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

EXTERNAL RADIATION SAFETY 521
Figure 10-4. Conditions for setting up Eq. (10.13).
The radiation doses rate from a source that is substantially less than infinitely
thick, containing a uniformly distributed gamma-emitting isotope, may be estimated
from the effective surface activity after allowing for self-absorption within the slab.
Consider a large slab of thickness t m (Fig. 10-4), containing Cv MBq/m 3 of uniformly
distributed radioactivity. The linear absorption coefficient of the slab material is μ.
The activity on the surface due to the radioactivity in the layer dx at a depth of
x is
d(Ca) = Cv d xe −μx . (10.13)
Integrating Eq. (10.13) over the total thickness t yields the effective surface activity:
Ca =
t
0
Cve −μx dx = Cv
μ (1 − e −μt ). (10.14)
Substituting Eq. (10.14) into Eq. (10.10) yields
˙
H = πƔ
Sv · m2
MBq · h × Cv MBq/m3 μ m−1 (1 − e −μt ) × ln r 2 + h2 h2 Sv
. (10.15)
h
In traditional units, where activity is in curies and Ɣ is in units of rems per Ci per
hour at 1 m, Eq. (10.15) becomes
H ˙
rem · m2
= πƔ
Ci · h × Cv Ci/m3 μ m−1 × (1 − e −μt ) × ln r 2 + h2 h2 rems
. (10.16)
h
In the illustration above where the surface dose rate of the concrete in the 30-gallon
drum was calculated as 60 mrems/h, let us calculate the dose rate on the central
axis of the cylinder at a height of 30.5 cm (1 ft.) above the top using Eq. (10.16).
The absorption coefficient for 0.661-MeV gammas in water is 0.032 cm 2 /g, and