Biomedical Engineering Reference
In-Depth Information
thickness of a shield for which the photon intensity in a narrow beam is reduced to
1/e
of its original value is called the relaxation length. One relaxation length, there-
fore, is equal to
1/
µ
, the mean free path. The dependence of
B
in the figures on
shield thickness is expressed by its variation with the number of relaxation lengths,
µx
. In addition to isotropic point sources, Fig. 15.6 shows an example of buildup
factors for a broad, parallel beam of monoenergetic photons normally incident on
a uranium slab.
Figures 15.1-15.6 can be used with Eq. (15.2) to calculate the shielding thickness
x
necessary to reduce gamma-ray intensity from a value
I
0
to
I
.Sincetheexpo-
nential attenuation factor
e
-
µx
and the buildup factor
B
both depend on
x
,which
is originally unknown, the appropriate thickness for a given problem usually has
to be found by making successive approximations until Eq. (15.2) is satisfied. An
initial (low) estimate of the amount of shielding needed can be obtained by solving
Eq. (15.2) for
µ
1.One
can then add some additional shielding and see whether the values of
B
and the
exponential for the new thickness satisfy Eq. (15.2).
Two examples will illustrate gamma-ray shielding calculations.
x
with assumed narrow-beam geometry, that is, with
B
=
Example
Calculate the thickness of a lead shield needed to reduce the exposure rate 1 m from a
10-Ci point source of
42
Kto2.5mRh
-1
. The decay scheme of the
-
emitter is shown
β
in Fig. 15.7. The daughter
42
Ca is stable.
Fig. 15.2
Exposure buildup factors,
B
, in water for point
sources of monoenergetic photons of energies from 0.1 MeV to
10 MeV as functions of the number of relaxation lengths,
µ
x
.
