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

570 CHAPTER 10
Using a value 2.7 mSv/h per MBq (10 4 mrems/h per mCi) at 1 cm for Ɣ, 0.022 cm −1
for μ in case of 2.26-MeV photons in water, and 34 cm for the radius gives
˙D = 1
2
Bq
· cm2
× 30 × 10−6 × 2.7mSv
cm3 MBq · h ×
˙D = 1.2 × 10 −2 mSv/h(1.2 mrems/h).
4π
0.022 cm −1 (1 − e −0.022 × 34 )
The dose rate at the surface of the shield due to both neutrons and gamma rays
is 22 μSv/h (2.2 mrems/h), which is very close to the desired figure of 20 μSv/h
(2 mrems/h). The gamma-ray dose rate could be reduced either by increasing the
gamma-ray absorption coefficient of the water shield by dissolving a high-atomicnumbered
substance, such as BaCl2, or by reducing the rate of production of the
gamma radiation. Of these possible alternatives, the simplest one is the reduction in
the production of gamma radiation. This is easily accomplished merely by dissolving
a boron compound in the water. Boron captures thermal neutrons with a capture
cross section of 755 b, according to the reaction 10 B + 1 n → 7 Li + γ (0.48 MeV).
The 0.48-MeV gamma is emitted in 93% of the captures. Either sodium tetraborate
(borax), Na2B4O7 · 10H2O, or boric acid, H3BO3, both of which are highly soluble
in water and very inexpensive, may be considered for this application. If suppression
of gamma radiation is the objective, boric acid may be preferred over borax, since
the sodium in the borax has a relatively high cross section, 505 mb, for the 23 Na(n,
γ ) 24 Na reaction. As a consequence of this reaction, a 6.96-MeV capture gamma is
emitted and radioactive 24 Na, which emits one 1.39-MeV beta, one 1.37-MeV gamma,
and one 2.75-MeV gamma per disintegration is produced.
The solubility of boric acid in water at room temperature is 63.2 g/L. The
formula weight of H3BO3 is 61.84. The concentration of boron atoms in the saturated
solution is
Cboron =
63.2 g L
molecules atom B
× 10−3 × 6.02 × 1023 × 1
L mL mol molecule
61.84 g
mol
Cboron = 6.15 × 10 20 atoms/mL.
If we consider the macroscopic cross sections for thermal-neutron capture of the
dissolved boron B and of the hydrogen H, we find that
H
B
= 0.13 cm−1
= 0.31.
0.42 cm−1 The flux of 2.26-MeV hydrogen gamma rays, and consequently the dose
rate, will be reduced by this factor to 0.31 × 0.012 mSv/h = 3.7 × 10 −3 mSv/h
(0.37 mrem/h). The dose rate due to the 10 B capture gammas, which is calculated
from Eq. (10.37) using a photon specific activity of 0.69 × 30 × 10 −6 “MBq”/cm 3
(5.6 × 10 −7 “mCi”/cm 3 ), an absorption coefficient for 0.48-MeV photons in water
of 0.033 cm −1 , and a value for Ɣ of 0.62 mGy-cm 2 /MBq-h (2300 mrads-cm 2 /mCi-h),