Question

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

• A. $20$
• B. $40$
• C. $60$
• D. $80$

Answer 1

Answer: (D)

$80$

Answer 2

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