Environmental Engineering Reference
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where
N
b
,
N
c
,
A
b
,
A
c
are the count rates and activities of RaB and RaC, respectively, in the lungs at
time
t
after exposure time θ. Then
e
e
(
N
+
N
)
/2
A
0
b
,
0
c
,
0
0
k
=
=
2
(
N
+
N
) (
/
A
+
A
)
b
c
b
c
N
=
e A N
,
=
e A
b
,
0
b
0
c
,
0
c
c
N
=
e A N
,
=
e A
b
b
b
c
c
c
(
e A
+
e A A
)(
+
A
)
b
0
c
0
c
b
k
=
2
2
A e A
(
+
e A
)
0
b
b
c
c
and inally
(
1
+
e
/
e
)(
1
+
A A
/
)
c
b
c
b
k q t
( , )
=
2
2[1
+
(
e
/
e A A
)(
/
)
]
c
b
c
b
When the shift of equilibrium between RaA, RaB, and RAC in the air changes from 1:1:1 to
1:0.03:0.01, the ratio of
A
c
(
t
)/
A
b
(
t
) in the lungs changes from 0.31 to 2.93. But due to the mode of the
function
k
2
(the ratios
e
c
/
e
b
and
A
c
/
A
b
are both in the numerator and denominator), the difference in
k
2
is not signiicant. For example, for a NaI(Tl) crystal 80 × 40 mm, the change in
k
2
is not more than
20% (Ruzer and Urusov, 1969).
In calculating the detection eficiency for RaB and RaC, we have to take into account the number
of gamma quanta per decay for RaB (0.823) and RaC (1.397) with their average energies of 0.316
and 0.717 MeV, respectively.
Relative eficiency
e
c
/
e
b
was calculated for the 80 × 40 mm NaI(Tl) crystal and the model of the
lungs (Ruzer and Urusov, 1969) according to the formula
=
∑
h k k k
e
e
i
l i b i c i
,
,
,
c
b
∑
h k k k
j
l j b j c j
,
,
,
where
h
is the yield of the correspondent gamma-line
k
l
and
k
b
are the absorption coeficients of the lungs and the body, respectively
k
c
is the detection eficiency of the crystal
Indexes
i
and
j
belong to RaC and RaB, respectively
Simplifying the expression for the average absorbed dose, assuming that the mass
m
of the lung
is 1000 g,
D
m
−
7
=
8 5 1
.
0
×
0
k k k N
0 γ
θ
mrad
(15.7)
1 2 3
,
where
θ is the duration of the inhalation
N
0,γ
is the count rate above the “background” (the “background” is the count rate measured for
the person before entering the workplace)
k
1
is the correction coeficient for decay of radon progeny in the lungs after the end of exposure
k
3
is the reciprocal of detection eficiency of the gamma-radiation of radon progeny in equilibrium
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