Domain: Nuclear / reactor chemistry

The core of a certain research reactor, operating at a power of 250 kW, consists of an assembly of uranium rods and water, with a metal volume fraction of 0.75. The core has a volume of 32 L and is surrounded by a water reflector 15 cm thick. It is proposed to shield this reactor by 150 cm of unit-density water. Estimate the fast neutron dose rate (in mrem/hr) at the surface of this shield. The macroscopic removal cross-section of uranium is 0.174 cm^-1. A flux of 6.8 n/cm^2·s produces a dose equivalent rate of 1 mrem/hr.

Grading rubric:
criterion: States the total fission rate within the range of 7.7 × 10^15 to 7.9 × 10^15 fissions/s.
weight: 10
criterion: Uses the ratio of fission rate to core volume to define the volumetric fission rate.
weight: 10
criterion: Multiplies the volumetric fission rate by the average neutron yield (2.42) to find source strength.
weight: 10
criterion: Calculates the neutron source strength (S_v) between 5.8 × 10^11 and 6.0 × 10^11 n/(cm^3·s).
weight: 10
criterion: States the effective mixture removal cross section within a ±0.005 cm^−1 tolerance of 0.156 cm^−1.
weight: 10
criterion: Uses a point-kernel or geometric factor appropriate for a spherical source distribution.
weight: 10
criterion: Reports the emergent fast-neutron flux at the outer surface as approximately 5.48 × 10^1 n·cm^−2·s^−1.
weight: 20
criterion: Reports the final dose rate at the shield surface as approximately 8.1 mrem/h.
weight: 20

Answer:
approximately 8.1 mrem/h