9.2 Geometrical Efficiency
149
through the crystal, or a plastic phosphor may be machined to such a shape that it
offers the maximum surface area to the solution of β-emitter.
Reproducible geometrical conditions are often achieved more readily by counting
liquids rather than solids (as it is very difficult to prepare an identical solid sample
source).
9.2.1 Self-absorption
In Chap. 8, we discussed that when sources for counting purposes were prepared
from the solution containing different amount of BaSO 4 with the same amount of
35 S activity, a saturation thickness was observed. In this experiment, the activity was
found to decrease with an increase in the amount of BaSO 4 . Alternatively, we can
repeat this experiment in a slightly different fashion. In a test tube, let us add a fixed
amount of BaCl 2 to a solution of Na 2 SO 4 labeled with
35 S. Then the entire amount
of BaCl 2 is precipitated as BaSO 4 . The test tube is centrifuged and the supernatant
is decanted. The precipitate is washed several times with water. A slurry of the
precipitate is made. Ten planchets are taken and are numbered as 1 to 10. Starting
from planchet No. 1, the slurry is added to each planchet in increasing amount i.e., 1,
2, 3, 4, 5, 6, 7, 8, 9, and 10 ml up to the 10th planchet. During the addition, care has
to be taken that the slurry should not overspill. For this purpose, planchets are kept
under the infra-red lamp and as the solution dries and the required amount of slurry
is added slowly. This way we have 10 planchets containing an increasing amount of
BaSO 4 labeled with
35 S. After the planchets are dried, the activity of each planchet is
calculated using a G.M. counter and the calculated activity versus amount of BaSO 4
is plotted. Care is taken that the precipitate has formed a uniform thickness (like Fig.
8.1A). One would expect to observe a linear increase in the activity with the amount
of BaSO 4 added, but on the contrary, the activity increases exponentially with an
increase in the amount of BaSO 4 (or so to say with an increase in the thickness of
the source) and reaches to a maximum value (constant value) beyond which there
is no increase in activity in spite of the fact that the planchet contains more activity
of BaSO 4 labeled with
35 S (Fig. 9.2). The thickness corresponding to this maximum
activity is known as a saturation thickness. Any further increase in the source
thickness beyond this value does not increase the count rate further.
Why do we observe such behavior? In Chap. 8, we explained the reasons for getting
this behavior. But it is important to realize that in the earlier experiment, the total
activity of Sulfur-35 added to each planchet was the same, but the amount of BaSO 4
precipitated in each planchet was different. As a result, the saturation thickness
activity was minimum. In the present experiment, the activity added to each planchet
with the increase in total weight of BaSO 4 . In other words, though activity, as well
as the weight of the precipitate increased in this experiment, but yet we get the effect
of saturation thickness. In order to understand this behavior, let’s divide the entire
thickness of the precipitate into many imaginary infinitesimal thin layers of BaSO 4
149
through the crystal, or a plastic phosphor may be machined to such a shape that it
offers the maximum surface area to the solution of β-emitter.
Reproducible geometrical conditions are often achieved more readily by counting
liquids rather than solids (as it is very difficult to prepare an identical solid sample
source).
9.2.1 Self-absorption
In Chap. 8, we discussed that when sources for counting purposes were prepared
from the solution containing different amount of BaSO 4 with the same amount of
35 S activity, a saturation thickness was observed. In this experiment, the activity was
found to decrease with an increase in the amount of BaSO 4 . Alternatively, we can
repeat this experiment in a slightly different fashion. In a test tube, let us add a fixed
amount of BaCl 2 to a solution of Na 2 SO 4 labeled with
35 S. Then the entire amount
of BaCl 2 is precipitated as BaSO 4 . The test tube is centrifuged and the supernatant
is decanted. The precipitate is washed several times with water. A slurry of the
precipitate is made. Ten planchets are taken and are numbered as 1 to 10. Starting
from planchet No. 1, the slurry is added to each planchet in increasing amount i.e., 1,
2, 3, 4, 5, 6, 7, 8, 9, and 10 ml up to the 10th planchet. During the addition, care has
to be taken that the slurry should not overspill. For this purpose, planchets are kept
under the infra-red lamp and as the solution dries and the required amount of slurry
is added slowly. This way we have 10 planchets containing an increasing amount of
BaSO 4 labeled with
35 S. After the planchets are dried, the activity of each planchet is
calculated using a G.M. counter and the calculated activity versus amount of BaSO 4
is plotted. Care is taken that the precipitate has formed a uniform thickness (like Fig.
8.1A). One would expect to observe a linear increase in the activity with the amount
of BaSO 4 added, but on the contrary, the activity increases exponentially with an
increase in the amount of BaSO 4 (or so to say with an increase in the thickness of
the source) and reaches to a maximum value (constant value) beyond which there
is no increase in activity in spite of the fact that the planchet contains more activity
of BaSO 4 labeled with
35 S (Fig. 9.2). The thickness corresponding to this maximum
activity is known as a saturation thickness. Any further increase in the source
thickness beyond this value does not increase the count rate further.
Why do we observe such behavior? In Chap. 8, we explained the reasons for getting
this behavior. But it is important to realize that in the earlier experiment, the total
activity of Sulfur-35 added to each planchet was the same, but the amount of BaSO 4
precipitated in each planchet was different. As a result, the saturation thickness
activity was minimum. In the present experiment, the activity added to each planchet
with the increase in total weight of BaSO 4 . In other words, though activity, as well
as the weight of the precipitate increased in this experiment, but yet we get the effect
of saturation thickness. In order to understand this behavior, let’s divide the entire
thickness of the precipitate into many imaginary infinitesimal thin layers of BaSO 4