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JEE Main 2021 (27 Aug, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2021 (27 Aug, Shift 1)

Q58JEE Main 2021 · 27 AUG · SHIFT 1Medium

Law of Radioactive Decay

There are 1010 radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $\left(\sqrt{2} = 1.414\right)$

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Answer: (b)

The question means $10^{10}$ nuclei. $N = N_0\left(\frac{1}{2}\right)^{t/T}$ with $t/T = \frac{30}{60} = \frac{1}{2}$ .
$N = \frac{10^{10}}{\sqrt2} = \frac{10^{10}}{1.414} \approx 7.07\times10^9$ .
So the answer is (b) $7\times10^9$ .

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