Samples of two radioactive nuclides,X and Y,e | vedclass

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(D) The activity of a radioactive sample at time $t$ is given by $A(t) = A_0 (1/2)^n$,where $n = t / T_{1/2}$ is the number of half-lives elapsed.For

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$\frac{3}{8} A_0$

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(D) The activity of a radioactive sample at time $t$ is given by $A(t) = A_0 (1/2)^n$,where $n = t / T_{1/2}$ is the number of half-lives elapsed.For nuclide $X$ at $t = 48$ years:Number of half-lives $n_X = 48 / 24 = 2$.Activity $A_X = A_0 (1/2)^2 = A_0 / 4$.For nuclide $Y$ at $t = 48$ years:Number of half-lives $n_Y = 48 / 16 = 3$.Activity $A_Y = A_0 (1/2)^3 = A_0 / 8$.The total activity of the mixture is the sum of the individual activities:$A_{total} = A_X + A_Y = A_0 / 4 + A_0 / 8 = (2 A_0 + A_0) / 8 = 3 A_0 / 8$.

Samples of two radioactive nuclides,$X$ and $Y$,each have equal activity $A_0$ 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?

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