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  4. The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gest reduced to 6.25 % of its initial value of x is

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Q. The half life of a radioactive substance is $5$ years. After $x$ years a given sample of the radioactive substance gest reduced to $6.25 \%$ of its initial value of $x$ is _____

JEE MainJEE Main 2022Nuclei

Solution:

$T 1 / 2=5$ year
$N = N _{0}\left(\frac{1}{2}\right)^{\text {No of half lives }}$
$\frac{ N }{ N _{0}}=\frac{1}{16}=\left(\frac{1}{2}\right)^{4}$
Time $=4$ half lives $=20$ years