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

NEETNEET 2021Nuclei

Solution:

$A=\frac{A_{0}}{2^{t / T_{1 / 2}}} \Rightarrow \frac{A}{A_{0}}$
$=2^{-t / T_{1 / 2}}=2^{-\frac{150}{100}}$
$=2^{-3 / 2}=\frac{1}{2 \sqrt{2}}$