A sample of unknown composition is checked for sodium by thermal-neutron activation…
PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Radioactivity and decay modes · Radiation interactions, detection and dosimetry
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Problem
A sample of unknown composition is checked for sodium by thermal-neutron activation analysis, using 23Na(n,γ)24Na, thermal cross section σ=0.53b, 24Na half-life 15.0h, decaying with a 1368.5keV gamma ray emitted in essentially every decay. The sample is irradiated for 1.00h in a thermal flux ϕ=1.0×1013cm−2s−1, then counted immediately for 10.0min in a detector of 5.0% full-energy efficiency at that line. In that counting window the background under the peak is measured to be 900 counts.
((a)) Using the rule that a signal is detectable once it exceeds three standard deviations of the background (a simpler and looser rule than Chapter 10's detection limit LD=2.71+4.65B), find the minimum number of counts under the peak that would count as a detection.
((b)) Neglecting decay during the 10.0min count (it is small compared with the 15.0h half-life) and neglecting any delay between the end of irradiation and the start of counting, find the minimum detectable mass of sodium.