Required Practical 12: Gamma Inverse-Square Law

Use a school-approved sealed gamma source and suitable detector in the supervised laboratory procedure. Keep source and detector aligned, measure their separation consistently from the effective source position and account for the detector’s sensitive region rather than the outside casing alone.

Measure background for a sufficiently long period with the source stored away. Take counts for known intervals at several distances, keeping the detector settings and orientation unchanged. Subtract background count rate from the total count rate. Follow the centre’s local rules, including minimising handling time, maximising distance when not measuring and using the specified storage and handling tools.

For a sufficiently small isotropic source and detector far enough apart, geometric spreading gives intensity proportional to 1/r². Plot corrected count rate against 1/r²; an approximately straight line through the origin supports the model over the tested range.

At very short distances, finite source and detector size make a point-geometry approximation poor, and small distance errors create large fractional effects. Scattering, absorption or detector dead time can also cause departures. A residual intercept may indicate imperfect background subtraction.

Radioactive counts fluctuate even with an unchanged source. For N independent counts, a useful counting uncertainty is approximately √N. A longer counting interval usually improves fractional precision because √N/N decreases as N grows.

Uncertainties from total and background measurements both affect the corrected rate. At large distances, the net signal may be small relative to background, so a short count is especially unreliable. Quote the count duration with the result and distinguish random scatter from a consistent distance-offset error.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.