where , N o is number of atoms at time t = 0 and N is number of atoms at time t .
Half-life of a Radioactive Element
The time is which the half number of atoms present initially in any sample decays , is called half-life ( T ) of that radioactive element .
Relation between half-life and disintegration constant is given by
T = log 2 e / λ = 0.6931 / λ
Average Life or Mean Life ( τ )
Average life or mean life ( τ ) of a radioactive element is the ratio of total life time of all the atoms and total number of atoms present initially in the sample .
Relation between average life and decay constant τ = 1 / λ Relation between half-life and average life τ = 1.44 T
The number of atoms left undecayed after n half-lifes is given by N = N o ( 1 / 2 ) n = N o ( 1 / 2 ) t / T where , n = t / T , here t = total time .
Activity of a Radioactive Element
The activity of a radioactive element is equal to its rate of disintegration .
Activity R = ( – dN / dt ) Activity of the sample after time t ,
R = R o e -λt
Its SI unit is Becquerel ( Bq ).