Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

650 CHAPTER 12
Note that in this case we used absorption cross sections for 2200 m s −1 neutrons,
which leads to a conservative result when making criticality calculations for nuclear
safety.
The effective multiplication constant is useful for estimating the minimum concentration
of a fissile material in a solution of moderator that could become critical.
W Example 12.4
Estimate the minimum concentration of 93% enriched uranyl sulfate, UO2SO4, in
water in order that the solution form a critical mass.
Solution
The minimum concentration will occur when the size (or volume) of the solution
is infinitely large. In that case, in order to attain criticality,
keff = ηεpf = 1.
The value for η is calculated from Eq. (12.7), using the molar ratio of 0.27 : 3.66 from
the table in example 12.3 for 238 N/ 235 N:
549
η =
650 + 0.27
× 2.5 = 2.11.
× 2.8
3.66
To calculate f using Eq. (12.14), let us arrange the data as shown in the following
table, letting M represent the number of moles of UO2SO4 that is to be added to
1 mol of water, to give the minimum concentration that will result in k∞ = 1. In
Example 12.3, we calculated an atomic ratio of 235U : U to be 3.66 : 3.93. Using this
value gives the following:
MATERIAL σa, BARNS MOLES σa × MOLES
Uranium-235 650
3.66
M
3.93
605 M
Uranium-238 2.8
0.27
M
3.93
0.192 M
Water 0.664 1 0.664
O2SO4 0.491 M 0.491M
From the definition of f , Eq. (12.14), we have
f =
605M + 0.192M
605M + 0.192M + 0.664 + 0.491M =
605.2M
605.7M + 0.664 .