Biomedical Engineering Reference
In-Depth Information
D
to exposure rate
X
Using hours as the unit of time and changing from dose rate
[Eq. (12.4)] gives
10
-6
CE
r
2
1.27
×
Gy
s
×
3600
s
1R
0.0088 Gy
X
=
h
×
0.5
CE
r
2
Rh
-1
.
=
(12.27)
This simple formula can be used to estimate the exposure rate from a point source
that emits gamma rays.
The specific gamma-ray constant,
˙
, for a nuclide is defined by writing
C
r
2
.
X
=
˙
(12.28)
This constant, which numerically gives the exposure rate per unit activity at unit
distance, is usually expressed in Rm
2
Ci
-1
h
-1
. Comparison with Eq. (12.27) shows
that the specific gamma-ray constant in these units is given approximately by
˙
=
0.5
E
,with
E
in MeV.
Example
(a) Estimate the specific gamma-ray constant for
137
Cs. (b) Estimate the exposure rate
at a distance of 1.7 m from a 100-mCi point source of
137
Cs.
Solution
(a) The isotope emits only a 0.662-MeV gamma ray in 85% of its transformations
(Appendix D). The average energy per disintegration released as gamma radiation is
therefore 0.85
×
0.662
=
0.563 MeV. The estimated specific gamma-ray constant for
137
Cs is therefore
˙
0.28 Rm
2
Ci
-1
h
-1
.
(b) From Eq. (12.28), the exposure rate at a distance
r
=
=
0.5
E
=
1.7 m from a point source
of activity
C
=
100 mCi
=
0. 1 Ci is
0.28
Rm
2
Ci h
0.1 Ci
(1.7 m)
2
=
X
10
-3
Rh
-1
9.7 mRh
-1
.
=
×
9.7
×
=
(12.29)
The accuracy of the approximations leading to Eq. (12.27) varies from nuclide to
nuclide. The measured specific gamma-ray constant for
137
Cs, 0.32 Rm
2
Ci
-1
h
-1
,
is somewhat larger than the estimate just obtained. For
60
Co, which emits two
gamma photons per disintegration, with energies 1.173 MeV and 1.332 MeV, the
estimated specific gamma-ray constant is 0.5(1.173 + 1.332)
1.3 Rm
2
Ci
-1
h
-1
,in
=
agreement with the measured value.
In addition to gamma rays, other photons can be emitted from a radionuclide.
125
I, for example, decays by electron capture, giving rise to the emission of char-
acteristic X rays (the major radiation) plus a relatively infrequent, soft (35-keV)
gamma photon. Internal bremsstrahlung from a beta particle
(
+
)
or cap-
tured electron accelerated near the nucleus can also occur, though this contribution
is often negligible. The exposure-rate constant,
-
or
β
β
˙
δ
, of a radionuclide is defined like
