{"term":{"id":"03515","doi":"10.1351\/goldbook.L03515","code":"L03515","status":"current","longtitle":"IUPAC Gold Book - lifetime, τ","title":"lifetime","contains":"mean lifetime, @L03515-1@","index":"quantity","termversion":"2.3.3","lastupdated":"2014-02-24","definitions":[{"id":"1","text":"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 quencher 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."},"links":[{"title":"quencher","type":"internal","url":"https:\/\/goldbook.iupac.org\/terms\/view\/Q05006"}],"math":[{"alttext":"1\/e","latex":"1\/\\text{e}"},{"alttext":"c(t = τ) = c(t = 0)\/e","latex":"c(t = \\tau) = \\frac{c(t\\,=\\,0)}{e}"},{"alttext":"τ = 1 k = 1 ∑ i k i","latex":"\\tau = \\frac{1}{k} = \\frac{1}{\\sum_{i}k_{i} }"},{"meaning":"First order rate constant for all decay processes in the decaying state","type":"quantity","alttext":"ki","latex":"k_{i}"},{"alttext":"τ 1\/2","latex":"\\tau_{1\/2}"},{"alttext":"c(t = τ(1\/2)) = c(t = 0)\/2","latex":"c(t = \\tau_{1\/2}) = \\frac{c(t\\,=\\,0)}{2}"},{"alttext":"τ 1\/2 = ln 2 τ","latex":"\\tau_{1\/2} = \\text{ln}2\\, \\tau"}],"sources":["PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 363 (https:\/\/doi.org\/10.1351\/pac200779030293)"]}],"links":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/L03515\/html","json":"https:\/\/goldbook.iupac.org\/terms\/view\/L03515\/json","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/L03515\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/L03515\/plain","pdf":"https:\/\/goldbook.iupac.org\/terms\/view\/L03515\/pdf"},"citation":"Citation: 'lifetime' in IUPAC Compendium of Chemical Terminology, 3rd ed. International Union of Pure and Applied Chemistry; 2006. Online version 3.0.1, 2019. 10.1351\/goldbook.L03515","license":"The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/) for individual terms.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2024-07-17T09:50:29+00:00"}}