Biomedical Engineering Reference
In-Depth Information
Fig. 12.9
Uniform, parallel beam of charged particles normally
incident on thick tissue slab. Fluence rate
=
ϕ
cm
-2
s
-1
.
Point Source of Gamma Rays
We next derive a simple formula for computing the exposure rate in air from a
point gamma source of activity
C
that emits an average photon energy
E
per disin-
tegration. The rate of energy release in the form of gamma photons escaping from
the source is
CE
. Neglecting attenuation in air, we can write for the energy fluence
rate, or intensity, through the surface of a sphere of radius
r
centered about the
source
˙
πr
2
)
. For monoenergetic photons, it follows from Eq. (8.61) that
the absorbed dose rate in air at the distance
r
from the source is
=
CE
/(4
µ
en
ρ
CE
πr
2
µ
en
D
=
˙
=
.
(12.24)
4
ρ
Here,
µ
en
/
ρ
is the mass energy-absorption coefficient of air for the photons. In-
spection of Fig. 8.12 shows that this coefficient has roughly the same value for
photons with energies between about 60 keV and 2 MeV:
µ
en
/
ρ
=
0.027
cm
2
g
-1
=
0.0027
m
2
kg
-1
. Therefore, we can apply Eq. (12.24) to any mixture of photons in
this energy range, writing
2.15
×
10
-4
CE
r
2
CE
r
2
0.0027
4
D
=
=
.
(12.25)
π
With
C
in Bq (s
-1
),
E
in J, and
r
inm,
D
is in Gy s
-1
. This relationship can be brought
into a more convenient form. Expressing the activity
C
in Ci and the energy
E
in
MeV, we have
10
-4
10
10
10
-13
2.15
×
×
C
×
3.7
×
×
E
×
1.60
×
D
=
r
2
10
-6
CE
r
2
1.27
×
Gy s
-1
.
=
(12.26)
