Samples of two radioactive nuclides, X and Y, each have equal activity A0 at time t = 0. X has half-life of 24 years and Y a half-life of 16 years. The samples are mixed together. What will be the total activity of the mixture at t = 48 years ?

GivenX has activity A0 at t = 0  and its half-life is 24 years.Y has activity A0 at t = 0  and its half-life is 16 years.At t = 24 years ⇒activity of X=12A0At t = 48 years ⇒activity of X=14A0At t = 16 years ⇒activity of Y=12A0At t = 32 years ⇒activity of Y=14A0At t = 48 years ⇒activity of Y=18A0Thus total activity of the mixture of X and Y at t = 48 years is 14A0+18A0=X=38A0