https://doi.org/10.1351/goldbook.L03515

Lifetime of a molecular entity, which decays by first-order kinetics, is the time needed for a concentration of the entity to decrease to \(1/\text{e}\) of its original value, *i.e.,* \(c(t = \tau) = \frac{c(t\,=\,0)}{e}\). Statistically, it represents the life expectation of the entity. It is equal to the reciprocal of the sum of the first-order rate constants of all processes causing the decay of the molecular entity.**Notes: **

*Source: *

PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 363 (https://doi.org/10.1351/pac200779030293)

- Mathematical definition: \(\tau = \frac{1}{k} = \frac{1}{\sum_{i}k_{i} }\) with \(k_{i}\) the first-order rate constants for all decay processes of the decaying state.
- Lifetime is used sometimes for processes, which are not first order. However, in such cases, the lifetime depends on the initial concentration of the entity, or of a @Q05006@ and, therefore, only an initial or a mean lifetime can be defined. In this case it should be called
*decay time*. - Occasionally, the term
*half-life*(\(\tau_{1/2}\)) is used, representing the time needed for the concentration of an entity to decrease to one half of its original value*, i.e.*, \(c(t = \tau_{1/2}) = \frac{c(t\,=\,0)}{2}\). For first-order reactions, \(\tau_{1/2} = \text{ln}2\, \tau\).

PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 363 (https://doi.org/10.1351/pac200779030293)