AQA A Level Physics

Revision Notes

8.1.7 Required Practical: Inverse Square-Law for Gamma Radiation

Required Practical: Inverse Square-Law for Gamma Radiation

Aims of the Experiment

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


  • Independent variable = the count rate / activity of the source, C
  • Dependent variable = the distance between the source and detector, x (m)
  • Control variables
    • The time interval of each measurement
    • The same thickness of aluminium foil
    • The same gamma source

Equipment List

  • Resolution of equipment:
    • Metre ruler = 1 mm
    • Stopwatch = 0.005 s


  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 3 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, I, of the γ radiation from a point source depends on the distance, x, from the source

Intensity Equation

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

Count Rate Equation

  • Comparing this to the equation of a straight line, y = mx
    • y = C (counts min–1)
    • x = 1/x2 (m–2)
    • Gradient = constant, k


  1. Square each of the distances and subtract the background radiation from each count rate reading
  2. Plot a graph of the corrected count rate per minute against 1/x2
  3. If it is a straight line graph through the origin, this shows they are directly proportional, and the inverse square relationship is confirmed

Evaluating the Experiment

Systematic errors:
  • 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 being measured, the Geiger-Muller tube should be shielded with a sheet of 2–3 mm aluminium
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

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