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Attenuation coefficient & build up
factor
Submitted by
Sohail Imran
Submitted to
Dr. Asloob Ahmed Mudassar
Pakistan Institute of Engineering and Applied Sciences Nilore, Islamabad
Abstract:
In this experiment we determined the attenuation and build up factors for different
materials. Thickness was varied by changing the number of plates of different materials
between gamma ray source a(Cs-137) and detector. The counts were noted both for good
geometry and for bad geometry. Attenuation coefficient for Cu was observed as “0.5662 per
cm”, for Al it was “0.1943 per cm” and for lead it was “1.0613 per cm” for good and bad
geometry conditions respectively. The build-up factor showed an increase in magnitude
with increase in thickness of shielding material for both Cu and Al.
Introduction:
A radiation source is extremely hazardous to personnel and the materials which are
sensitive to nuclear radiations. These radiations emitted by the source must be properly
contained. Containment of radiations may be accomplished by keeping a material or by
constructing a shield which effectively absorbs the radiations before they penetrate the
shield. Economy often requires that a combination of two methods be used.
Working of NaI (Tl) detectors:
Thallium activated sodium iodide detector is the first practical solid detector used for
gamma rays and is still the most popular one for this purpose. The gamma rays interact in
the detector and they produce electrons and some cases produces positrons as well. When
these electrons move through the crustal they excite the atoms and while de-exciting, the
atoms produce a flash of light called scintillation. When the scintillations fall on the
photocathode of the photomultiplier, the electrons are produced. The initial pulse from
photocathode is very small which is amplified in stages, in a series of dynodes known as
photomultiplier tube.
Good geometry and bad geometry:
In order to find the buildup factor and linear attenuation coefficient to geometries
were used. In good geometry case two lead collimators were placed, one in front of gamma
ray source and the other in front of detector. Now only those gamma rays were detected
which either have suffered non collusion on the path or deflected negligibly. These counts of
the gamma rays are known as un-collided. While in bad geometry case the collimator placed
in front of detector was removed. Now the collided gamma rays were also arriving at the
detector along with un-collided rays. These counts are sum of collided and un-collided
gamma rays.
Apparatus:
Gamma ray source(Cs-137)
Plates of different materials (iron, aluminum, lead etc.)
Detector with necessary electronics.
Collimators
Power supply
Amplifiers
Pre amplifier
Multi-channel analyzer
Procedure:
In order to perform this experiment I took following steps
For good geometry, to lead collimators were used, one for source and other for
detector.
The whole system was in line and lead shielding around the source was sufficient.
The detector was connected with necessary electronics.
I switched on the apparatus at operating voltage with right EHT polarity.
I noted the counts for zero thickness of shielding material and increase the thickness
by changing the number of plates between source and detector. For each plate I
noted the counts.
For bad geometry I removed the lead collimator near the detector and noted the
counts from max thickness to zeros thickness of shielding material between the
source and detector.
I recorded background counts both for good geometry and bad geometry without
any source.
Observations and calculations:
The linear attenuation coefficient and build up factor of copper and aluminium is
calculated.
For Copper:
The thickness is varied in steps of plate thickness and three readings were taken at each
step.
Table: Good geometry
s.no Number of plates
Thickness ( cm )
Counts C1
Counts C2
Counts C3
Avg. counts ( C )
Ln( C )
1 0 0 83387 82613 82892 82964 11.33
2 1 1.3 38246 38002 38304 38184 10.55
3 2 2.6 17911 17944 17913 17923 9.79
4 3 3.9 8785 8699 8721 8735 9.08
5 4 5.2 4129 4307 4259 4232 8.35
6 5 6.5 2086 2054 2086 2075 7.64
If these results are plotted on a graph, the graph is a straight line, as shown in the
following figure.
Figure: Graph between thickness and “ln(counts)”
The attenuation of copper is the slope of graph between thickness and “ln (counts)”.
Slope of the graph is “0.5662”. Hence the attenuation coefficient of copper is “0.5662”.
Table: Bad geometry
s.no Number of plated
Thickness ( cm )
Counts C1
Counts C2
Counts C3
Average counts( C )
1 0 0 92605 93479 94495 93526
2 1 1.3 90759 91487 90868 91038
y = -0.5662x + 11.296
0.00
2.00
4.00
6.00
8.00
10.00
12.00
0 1 2 3 4 5 6 7
Ln (
C )
Thickness
3 2 2.6 227818 228288 225887 227331
4 3 3.9 256142 255965 256134 256080
5 4 5.2 168456 168375 168284 168372
6 5 6.5 88160 87746 87835 87914
Build up factor:
Good geometry counts = Cg
Bad geometry counts = Cb
Table: For copper
S.no Thickness ( cm )
Good geometry (Cg)
Bad geometry (Cb)
Build up factor
1 0 82964 93526 1.13
2 1.3 38184 91038 2.38
3 2.6 17923 227331 12.68
4 3.9 8735 256080 29.32
5 5.2 4232 168372 39.79
6 6.5 2075 87914 42.37
These results are plotted, as shown in the following figure.
