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The count rate from 100cm^(3) of a radio...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`
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