A hospital stores a point source of behind a lead wall
PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Radiation interactions, detection and dosimetry · Radiation interactions, detection and dosimetry
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Problem
A hospital stores a 50GBq point source of 137Cs behind a lead wall. Its ambient dose-equivalent rate obeys H˙=kγA/r2 with kγ=0.093mSvh−1m2GBq−1. A corridor used by members of the public lies r=4.0m from the source, on the far side of the wall, and is occupied continuously (occupancy factor 1, i.e.\ 8760h a year). The annual effective dose limit for a member of the public is 1mSv. At the 662keV line of 137Cs, lead has μatt=1.25cm−1, and once scattered photons are included a broad beam through a slab of thickness x transmits a fraction T=Be−μattx with build-up factor B=2.6, rather than the narrow-beam value e−μattx alone. Treat the source as a point emitting isotropically, with the wall the only attenuating material between source and corridor.
((a)) Find the dose-equivalent rate in the corridor with no shielding at all, and the average rate that would use up the whole annual public limit given the stated occupancy.
((b)) Find the lead thickness x needed so that the corridor rate, including build-up, does not exceed that limit. Then find the thickness a designer would specify by using narrow-beam attenuation alone (setting B=1 in the transmission law), and state what multiple of the annual limit that thinner wall would actually deliver.
((c)) Instead of adding more lead, the source could be relocated so the corridor is r=8.0m away. Find the lead thickness then needed (with build-up included), and compare the thickness saved with two half-value layers of lead.