In a radioactive substance at t = 0, the number of atoms are 16 × 10⁴. Its half-life period is 4 years. The number of atoms will remain 1 × 10⁴ after interval of

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8 years

16 years

20 years

24 years

answer is B.

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Detailed Solution

$N = N_{0} {(\frac{1}{2})}^{\frac{t}{T}} \frac{1}{2} \Rightarrow \frac{1 \times 10^{4}}{16 \times 10^{4}} = {(\frac{1}{2})}^{\frac{t}{4}} \Rightarrow {(\frac{1}{2})}^{4} = {(\frac{1}{2})}^{\frac{t}{4}} \Rightarrow t = 16 years$

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