Introduction

All forms of radiation follow the inverse square law.  That is the intensity of radiation declines as to the square of the distance from the source.  This can be mentally justified quite simply by considering the relative areas of concentric spheres.  The area of a sphere is given by:

    A = 4πR²

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This tells us how the area of the ‘front’ expands from the origin.  If it needs to cover an area proportional to R2 then it is going to be weakened or attenuated by 1/R2 as the same amount of radiation now has to cover an area that has increased by a factor of R².

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• Question: What is the area that a light source illuminates after one millionth of second, two millionths of a second, three millionths through to 10 millionths.  Draw a graph of time on the x-axis against area on the y-axis.

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Johannes Kepler, the astronomer, would appear to be the first to argue (in 1604) that the intensity of light from a source obeys the inverse square law.

Gamma rays are electromagnetic radiation, the same as light and radio waves, but at a high frequency, which means a high energy.  In fact, they are the highest frequency form of electromagnetic radiation observed.  They were first discovered by a French chemist called Paul Villard while investigating the radiation from the element radium.  It was our old stamp collecting friend Ernest Rutherford, who named them gamma rays.

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In this experiment, we measure the background radiation and the count rates of gamma particles hitting a detector at a range of distances.  Plotting the results will verify the inverse square law. 

The objective

To show that gamma radiation follows the inverse square law in that the intensity falls off in proportion to one over the square of the distance from the source.

The apparatus

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You will need:

• Safe source of gamma radiation such as Cobalt 60;

• Geiger counter;

• 1 metre rule;

• Thick lead block;

• Stop watch.

Teachers, technicians and students must be aware of all regulations involved in handling radioactive substances.  Cobalt 60 is a common radioactive substance commonly used in this experiment and must be handled in accordance with these regulations.  Naturally, there are no safety concerns with using the e-practical.

The variables

The independent variable is the distance, and the dependent variable is the incident count rate.

The counter on the left counts the number of gamma rays hitting the detector that is to the right of it.  The counter and detector are connected by the cable.  To the right of the detector is a ruler.  At the far right is the gamma ray source.  There is also a large lead block that can be used to block the gamma rays.

The Physics

See the introduction above.

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The method 

Start by moving the lead block between the ruler and the source as close to the source as possible. Start your timer at the same time as you press the start button on the electronic counter. Stop the counter at 20 minutes.

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Now remove the lead block and move the source to 60 cm on the ruler. Count the particles for a 10-minute period. Repeat this for distances at 10-cm intervals down to 10 cm. You can time for less than 5 minutes where the counts are high. Do not forget to record the actual period length.