Gamma radiation: inverse square law

Demonstration

Gamma radiation is part of the electromagnetic spectrum. It is not absorbed by the air, but its intensity decreases because it spreads out. Therefore, the intensity varies with the inverse square of distance: it follows an inverse square law. You can show this in the laboratory and use it as evidence to support the fact that gamma radiation is a part of the electromagnetic spectrum.

Apparatus and Materials

• Holder for radioactive sources
• Geiger-Müller tube
• Holder for Geiger-Müller tube
• Scaler
• Metre rule
• Sealed "pure" gamma source, cobalt-60 (⁶⁰Co), 5 μCi or sealed radium source
• Set of absorbers (e.g. paper, aluminium and lead of varying thickness)

Health & Safety and Technical Notes

See guidance notes on...

Managing radioactive materials in schools

Read our standard health & safety guidance

Note that 5 μCi is equivalent to 185 kBq.

Cobalt-60 is the best pure gamma source. However, you may have a sealed radium source in your school. This gives out alpha, beta and gamma radiation. You can use it for this experiment by putting a thick aluminium shield in front of it. This will cut out the alpha and beta radiations.

An alternative is to try using a Geiger-Muller tube sideways. The gamma radiation will pass through the sides of the tube but alpha and beta will not. You can do a quick check by doubling and tripling the distance between the source and the axis of Geiger-Muller tube and seeing if the count follows an inverse square law (by dropping to a quarter and a ninth).

Using the Geiger-Muller tube sideways has an added advantage that you have an accurate measure of where the distance is zero. It is along the axis of the tube.

Education suppliers stock a set of absorbers ranging from tissue paper to thick lead. This is a useful piece of equipment to have in your prep room. You can make up your own set. This should include: tissue paper, plain paper, some thin metal foil (e.g. cigarette paper, wrapping from a chocolate from an assortment box and a small piece of gold leaf}

Procedure

Setting up...

1. Set up the Geiger-Muller tube and attach it to the scaler.
2. Clamp a metre rule to the bench and line it up with your zero point (in the Geiger-Muller tube).
3. With some Geiger-Muller tubes, the gamma radiation will pass through the side. So set the Geiger-Muller tube up at right angles to the metre rule. The zero point is then the axis of the tube.
4. You can check your zero point by doing some quick readings before the lesson. When you double the distance, the count should be a quarter. If it is more than a quarter, then move the tube towards the source to re-zero it. If it is less than a quarter, then your zero point is closer than you reckoned: move the tube away from the source to re-zero it.
Carrying out...
5. Measure the background count with the source far away.
6. Start with the gamma source 10 cm from the zero point.
7. Increase the distance and take measurements of count rate at 20 cm, 30 cm, 40 cm, 60 cm and 80 cm.
8. Correct the count rates for the background count.
9. Plot a graph of corrected count-rate against distance. You could use a spreadsheet program to do this.

Teaching Notes

• The shape of the graph shows that count rate decreases with distance. You can show that it is an inverse square by checking that the count rate quarters when the distance doubles (10 cm to 20 cm; 20 cm to 40 cm; 30 cm to 60 cm), falls to a ninth when it trebles (10 cm to 30 cm; 20 cm to 60 cm) and drops to a sixteenth when the distance is quadrupled (10 cm to 40 cm; 20 cm to 80 cm). (This is only true assuming the source is a small area compared with the cross-section of the detector. Keep minimum distance large!)
• A graph of count rate against 1distance² is a straight line.
• This is the same law that governs all electromagnetic radiation (see, for example

  The Sun's luminosity

  This is some evidence that gamma radiation is part of the electromagnetic spectrum.
• The moral of this story is that in order to protect yourself from gamma radiation the best thing to do is to move farther away. At 10 times the distance you will be 100 times as safe.

This experiment was safety-tested in May 2006