Question

The count rate from `100cm^(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

Correct Answer - C
Initial count rate of `1 cm^(3)` of liquid `=(C)/(100)`
After 3 half-lives, count rate of the liquid `=(1)/(8)xx(C)/(100)`
Let V be the volume of the remaining liquid. The CR of this liquid `=(VC)/(800), (C)/(10)=(VC)/(800)rArrV=80`