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Q.
In a radioactive substance at t = 0, the number of atoms is $ 8 \times 10^4 $ , its half-life period is 3 yr. the number of atoms $ 1 \times 10^4 $ will remain after interval
Nuclei
Solution:
By formuia, $ N = N_0 \bigg(\frac{1}{2} \bigg)^{t/T} $
or $ 10^4 = 8 \times 10^4 \bigg(\frac{1}{2} \bigg)^{t/3} $
or $ \bigg (\frac{1}{8} \bigg ) = \bigg(\frac{1}{2} \bigg)^{t/3} $
or $ \bigg (\frac{1}{2} \bigg)^3 = \bigg (\frac{1}{2} \bigg)^{t/3} $
$ \Rightarrow 3 = \frac{t}{3} $
Hence, $ t = 9 yr $