Half-Life Calculator

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. The half-life (t½) is the time required for half of the radioactive atoms in a sample to decay. It is a fundamental physical constant for each isotope: carbon-14 has a half-life of about 5,730 years, while uranium-238 has a half-life of roughly 4.5 billion years.

Decay follows first-order kinetics, meaning the rate of decay is proportional to the number of remaining radioactive nuclei. This produces an exponential decay curve described by the equation N(t) = N₀ × (½)^(t / t½), where N(t) is the remaining quantity, N₀ is the initial amount, and t is elapsed time. The decay constant λ = ln(2) / t½ provides an alternative formulation: N(t) = N₀ × e^(-λt).

Applications in Dating and Medicine

Radiometric dating uses known half-lives to determine the age of materials. Carbon-14 dating is used for organic remains up to about 50,000 years old. For older materials, geologists use potassium-argon dating (half-life 1.25 billion years) or uranium-lead dating (half-life 4.5 billion years) to date rocks and minerals billions of years old.

In pharmacokinetics, the concept of half-life describes how quickly a drug is eliminated from the body. Drugs with short half-lives require frequent dosing to maintain therapeutic concentrations, while those with long half-lives may accumulate if doses are given too close together. The effective half-life combines physical decay with biological elimination.

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