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  4. The half life of Bi 210 is 5 days. What time is taken by (7 / 8) th part of the sample to decay?

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Q. The half life of $Bi ^{210}$ is 5 days. What time is taken by $(7 / 8)^{ th }$ part of the sample to decay?

Nuclei

Solution:

$N = N _{0}\left[\frac{1}{2}\right]^{1 / T }$
$N =\left(1-\frac{7}{8}\right) N _{0}$
$\frac{ N _{0}}{8}= N _{0}\left[\frac{1}{2}\right]^{1 / 5}$
$\left(\frac{1}{2}\right)^{3}=\left[\frac{1}{2}\right]^{1 / 5}$
$ \Rightarrow t =15$ days.