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
- Without the source present, count for at least 5 minutes to determine the background count rate B (counts per second).
- 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.
- Corrected count rate: $I = C - B$.
- Repeat for at least eight distances from ~5 cm to ~40 cm.
- 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.
Q13 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.
Q24 marks
Describe the safety precautions that must be followed when using a gamma source in the laboratory.
Q32 marks
Explain why it is essential to subtract the background count rate from each reading.