Basic Physics of Nuclear Medicine/Print version

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The Inverse Square Law

Before we finish this chapter we are going to consider what happens as we move our absorber away from the radiation source. In other words we are going to think about the influence of distance on the intensity of the radiation beam. You will find that a useful result emerges from this that has a very important impact on radiation safety.

The radiation produced in a radioactive source is emitted in all directions. We can consider that spheres of equal radiation intensity exist around the source with the number of photons/particles spreading out as we move away from the source.

Consider an area on the surface of one of these spheres and assume that there are a certain number of photons/particles passing though it. If we now consider a sphere at a greater distance from the source the same number of photons/particles will now be spread out over a bigger area. Following this line of thought it is easy to appreciate that the radiation intensity, I will decrease with the square of the distance, r from the source, i.e.

 I \propto \frac{1}{r^2}


This effect is known as the Inverse Square Law. As a result if we double the distance from a source, we reduce the intensity by a factor of two squared, that is 4. If we triple the distance the intensity is reduced by a factor of 9, that is three squared, and so on.

This is a very useful piece of information if you are working with a source of radiation and are interested in minimising the dose of radiation you will receive.