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Radioactive Decay: Mean Lifetime τ
The
mean lifetime τ
, i.e. the average lifetime of a given radioactive nucleus is the
average value of t calculated as:
λ− λ
∫
∫
∞
∞
dt )t
exp( t
N )t( tdN
The mean lifetime τ, is the reciprocal of the decay constant λ, and this result comes
natural since the decay constant has the physical meaning of the disintegration
probability, i.e. the fraction of decays taking place per unit time.
Apparently, within time
λ
=
=
= =τ
∫
∞
1
N
)t(dN
t
0
0
0
0
0
τ the initial number of nuclei decreases by a factor of e (e ≈ 2.7183):
2/1
2/1
2/1
T
4427 .1
69315 .0
T
2ln
T 1
=
= =
λ
=τ