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The count rate from 100 \mathrm{~cm}^3 of a radioactive liquid is \mathrm{c}. Some of this is now discarded. The count rate of the remaining liquid is found to be \mathrm{c} / 10  after  three half-lives. The volume of the remaining liquid, in \mathrm{cm}^3, is
 

Option: 1

20


Option: 2

40


Option: 3

60


Option: 4

80


Answers (1)


Initial count rate (CR) for  1\mathrm{~cm}^3 of liquid =\frac{c}{100}
After 3 half-lives, CR for 1 \mathrm{~cm}^3 of liquid =\frac{1}{8} \times \frac{\mathrm{c}}{100}
Let the volume of the remaining liquid = \mathrm{V} \mathrm{cm}{ }^3.
\therefore CR of this liquid = \mathrm{V} \times \frac{\mathrm{c}}{800}=\frac{\mathrm{c}}{10} \quad \Rightarrow \mathrm{V}=80

Posted by

Ramraj Saini

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