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/e of its original value, i.e.,
c(t = τ) = 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.
- Mathematical definition: τ = 1 k = 1 ∑ i k i with ki 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 (τ 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 = τ(1/2)) = c(t = 0)/2. For first-order reactions, τ 1/2 = ln 2 τ.
PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 363 (https://doi.org/10.1351/pac200779030293)