Required Practical: Inverse Square-Law for Gamma Radiation (AQA A Level Physics): Revision Note

Required practical: inverse square-law for gamma radiation

Aim of the experiment

• The aim of this experiment is to verify the inverse square law for gamma radiation of a known gamma-emitting radioactive source

Variables

• Independent variable = the distance between the source and detector, x (m)

• Dependent variable = the count rate / activity of the source, C

• Control variables:

  • The time interval of each measurement

  • The same thickness of aluminium foil

  • The same gamma source

  • The same GM tube

Equipment list

• Resolution of equipment:

  • Metre ruler = 1 mm

  • Stopwatch = 0.01 s

Method

1. Measure the background radiation using a Geiger Muller tube without the gamma source in the room, take several readings and find an average.

2. Next, put the gamma source at a set starting distance (e.g. 5 cm) from the GM tube and measure the number of counts in 60 seconds.

3. Record three measurements for each distance and take an average.

4. Repeat this for several distances going up in 5 cm intervals.

• A suitable table of results might look like this:

Analysing the results

• According to the inverse square law, the intensity, , of the gamma radiation from a point source depends on the distance, , from the source

• Intensity is proportional to the corrected count rate, , so:

• Rearranging this equation gives:

• Comparing this to the equation of a straight line,

  • 

  • (m)

  • Gradient = constant,

1. Subtract the background radiation from each count rate reading to give the corrected count rate, .

2. Plot a graph of against distance .

3. If it is a straight-line graph, this shows they are directly proportional, and the inverse square relationship is confirmed.

Evaluating the experiment

• Systematic errors:

  • The main source of systematic error in this experiment is in the measurement of distance

    • It is unlikely that the source is at the end of the tube, and it is unlikely that the detector is at the end of the GM tube

    • This means the measured distance is likely to be smaller than the actual distance

    • By plotting a graph of  against , this discrepancy can be easily read off the graph where the line meets the negative x-axis

      

  • The Geiger counter may suffer from an issue called “dead time”

    • This is when multiple counts happen simultaneously within ~100 μs and the counter only registers one

    • This is a more common problem in older detectors, so using a more modern Geiger counter should reduce this problem

  • The source may not be a pure gamma emitter

    • To prevent any alpha or beta radiation from being measured, the Geiger-Muller tube should be shielded with a sheet of 2–3 mm aluminium

    • If alpha or beta emissions make it to the detector, this is likely to affect the shape of the graph, making it curve slightly

• Random errors:

  • Radioactive decay is random, so repeat readings are vital in this experiment

  • Measure the count over the longest time span possible

    • A larger count helps reduce the statistical percentage uncertainty inherent in smaller readings

    • This is because the percentage error is proportional to the inverse-square root of the count

Safety considerations

• For the gamma source:

  • Reduce the exposure time by keeping it in a lead-lined box when not in use

  • Handle with long tongs

  • Do not point the source at anyone and keep a large distance (as activity reduces by an inverse square law)

• Safety clothing such as a lab coat, gloves and goggles must be worn