Figure: Graph between thickness and build up factor
For Aluminium:
Table: Good geometry
s.no Number of plates
Thickness (cm)
Counts C1
Counts C2
Counts C3
Average counts( C )
Ln ( C )
1 0 0 83387 82613 82982 82994 11.33
2 1 0.63 77209 76513 76983 76902 11.25
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7
Bu
ild u
p f
acto
r
Thickness
3 2 1.26 67329 67472 67365 67389 11.12
4 3 1.89 59391 58902 59101 59131 10.99
5 4 2.52 52013 51603 52155 51924 10.86
6 5 3.15 45690 46100 45512 45767 10.73
These results were then plotted. The graph is nearly straight line.
Figure: Graph between thickness and “ln(counts)”
The slop of the graph is “0.1943”. So the linear attenuation coefficient of aluminium
is “0.1943”.
Table: Bad geometry
s.no Number of plates
Thickness (cm)
Counts C1
Counts C2
Counts C3
Average counts( C )
1 0 0 92605 93479 94495 93526
2 1 0.63 80658 80655 81746 81020
3 2 1.26 77287 77221 77090 77199
4 3 1.89 78569 78791 79705 79022
5 4 2.52 79834 80388 80719 80314
6 5 3.15 82890 82845 82154 82630
Build up factor:
Good geometry counts = Cg
Bad geometry counts = Cb
Table: For Aluminium
S.no Thickness ( cm )
Good geometry (Cg)
Bad geometry (Cb)
Build up factor
1 0 82994 93526 1.13
2 0.63 76902 81020 1.05
y = -0.1943x + 11.351
10.70
10.80
10.90
11.00
11.10
11.20
11.30
11.40
0 0.5 1 1.5 2 2.5 3 3.5
LN(
C )
Thickness
3 1.26 67389 77199 1.15
4 1.89 59131 79022 1.34
5 2.52 51924 80314 1.55
6 3.15 45767 82630 1.81
The plot of these results looks like
Figure: Graph between thickness and build up factor
For Lead:
Table: Good geometry
s.no Number of plates
Thickness (cm)
Counts C1
Counts C2
Counts C3
Average counts( C )
Ln ( C )
1 0 0 83387 82613 82982 82994 11.33
2 1 0.83 19372 19448 19664 19495 9.88
3 2 1.66 8075 8171 8191 8146 9.01
4 3 2.49 3788 3640 3671 3700 8.22
5 4 3.32 1786 1749 1704 1746 7.47
6 5 4.15 844 865 894 868 6.77
These results were then plotted. The graph is nearly straight line.
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0 0.5 1 1.5 2 2.5 3 3.5
Bu
ild u
p f
acto
r
Thickness
Figure: Graph between thickness and “ln(counts)”
The slop of the graph is “1.0613”. So the linear attenuation coefficient of lead is
“1.0613”.
Table: Bad geometry
s.no Number of plates
Thickness (cm)
Counts C1
Counts C2
Counts C3
Average counts( C )
1 0 0 92605 93479 94495 93526
2 1 0.83 131058 129865 129866 130263
3 2 1.66 234445 235236 234572 234751
4 3 2.49 148498 148836 148611 148648
5 4 3.32 69343 68601 69084 69009
6 5 4.15 32163 32283 32159 32202
Build up factor:
Good geometry counts = Cg
Bad geometry counts = Cb
Table: For lead
S.no Thickness ( cm )
Good geometry (Cg)
Bad geometry (Cb)
Build up factor
1 0 82994 93526 1.126901
2 0.83 19495 130263 6.681981
3 1.66 8146 234751 28.81913
y = -1.0613x + 10.978
0.00
2.00
4.00
6.00
8.00
10.00
12.00
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Ln(
cou
nts
)
Thickness
4 2.49 3700 148648 40.17884
5 3.32 1746 69009 39.5167
6 4.15 868 32202 37.11295
The plot of these results looks like
Figure: Graph between thickness and build up factor
Discussion:
The results showed that the attenuation coefficient is max for lead. So for shielding,
lead is best. The buildup of factor for copper and aluminium varies linearly. But for lead the
buildup factor varied dramatically. Initially it increased but then started to decrease.
0
5
10
15
20
25
30
35
40
45
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Bu
ild u
p f
acto
r
Thickness
