Question

samples of two radioactive nuclide, X and Y, each have equal activity A at time t=0. X has a half life of 24 years and Y has a half life of 16 years . The samples are mixed together . what will be the total activity of the mixture at t= 48 years​

Answer 1

Given, X has activity $A_0$ at t = 0 and its half life is 24 years

so, at t = 24 years $\implies$ activity of X = $\frac{1}{2}A_0$

at t = 48 years $\implies$ activity of X = $\frac{1}{4}A_0$

again, Y has activity $A_0$ at t = 0 and its half life is 16 years

so,at t = 16 years $\implies$ activity of Y = $\frac{1}{2}A_0$

at t = 48 years $\implies$ activity of Y = $\frac{1}{2^3}A_0=\frac{1}{8}A_0$

Thus, total activity of of the mixture X and Y at t = 48 years is $\frac{1}{4}A_0+\frac{1}{8}A_0$

= $\frac{3A_0}{8}$