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

Step-by-step explanation:

The number of particles detected per sec and the distance between the source and the detector is related as,

`N\propto(1)/(r^2)`

So, we can write,

`(N_1)/(N_2)=(r_2^2)/(r_1^2)`

Substituting the values we get,

`\begin{gathered} (2000)/(N_2)=(10^2)/(1^2) \\ N_2=(2000)/(100) \\ N_2=20 \end{gathered}`

Hence, the required count is 20 per second.