# Half-life

*This article is about*

**decomposition**. For other uses of the term**Half-life**, please see Half-life (disambiguation).For any reactant subject to first-order decomposition, the amount of time needed for one half of the substance to decay is referred to as the **half-life** of that compound. Although the term is often associated with radioactive decay, it also applies equally to chemical decomposition, such as the decomposition of azomethane (CH_{3}N=NCH_{3}) into methane and nitrogen gas. Many compounds decay so slowly that it is impractical to wait for half of the material to decay to determine the half-life. In such cases, a convenient fact is that the half-life is 693 times the amount of time required for 0.1% of the substance to decay. Using the value of the half-life of a compound, one can predict both future and past quantities.

Note: The approximation is used in this article.

## Mathematics

The future concentration of a substance, *C*_{1}, after some passage of time , can easily be calculated if the present concentration *C*_{0} and the half-life *t _{h}* are known:

For a reaction is the first-order for a particular reactant A, and first-order overall, the chemical rate constant for the reaction *k* is related to the half-life by this equation:

## Average Lifetime

For a substance undergoing exponential decay, the *average* lifetime *t _{avg}* of the substance is related to the half-life via the equation

- .

The average lifetime arises when using the number *e*, rather than 1/2, as the base value in an exponential decay equation: