halflives

A half-life, or halflife, is the time required for a quantity to reduce to half of its initial value. The concept is widely used in physics, chemistry, and biology to describe processes that decrease proportionally to the remaining amount, such as radioactive decay and some first-order reactions.

For exponential decay, the quantity N at time t is N(t) = N0 e^(-λt), where λ is the decay constant. The half-life t1/2 is related by t1/2 = ln(2) / λ. In radioactive decay, the half-life is intrinsic to the nuclide, while in chemical or biological contexts it can reflect a combination of processes and conditions. The effective or apparent half-life can differ from the intrinsic one if there is ongoing production or input, or if the system exchanges material with its surroundings.

Examples include carbon-14, with a half-life of about 5,730 years, and uranium-238, with a half-life of about 4.47 billion years. In biology and medicine, the biological or elimination half-life describes the time for a substance to be reduced by half in the body due to metabolic clearance or excretion, independent of ongoing intake. The effective half-life for a drug combines its biological half-life with any ongoing dosing or distribution between compartments.

Understanding halflives informs scheduling for medical isotopes, dosing regimens, environmental assessments, and safety planning. They are typically determined from measurements of activity or concentration over time by analyzing the slope of the natural logarithm of the quantity.