The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not.
One of the most well-known applications of half-life is carbon-14 dating.
half life = [ time • ln (2) ] ÷ ln (beginning amount ÷ ending amount) half life = [ 11 • .69315 ] ÷ ln (326.04 ÷ 126) half life = [ 15.870 ] ÷ ln (2.5876) half life = 7.6247 ÷ .95073 half life = 8.0198 days A typical "half-life problem" might be worded: Tungsten 181 has a "k" value of -0.005723757/days. Half-Life = ln(.5) ÷ k Half-Life = -.693147 ÷ -0.005723757 Half-Life = 121.1 days Scroll down for 4 more half-life problems.
) is the time required for a quantity to reduce to half of its initial value.
This is the exact solution; evaluate the natural log with a calculator to get the decimal approximation k = -0.000436 .
A typical "half-life problem" might be worded: Tungsten 181 has a λ value of 0.005723757/days. Half-Life = ln(2) ÷ λ Half-Life = .693147 ÷ 0.005723757 Half-Life = 121.1 days Scroll down for 4 more half-life problems.
The half-life of carbon-14 is approximately 5,730 years, and it can be reliably used to measure dates up to around 50,000 years ago.
The process of carbon-14 dating was developed by William Libby, and is based on the fact that carbon-14 is constantly being made in the atmosphere.
Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.
There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.