Given:
The distances are,
[tex]\begin{gathered} r_1=1\text{ m} \\ r_2=10\text{ m} \end{gathered}[/tex]The sample emits
[tex]N_1=2000\text{ counts per second}[/tex]To find:
The counts per second when the detector is 10 meters from the sample
Explanation:
The number of particles detected per sec and the distance between the source and the detector is related as,
[tex]N\propto\frac{1}{r^2}[/tex]So, we can write,
[tex]\frac{N_1}{N_2}=\frac{r_2^2}{r_1^2}[/tex]Substituting the values we get,
[tex]\begin{gathered} \frac{2000}{N_2}=\frac{10^2}{1^2} \\ N_2=\frac{2000}{100} \\ N_2=20 \end{gathered}[/tex]Hence, the required count is 20 per second.
