Samples of two radioactive nuclides, X and Y , each have equal activity A_0 at time t = 0 . X

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13.Nuclei

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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 $Y$ a half life of $16$ years. The samples are mixed together.What will be the total activity of the mixture at $t = 48$ years ?

A

$\frac{1}{2}\,A_0$

B

$\frac{1}{4}\,A_0$

C

$\frac{3}{16}\,A_0$

D

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

Solution

If initial activity is $A_{0}$

After $'n'$ half lifes, activity would reduce to $\frac{A_{0}}{2^{n}}$ because number of nuclei would reduce by that much.

In $48$ hours, substance $X$ would undergo two half lives.

Its new activity would become $\frac{A_{0}}{4}$ substance $Y$ would undergo three half lives.

Its new activity would become $\frac{A_{0}}{8}$

The total activity would be the sum:

$\frac{A_{0}}{4}+\frac{A_{0}}{8}=\frac{3 A_{0}}{8}$

Standard 12

Physics

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