Environmental Engineering Reference
In-Depth Information
The inal expression for the alpha-activity of
218
Po and
214
Po on the ilter (i.e., lungs) is
{
}
(
)
+
(
)
(
)
+
(
)
⎣
⎦
+
A
α
=
vk q F
θ
,
t
F
θ
,
t
q F
θ
,
t
q F
θ
,
t
(15.1)
a
a
a c
,
b b c
,
c
c c
,
Correspondingly, the beta- and gamma-activity of
214
Pb and
214
Bi is
{
}
(
)
+
(
)
(
)
+
(
)
(
)
⎣
⎦
+
⎣
⎦
+
A
=
vk q F
θ
,
t
F
θ
,
t
q F
θ
,
t
F
θ
,
t
q F
θ
t
(15.2)
β γ
,
a
a b
,
a c
,
b
b b
,
b c
,
c
c c
,
The integral absorbed dose to the lung will be
( )
( )
D E A t
=
d
t E
+
×
A t
d
t
(15.3)
A
a
c
c
where
E
A
and
E
c
are the energies of the alpha-particles of
218
Po and
214
Po.
After a series of transformations, Equation 15.3 can be present in the form
( )
+
( )
+
( )
⎣
⎦
D
=
vk q X
θ
q X
θ
q X
θ
(15.4)
a
a
a
b
b
c
c
where
X
i
represents the contribution of each decay product in the absorbed dose. Expressions (15.1)
and (15.2) are true for the dose to the whole lung. But practically measurements were made over the
pulmonary region of the lung. By comparing (15.2) and (15.3), the correlation between the integral
absorbed alpha-dose to the lung and the gamma-activity of
214
Pb and
214
Bi
A
γ
can be presented in
the form
(
)
D
=
A F
θ η η
, ;
t
;
(15.5)
a
γ
ba
ca
where
F
is the ratio of the right-hand sides of Equations 15.1 and 15.2
θ is the duration of exposure
t
is the time after exposure; η
ba
=
q
b
/
q
a
and η
ca
=
q
c
/
q
a
The direct correlation between the absorbed dose from alpha-emitters
218
Po and
214
Po and beta-
and gamma-emitters
214
Pb and
214
Bi in the lungs was at irst introduced in Ruzer (1958,1960a,b,1968).
As a irst step, it is important to know to what extent function
F
depends on shift of equilibrium
between
218
Po,
214
Pb, and
214
Bi. The results of the calculations are presented in Table 15.1.
The results in Table 15.1 suggest that by measuring directly the gamma-activity in the lungs,
we could avoid the radon decay products concentration measurements. In this case, the maximum
deviation from the mean value will be not more than 15%.
The inal expression for the integral absorbed dose of alpha-radiation for an exposure time of
more than 3 h can be written as
8
D
a
=
2 . ×10
A
θ
erg
(15.6)
γ
where
θ is the duration of inhalation in hours
A
γ
is the activity of gamma-emitters in Ci.
For the maximum permissible concentration (APC) of 30 pCi/L (1100 Bq/m
3
) (or in terms of
[PAEC] 3.8 × 10
4
MeV/L), a breathing rate of 20 L/min, and a standard lung deposition coeficient
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