to decrease to half of its initial value. It is a characteristic time scale for processes such as radioactive decay, chemical reactions, and the biological clearance of substances. The concept is widely used in physics, chemistry, medicine, and environmental science.

In mathematical terms, the quantity N(t) at time t is N(t) = N0 × (1/2)^(t/t1/2). For processes that proceed at a constant rate, the half-life relates to the decay constant λ by t1/2 = ln 2 / λ. The same idea applies to concentrations in pharmacokinetics and to populations of unstable particles.

In radioactivity, the half-life is a fixed property of a nuclide and is independent of sample size, geometry, or initial activity. Examples include carbon-14 (about 5730 years), uranium-238 (about 4.47 billion years), and iodine-131 (about 8 days).

Applications include dating of archaeological and geological samples, medical imaging and radiotherapy using radiopharmaceuticals, drug dosing schedules, risk assessment, and environmental monitoring.

Measurement involves monitoring quantity or activity over time and fitting to an exponential decay model. Determination assumes a closed system and constant external conditions; real-world data may reflect biokinetic processes, mixing, or multiple decay channels.

Note that a half-life does not indicate the time to reach zero; in continuous decay, the quantity asymptotically approaches zero.

The term is also encountered in other contexts, such as biology and pharmacology, where biological or drug half-lives describe clearance from the body. The video game Half-Life shares the name but is a separate topic.