Required Practicals / AQA / Practical 12
12 A2 3.8.1.6

Inverse square law for gamma radiation

Verify the inverse square law for gamma radiation by measuring count rate at different distances from a gamma source.

Apparatus

  • Sealed gamma source (e.g. Cs-137 or Co-60) in its shielded container
  • Geiger-Muller tube and counter or ratemeter
  • Metre rule and retort stand
  • Lead absorber sheet
  • Stopwatch

Safety

  • Handle the source only with tongs; never touch it directly. Keep exposure time to a minimum.
  • Ensure a radiation risk assessment has been completed; the source must be returned to its shielded container when not in use.
  • Keep all observers at least 0.5 m from the source.

Method

  1. Without the source present, count for at least 5 minutes to determine the background count rate B (counts per second).
  2. Place the source at distance x (measured from source to GM tube window) using a retort stand. Count for 2 minutes; record total counts and calculate count rate C.
  3. Corrected count rate: $I = C - B$.
  4. Repeat for at least eight distances from ~5 cm to ~40 cm.
  5. Plot I against $1/x^2$: straight line through the origin confirms the inverse square law.

Key Variables

Independent Distance x from source to GM tube
Dependent Corrected count rate I
Controlled Same source activity throughout; Same GM tube and counter; Background count rate measured separately

Analysis and Results

  • For gamma radiation (negligible absorption in air): $I = k/x^2$.
  • Plot I vs $1/x^2$: straight line through origin, gradient $= k$.
  • Alternatively, plot $\ln I$ vs $\ln x$: gradient of $-2$ confirms the inverse square law.
  • The background must be subtracted; failure to do so adds a constant offset and distorts the graph.

Common Errors

  • Not measuring and subtracting the background count rate.
  • Measuring x from the shielding container rather than from the source itself.
  • Counting for too short a time at large distances (low count rates have large statistical uncertainty).
  • Plotting I against x (a curve) instead of I against $1/x^2$ (a straight line).

Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.

Q1 3 marks

A gamma source gives a corrected count rate of 320 counts per minute at 20 cm. Predict the count rate at 40 cm, assuming the inverse square law holds.

Q2 4 marks

Describe the safety precautions that must be followed when using a gamma source in the laboratory.

Q3 2 marks

Explain why it is essential to subtract the background count rate from each reading.