Deciding Whether a Gamma Peak Is Reportable
A laboratory counts 500 g of dried soil in a Marinelli beaker for 600 s. At the 662 keV line, the gross peak area is 320 counts. A blank counted for the same time gives 200 counts in the same region. The detector efficiency at 662 keV is 0.12 counts per emitted photon, and the Cs-137 gamma yield is 0.85. The clearance criterion used by the facility for this nuclide in soil is 100 Bq/kg. The spectroscopy software flags any net peak above 100 counts as positive and automatically subtracts background. A colleague notices that the energy calibration may have shifted by 5% because the multichannel analyzer was serviced the previous day. The analyst must decide whether the result is statistically significant, whether the sample can be released, and whether a re-count is needed.
1. Compute the net counts, counting uncertainty, and activity with uncertainty.
Read the worked answer
Net peak = 320 - 200 = 120 counts. The counting uncertainty on the net is sqrt(320 + 200) = sqrt(520) = 22.8 counts (1 sigma), so the net is 120/22.8 = 5.3 sigma above background. Activity = net / (efficiency × yield × time × mass) = 120 / (0.12 × 0.85 × 600 s × 0.5 kg) = 120/30.6 = 3.92 Bq/kg. The 1 sigma activity uncertainty is 22.8/30.6 = 0.75 Bq/kg. So the result is 3.9 ± 0.7 Bq/kg (1 sigma), or about ±1.5 Bq/kg at 2 sigma.
2. Decide whether the result is significant and whether the sample can be released. Explain how the possible gain shift affects the decision.
Read the worked answer
The peak is statistically significant at about 5 sigma, so it is not a random fluctuation of the blank. The activity is far below the 100 Bq/kg clearance criterion; even a 2 sigma upper bound is about 5.4 Bq/kg, so release is defensible. However, the 100-count software flag is only a screening threshold, not a decision criterion; the analyst must use the uncertainty and the actual activity. The possible 5% gain shift at 662 keV is about 33 keV, enough to move the peak out of the region of interest. That could bias the gross count and the background subtraction. The analyst should check the peak centroid and shape, verify the calibration, and re-count or re-analyze before final release. Because the result is so far below the criterion, a re-count is a data-quality action rather than an urgent safety action.