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  4. What fraction of a radioactive material will get disintegrated in a period of two half-lives?

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Q. What fraction of a radioactive material will get disintegrated in a period of two half-lives?

Chhattisgarh PMTChhattisgarh PMT 2004

Solution:

Amount of radioactive material left after two half-lives
$N=N_{0}\left(\frac{1}{2}\right)^{2 T / T}=\frac{N_{0}}{4}$
$ \therefore $ Radioactive material decayed
$=N_{0}-\frac{N_{0}}{4}=\frac{3}{4} N_{0}$
Thus, three-fourth part of the radioactive material will get disintegrated after two half-lives.