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Q.
Half life of a radioactive element is $12.5$ hour and its quantity is $256\, g$. After how much time its quantity will remain 1 g?
Atoms
Solution:
$\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n} n \rightarrow$ no. of decays.
$\frac{1}{256}=\left(\frac{1}{2}\right)^{8}=\left(\frac{1}{2}\right)^{n}$
$ \therefore n=8$
Time for $8$ half life $=100$ hours.