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).