Question

If a sample emits 2000 counts per second when the detector is 1 meter from the sample, how many counts per second would be observed when the detector is 10 meters from the sample?

Answer 1

Given:

The distances are,

$\begin{gathered} r_1=1\text{ m} \\ r_2=10\text{ m} \end{gathered}$

The sample emits

$N_1=2000\text{ counts per second}$

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,

$N\propto\frac{1}{r^2}$

So, we can write,

$\frac{N_1}{N_2}=\frac{r_2^2}{r_1^2}$

Substituting the values we get,

$\begin{gathered} \frac{2000}{N_2}=\frac{10^2}{1^2} \\ N_2=\frac{2000}{100} \\ N_2=20 \end{gathered}$

Hence, the required count is 20 per second.