## lifetime, $$\tau$$

Also contains definitions of: mean lifetime, $$\tau$$
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/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.
Notes:
1. Mathematical definition: τ = 1 k = 1 ∑ i k i with ki the first-order rate constants for all decay processes of the decaying state.
2. 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 @[email protected] and, therefore, only an initial or a mean lifetime can be defined. In this case it should be called decay time.
3. 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.
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)