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.

Note: The approximation $\ \ln(2)\approx 0.693\$ is used in this article.

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 by this equation:

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

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

$t_{avg}=0.693\ t_{h}$.

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

$C_{1}=C_{0}\ e^{-{\frac {\Delta t}{t_{avg}}}}$