Required Practicals / Edexcel / Practical 16
16 A2 CP16

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

  1. Measure background count rate B (count for 5 minutes without the source; divide by 300 to get counts per second).
  2. Position the source at distance x from the GM tube window. Count for at least 2 minutes; calculate corrected count rate $I = C - B$.
  3. Repeat for eight to ten distances from ~5 cm to ~50 cm.
  4. Plot I vs $1/x^2$: straight line through origin confirms the inverse square law.
  5. 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.

Q1 3 marks

At 15 cm, the corrected count rate from a gamma source is 720 counts per minute. Predict the count rate at 45 cm.

Q2 2 marks

Explain why the inverse square law applies to gamma radiation in air but would not apply to alpha radiation at the same distances.