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

where
C = cost per unit volume of the shield,
A = area of the shield, and
t = thickness of the shield.
EXTERNAL RADIATION SAFETY 573
The decreased radiation detriment due to the additional shielding, expressed as
decreased collective dose, is given by
S = ˙
He −μt × f × N × τ, (10.44)
where
H ˙ = maximum dose-equivalent rate in the shielded area,
f = ratio of the average to maximum dose rates in the shielded area,
N = number of people in the shielded area,
τ = lifetime of the shielded installation,
μ = effective attenuation coefficient of shielding material, and
t = thickness of the additional shielding.
When we differentiate X and S with respect to the shield thickness t, we get
and
dX
dt
= C × A (10.45)
dS
dt = ˙
H × f × N × τ(−μ)e −μt . (10.46)
Substituting these two derivatives into Eq. (10.42), we have
CA= α × ˙
H × f × N × τ × μe −μt
(10.47)
e −μt CA
=
. (10.48)
α × H ˙ × f × N × τ × μ
Equation (10.48) may be solved for t, the optimum shield thickness:
CA
1
t = ln
× . (10.49)
α × H ˙ × f × N × τ × μ −μ