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Q.
A certain radioactive substance has a half life of $5$ years. For a nucleus in a sample of the element, the probability of decay in ten years is
Nuclei
Solution:
Number of half lives, $n=\frac{10}{5}=2$
$\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n}$
$=\left(\frac{1}{2}\right)^{2}=\frac{1}{4}$
$ \Rightarrow N=\frac{1}{4} N_{0}$
Amount decayed $=N_{0}-N$
$=N_{0}-\frac{1}{4} N_{0}=\frac{3}{4} N_{0}$
Hence, the probability of decay in ten years is $75 \%$.