Inverse square law for gamma radiation (CP16)
Verify the inverse square law for gamma radiation by measuring corrected count rate at different distances.
Apparatus
- Sealed gamma source (Cs-137 or Co-60)
- Geiger-Muller tube and counter or ratemeter
- Metre rule and retort stand
- Stopwatch
Safety
- Handle the source with tongs only. Minimise exposure time.
- Return source to its lead container immediately when not taking readings.
- Complete a radiation risk assessment before the experiment.
Method
- Measure background count rate B (count for 5 minutes without the source; divide by 300 to get counts per second).
- Position the source at distance x from the GM tube window. Count for at least 2 minutes; calculate corrected count rate $I = C - B$.
- Repeat for eight to ten distances from ~5 cm to ~50 cm.
- Plot I vs $1/x^2$: straight line through origin confirms the inverse square law.
- Alternatively plot $\ln I$ vs $\ln x$: gradient should be $-2$.
Key Variables
Independent
Distance x
Dependent
Corrected count rate I
Controlled
Same source; Same GM tube and counter settings
Analysis and Results
- Gamma radiation is not significantly absorbed by air, so intensity follows $I = k/x^2$.
- Plot I vs $1/x^2$: straight line through origin.
- Background subtraction is essential; failure to subtract gives a non-zero intercept.
Common Errors
- Not subtracting background count rate.
- Measuring x from the lead shield rather than from the source itself.
- Counting for too short a time at large distances (high statistical uncertainty in low count rates).
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q13 marks
At 15 cm, the corrected count rate from a gamma source is 720 counts per minute. Predict the count rate at 45 cm.
Q22 marks
Explain why the inverse square law applies to gamma radiation in air but would not apply to alpha radiation at the same distances.