Gamma radiation — inverse-square law

AQA 3.8.1.2 · RP12

A-level Physics (7408) · Required practical 12 — method, techniques, safety, analysis and uncertainty. Includes errors documented in examiner reports.

Board and spec code confirmed against AQA 7408 · registry checked 2026-07-11How this checking works

Test whether background-corrected gamma count rate varies as the inverse square of source-to-detector distance.

Apparatus

Sealed gamma source in its labelled holder and the approved source store
Geiger–Müller tube with counter or digital rate meter
Metre rule with fixed source and detector reference markers
Clamps, stands and alignment guides
Stopwatch or counter timer and a spreadsheet for processing

Apparatus & techniques (AT)

AT a · analogue measurement

Measure source-to-detector distance from fixed effective reference positions using a metre rule.

AT b · digital instruments

Use a digital counter or rate meter with a fixed timing interval to record gamma detections.

AT k · ICT/data logging/processing

Process count rates, background correction, 1/r² values and counting uncertainties in a spreadsheet.

AT l · ionising radiation and detectors

Operate a Geiger–Müller detector with a sealed gamma source under the local ionising-radiation procedure.

Safety

Hazard

Ionising gamma radiation increases exposure risk.

Control

Use the minimum handling time, maximise distance, keep the source in its holder or shielded store, always move the source with handling tongs held at arm's length with the source window directed away from people, and follow the named radiation-protection supervisor's instructions.

Hazard

An unattended or misplaced sealed source creates a serious control failure.

Control

Keep a source-use record, maintain visual control, return the source immediately after measurements and confirm it is secured in the approved store.

Method

1With the source still stored, measure background counts for a long timed interval using the detector in the same position and with the same surroundings as the main investigation.
2Following local ionising-radiation rules, place the sealed source in its holder, align it with the detector and measure distance between the defined effective source and detector positions.
3Collect counts for the same stated time at several distances. Use sufficiently long count intervals for useful counting statistics and keep source, detector, alignment and surroundings unchanged.
4Return the source to its store whenever it is not being measured and after the final reading. Do not handle it directly or leave it unattended.
5Convert counts to rates, subtract the background rate, calculate 1/r² and retain the raw source-plus-background and background counts for uncertainty calculations.

CPAC focus (editorial)

This is an editorial study focus, not an AQA mapping of fixed CPAC competencies to this practical.

CPAC 2: Editorial focus: choose safe distances and count times that resolve the inverse-square trend above background.
CPAC 3: Editorial focus: minimise exposure using time, distance and shielding while following sealed-source handling rules.
CPAC 4: Editorial focus: retain timed raw and background counts with defined distance reference points.
CPAC 5: Editorial focus: apply √N statistics, propagate background uncertainty and test corrected rate against 1/r².

Variables

Independent

Distance from the effective gamma-source position to the detector's effective counting position

Dependent

Background-corrected count rate

Control

Gamma source and detector
Counting interval for the distance readings
Alignment, detector orientation and surrounding materials
Background-measurement arrangement

Results & processing

Plot corrected count rate against 1/r². A straight line supports the inverse-square relationship — the board writes it as I = k/x² — over the measured range.
For a raw count N collected in a fixed interval, use counting uncertainty √N; after background subtraction, combine the independent source-plus-background and scaled background uncertainties in quadrature.
Use more than two distances and inspect the intercept: a residual positive intercept can suggest incomplete background correction, scattering or an effective-distance offset.

Analysis skills

Subtract a separately measured background rate from source-plus-background rate.
Transform distance using 1/r² and test for a linear corrected-rate graph.
Calculate √N counting uncertainties and combine independently measured count-rate uncertainties in quadrature.

Uncertainty

Sources

Poisson variation in source-plus-background and background counts
Finite count time, especially where the corrected rate is low
Uncertainty in effective source and detector positions
Background drift, scattering and small alignment changes

Calculations

For N counts in time t, use count-rate uncertainty √N/t.
For corrected rate R = Rgross - Rbg, combine independent rate uncertainties as √(u_gross² + u_bg²).
Use percentage counting uncertainty 100/√N for a single raw count and propagate distance uncertainty through 1/r² where required.

Interpretation

Increasing count time raises N in proportion to time, so percentage counting uncertainty falls as 1/√time.
Longer counting reduces random counting uncertainty but does not remove biased distance references or an incorrect background rate.

Exam angles

Calculate and combine √N uncertainties for a background-corrected count rate.
Explain why longer count times reduce percentage random uncertainty by a square-root relationship.
Choose a graph that tests the inverse-square law with more than two distances.
Apply sealed-source controls specifically rather than suggesting generic calibration or same-person measurements.

Where students lose marks

Using half-range uncertainty for radioactive counts or writing the count uncertainty as N instead of √N.

Fix: Use √N for each Poisson count and combine independent background and source-plus-background contributions after scaling them to rates.

Examiner report: P3-21 · PDF p. 3

Subtracting a short, noisy background count without accounting for its uncertainty.

Fix: Measure background for a long interval, convert it to a rate and include its scaled √N uncertainty in the corrected rate.

Examiner report: P3-19 · PDF p. 3

Measuring distance from the outside edge of the source holder to the front casing of the detector without defining effective positions.

Fix: Use stated source-centre and detector-sensitive-volume reference marks consistently, and treat any offset as a systematic uncertainty.

Improve the method

Use longer count intervals, especially at large distances, to increase N and reduce the percentage counting uncertainty 100/√N.
Measure a long background interval and repeat it after the run to check for drift.
Fix the source and detector on an aligned track and use several distances spanning a useful range.

Source references

Specification: AQA 7408 specification §3.8.1.2 · PDF p. 42

Try it — exam-style

Hard

ORIGINAL

A detector records 900 source-plus-background counts in 60.0 s. Background measurement gives 144 counts in 120 s. Calculate the corrected count rate and its uncertainty, using √N counting uncertainties and combining independent rate uncertainties in quadrature.

[6 marks]

Total for this question: 6

Medium

ORIGINAL

The corrected count rate is 125 s⁻¹ at 0.200 m from a gamma source. Predict the corrected rate at 0.500 m if the inverse-square law applies.

[2 marks]

Total for this question: 2

Medium

ORIGINAL

A raw count has a percentage counting uncertainty of 6.0%. By what factor must the count time increase to reduce this to 3.0%, assuming the count rate is constant?

[3 marks]

Total for this question: 3

Questions are written in the style of past AQA papers — never copied from them.

Drill it properly

A-level Physics spec coverage

Nuclear physics, radiation and uncertainty practice for 7408.

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