Question

In a physics lab experiment concerning radioactive decay: If your background count rate is 200 counts in 2 minutes and the raw counts in 6 seconds is 100 when the source is 20 cm from the detector, what is the expected number of counts in 6 seconds when the detector is 10 cm from the source?

How would you go about solving this?

Answer 1

The background count rate (let us call it rb) is 200 per 2 minute i.e. 100 per minute.

Now at distance of 20cm from the sample, count is 100 per 6 seconds i.e. 100x10 in 60 seconds i.e. 1000 per minute.

Out of this, 100 per minute is from background count. So actually count rate of the source is only 900 per minute.

Now if we reduce the distance to 10 cm i.e. half, the radiation received from the source will become four times. This can be explained as follows:

The radiation from the source spreads out in a spherical region. If we reduce the radius of this sphere to half, its surface area
() becomes one-fourth and hence radiation incident per unit area becomes four times.

So now the radiation received from the source will be 4 x 900 = 3600 per minute.

Total count will also include the background count which remains same i.e. 100 per minute.

So total count rate will now be 3700 per minute.