Activity of radioactive element decreased to one-third of original activity $R_{0}$ in 9 years. After further 9 yrs, its activity will be

R_{0}

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\frac{2}{3} R_{0}

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\frac{R_{0}}{9}

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\frac{R_{0}}{6}

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Solution

The correct option is B $\frac{R_{0}}{9}$
Given in 9 years $\frac{R_{1}}{R_{0}} = \frac{1}{3}$
Hence in the next 9 years $\frac{R_{2}}{R_{1}} = \frac{1}{3}$
$\Rightarrow R_{2} = \frac{R_{1}}{3} = \frac{1}{3} \times \frac{R_{0}}{3} = \frac{R_{0}}{9}$

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