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 (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.

Mathematics

The future concentration of a substance, C₁, after some passage of time $\Delta$T, can easily be calculated if the present concentration, C₀, and the half-life, T_h, are known:

$C_{1}=C_{0}\left({\frac {1}{2}}\right)^{\frac {\Delta _{T}}{T_{h}}}$

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 T_h by this equation:

$T_{h}={\frac {0.693}{k}}$

Average Lifetime

The average lifetime of a substance is related, but not equal, to the half-life.