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Law of Radioactive Decay question from NEET 2021

Q57NEET 2021Medium

Law of Radioactive Decay

The half life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:

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Answer: (c)

$\frac{A}{A_0} = \left(\frac{1}{2}\right)^{t/T} = \left(\frac{1}{2}\right)^{150/100} = \left(\frac{1}{2}\right)^{3/2}$ .
$\left(\frac{1}{2}\right)^{3/2} = \frac{1}{2\sqrt2}$ .
So the answer is (c) $\frac{1}{2\sqrt2}$ .

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