Question

Two radioactive nuclides, S and M, both have the same activity X at time t = 0. S and M have a half-life of 26 years and 16 years respectively. Now both samples S and M are mixed. Find out the total activity of the mixture at t = 50 years?

Answer 1

Half life= = ln (2) / (decay constant). => decay constant (lamda)= ln2/half-life

decay const(S)= ln2/26 =0.026 year^-1 and decay const(M)= ln2/16 =0.043 year^-1

Decay rate eqn --> N=N₀e^-lamda*t Since activity is directly propotional to amount of substance, decay of activity will have the same eqn => X=X₀e^-lamda*t

activity of S after 50 years = X e^-0.026*50 = X e^-1.3 =0.272X

activity of M after 50 years = X e^-0.043*50 = X e^-2.15 ​​​​​​​=0.116X

Total activity of mixture = 0.272X + 0.116X = 0.388X