# Inverse square law and radiation

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## Inverse square law and radiation

A point source of gamma rays emits in all directions about the source. It follows that the intensity of the gamma rays decreases with distance from the source because the rays are spread over greater areas as the distance increases.

Consider a point source of gamma rays situated in a vacuum. The radiation spreads in all directions about the source, and therefore when it is a distance x from the source it is spread over the surface of a sphere of radius x and area 4πx^{2}. If E is the energy radiated per unit time by the source, the intensity (energy per unit time per unit area) is given by I = E/4πx^{2} or simply as I ∝ 1/x^{2}. Thus the energy varies as the inverse square from the source.

This inverse square law can be verified using an arrangement as shown below. The procedure is slightly complicated by the fact that the distance between point of emission and detection (d = x +c in the diagram) is impossible to measure directly. As we shall see as x is measurable and c is a constant this is not a problem.

**Inverse Square Summary**

**Experimental arrangment for inverse square law**

**Inverse Square Law Graph**

The aim is verify that

I ∝ 1/d^{2}

i.e.

I ∝ 1/ (x +c)^{2}

Since I is proportional to the **corrected count rate** R (i.e. the actual count rate minus the background count rate) this can be written as

R ∝ 1/ (x +c)^{2}

Introducing a constant k and rearranging gives

x = kR^{-1/2}-c.

Hence a plot of x against R^{-1/2} turns out to be a straight line if the inverse square law has been verified.** As shown below the intercept when R ^{-1/2} is zero gives c.**

The inverse square law is important as it gives a measure of how the intensity of radiation falls off with distance from a source. This has implications for the storage and use of radioactive sources.