Half-life

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This editable Main Article is under development and subject to a disclaimer.

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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 (CH3N=NCH3) 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  ln⁡(2)≈0.693 is used in this article.

## Mathematics[edit]

The future concentration of a substance, C1, after some passage of time Δt, can easily be calculated if the present concentration C0 and the half-life th are known:

C1=C0(12)Δtth

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:

th=0.693k

## Average Lifetime[edit]

For a substance undergoing exponential decay, the average lifetime tavg of the substance is related to the half-life via the equation

tavg=0.693 th.

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

C1=C0 e−Δttavg