CPB Ljubljana 2018 course book

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:





N )t( tdN

exp( t

   1 dt )t





0

0

0

t

 





N



0

)t(dN



0

2 ln T 1

69315 .0 T

2/1

2/1





 



4427 .1

T

2/1



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 τ the initial number of radioactive nuclei decreases by a factor of e (e ≈ 2.7183):

) t(N 

exp( N



)t

0