Inverse-Square Law of Gamma Radiation (AQA A Level Physics): Revision Note

A source of gamma radiation is placed at a distance of 0.2 m away from a small radiation detector.

The detector records a corrected count rate of 200 Bq from the gamma source.

Calculate the count rate that would be recorded when the detector is moved to a distance of 0.5 m away from the source.

[2]

Answer:

Step 1: List the known quantities

• Initial count rate, $I_1=200\mathrm{Bq}$

• Initial distance, $x_1=0.2\mathrm{m}$

• Final count rate, $I_2$

• Final distance, $x_2=0.5\mathrm{m}$

Step 2: Write down the inverse square law equation

$\frac{I_1}{I_2}={\left(\frac{x_2}{x_1}\right)}^2$

Step 3: Rearrange and calculate the count rate at 0.5 m

$I_2=I_1\times {\left(\frac{x_1}{x_2}\right)}^2=200\times {\left(\frac{0.2}{0.5}\right)}^2$ [1 mark]

$I_2=32\mathrm{Bq}$ [1 mark]

As you can see from the worked example, the inverse square law applies to other quantities such as the activity, or count rate, of the gamma radiation as well as the intensity. However, you must remember that the inverse square law only applies to gamma radiation and not to alpha or beta radiation.

This is because gamma radiation is not absorbed by matter easily, whereas alpha and beta are absorbed quickly before they can spread out.