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Question 33

The activity of a radioactive sample decreases to one tenth of the original activity $$A_{0\ }$$ in a period of one year. After 9 more years its activity would be

For radioactive decay, the activity decreases exponentially.

Given that after one year,

$$A=\frac{A_0}{10}$$

Therefore, after each year the activity becomes one-tenth of its previous value.

After a total time of $$10$$ years,

$$A=A_0\left(\frac{1}{10}\right)^{10}$$

$$A=\frac{A_0}{10^{10}}$$

Therefore,  $${A=\frac{A_0}{10^{10}}}$$

Hence, the correct option is C.

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