- Mean lifetime
Given an assembly of elements, the number of which decreases ultimately to zero, the lifetime (also called the mean lifetime) is a certain number that characterizes the rate of reduction ("decay") of the assembly. Specifically, if the "individual lifetime" of an element of the assembly is the time elapsed between some reference time and the removal of that element from the assembly, the mean lifetime is the
arithmetic meanof the individual lifetimes.
Typically, the notion of mean lifetime is used in connection with
exponential decay. The remainder of this article confines itself to this particular decay pattern.
Mean lifetime in exponential decay
The mean lifetime τ of elements in an exponentially decaying assembly is equal to the reciprocal of the decay constant (cf. exponential decay). Thus, it is the time needed for the assembly to be reduced by a factor of "e". It is related to the
Thus the mean lifetime is 44% longer than the half-life, e.g.
Polonium-210 has a half-life of 138 days, and a mean lifetime of 200 days.
In exponential decay, the population is governed by the following formula:
where "t" is the time, "N" is the number of elements in the assembly at that time, is the population at the initial reference , and is a parameter characteristic of the decay called the
decay constant. The mean lifetime is the expected valueof the amount of time before an unstable object undergoes a decay. First, we let "c" be the normalizing factor to convert to a probability space.
We see that exponential decay is a scalar multiple of the
exponential distribution, which has a well-known expected value. We can compute it here using integration by parts.
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mean lifetime — vidutinė gyvavimo trukmė statusas T sritis fizika atitikmenys: angl. average lifetime; mean lifetime vok. mittlere Lebensdauer, f rus. среднее время жизни, n pranc. vie moyenne, f … Fizikos terminų žodynas
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mean life — noun : average life * * * Physics. 1. the average time that an unstable particle or nucleus survives before it decays. 2. See decay time. Also called average life, lifetime … Useful english dictionary
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