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
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
Updated On: Jul 7, 2022
- $20$
- $40$
- $60$
- $80$
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The Correct Option is D
Solution and Explanation
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 $V=80$
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Concepts Used:
Decay Rate
The disintegration of unstable heavy atomic nuclei into lighter, more stable, atomic nuclei, accompanied in the process by the emission of ionizing radiation (alpha particles, beta particles or gamma rays). This is a random process at the atomic level but, given a large number of similar atoms, the decay rate on average is predictable, and is usually measured by the half-life of the substance.
The equation for finding out the decay rate is given below:
