About Half-Life and Radioactive Decay
What Is Half-Life
Half-life is the time required for a quantity to reduce to half of its initial value. The term is most commonly used in nuclear physics to describe radioactive decay, but it also applies to chemical reactions, pharmacology, and other fields. The concept was first introduced by Ernest Rutherford in 1907 and has become fundamental to understanding how unstable substances change over time.
The Decay Formula
The mathematical formula for half-life decay is N equals N0 times 0.5 raised to the power of t divided by T, where N0 is the initial amount, t is the elapsed time, T is the half-life period, and N is the remaining amount. This exponential decay means the substance never truly reaches zero, but approaches it asymptotically. After one half-life, 50 percent remains. After two half-lives, 25 percent remains. After ten half-lives, less than 0.1 percent remains.
Common Half-Life Examples
Carbon-14 has a half-life of 5,730 years and is used in radiocarbon dating of archaeological artifacts. Iodine-131 has a half-life of about 8 days and is used in medical treatments. Uranium-238 has a half-life of 4.5 billion years and is used to date geological formations. Caffeine has a biological half-life of about 5 hours in healthy adults, which is why coffee consumed in the late afternoon can affect sleep.
Applications of Half-Life
Half-life calculations are essential in nuclear medicine for determining dosing schedules and radiation safety protocols. In archaeology, carbon dating uses the half-life of carbon-14 to estimate the age of organic materials. In pharmacology, drug half-lives determine how frequently a medication should be taken to maintain therapeutic levels. Environmental scientists use half-life to track how long pollutants persist in ecosystems.
Exponential vs Linear Decay
Half-life decay is exponential, meaning the rate of decay is proportional to the current amount. This is fundamentally different from linear decay where a constant amount is lost per time period. In exponential decay, the amount lost decreases over time because there is less substance to decay. This is why after infinite time, the amount approaches but never reaches zero in theory, though for practical purposes it becomes negligible after about 10 half-lives.