Required practical: verifying the inverse square law for gamma radiation

Nuclear Structure & Radiation — AQA A-Level Physics

Variables

Independent: distance x between source and detector (m).
Dependent: corrected count rate C.
Control: time interval of each measurement, same gamma source, same GM tube, aluminium foil to block alpha and beta.

Method

Measure background count rate with no source present. Take several readings and average.
Place the gamma source at a set starting distance (e.g. 5 cm) from the GM tube. Record counts in 60 seconds.
Take 3 readings at each distance and average. Repeat at 5 cm intervals up to 60 cm.
Subtract background from each reading to get corrected count rate C.

Analysis

If C ∝ 1/x², then 1/√C ∝ x.
Plot 1/√C (y-axis) against x (x-axis). A straight line through the origin confirms the inverse square law.
If the line does not pass through the origin, there is a systematic errorAn error that shifts all readings by the same amount in the same direction. Cannot be reduced by repeating measurements. in distance measurement (the source and detector are not at the ends of their housings).

Evaluation

Systematic errorAn error that shifts all readings by the same amount in the same direction. Cannot be reduced by repeating measurements.: the exact positions of source and detector within their tubes are unknown. Read the x-intercept correction from the graph.
Dead time: the GM tube may miss counts that arrive within ~100 μs of each other. Use a modern detector to reduce this.
Shield the GM tube with 2-3 mm aluminium to block any alpha or beta contamination.
Random errorAn error that causes readings to scatter unpredictably above and below the true value. Can be reduced by averaging repeated measurements.: radioactive decayThe spontaneous and random disintegration of an unstable nucleus, emitting radiation (alpha, beta, or gamma) to become more stable. is random. Use long counting times and repeat readings to reduce statistical uncertainty.

Examiner Tips and Tricks

The percentage uncertainty in a count is proportional to 1/√N where N is the number of counts.
Larger counts mean smaller percentage uncertainties — this is why you count for as long as possible.