This article is about the scientific and mathematical concept. Life in half a second pdf accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed. The number at the top is how many half-lives have elapsed.
A half-life usually describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition that states “half-life is the time required for exactly half of the entities to decay”. For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay. Some quantities decay by two exponential-decay processes simultaneously. There is a half-life describing any exponential-decay process. The half life of a species is the time it takes for the concentration of the substance to fall to half of its initial value.
In such cases, the half-life is defined the same way as before: as the time elapsed before half of the original quantity has decayed. However, unlike in an exponential decay, the half-life depends on the initial quantity, and the prospective half-life will change over time as the quantity decays. 5,730 years, regardless of how big or small the original quantity was. After another 5,730 years, one-quarter of the original will remain. On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is.
Perhaps a puddle of a certain size will evaporate down to half its original volume in one day. This is an example where the half-life reduces as time goes on. In other non-exponential decays, it can increase instead. The decay of a mixture of two or more materials which each decay exponentially, but with different half-lives, is not exponential. Mathematically, the sum of two exponential functions is not a single exponential function. A common example of such a situation is the waste of nuclear power stations, which is a mix of substances with vastly different half-lives. Consider a mixture of a rapidly decaying element A, with a half-life of 1 second, and a slowly decaying element B, with a half-life of 1 year.