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Determination of Mass Absorption Coefficients in Pb and Al, and the Range in Al,
For Radiations from Co-60 and Cs-137 Nuclides
D. R. Sieglaff, Augustana College, Rock Island, Illinois, USA
Submitted 22 April 2007
ABSTRACT
The mass absorption coefficient in Pb for 0.66 MeV and 1.33 MeV gamma ray photons, and that in Al for
0.66 MeV gamma ray photons, was measured using a NaI scintillator/PMT detector and MCA system. The
0.66 MeV gamma rays originated from a Cs-137 sample, and the 1.33 MeV gamma rays originated from a
Co-60 sample. The range in Al for 0.52 MeV beta rays from a Cs-137 sample was measured using a GM
detector.
INTRODUCTION
The “stopping power” of materials such as those used in this study for high energy gamma and beta
radiation is of great fundamental and practical importance. It is not possible to accurately predict from
theory what thickness of any given material will be sufficient to absorb a given fraction of an incident
stream of nuclear radiation. Fortunately, this information is available through experimental measurements
of the type presented here. The loss of energetic particles through interaction with matter is characterized
by an absorption coefficient associated with a decaying exponential model. It is interesting to note that, in
their interaction with matter, photons are annihilated (i.e. truly removed from the incident stream), while
electrons are merely brought to rest. Therefore, in addition to the absorption coefficient, it is meaningful to
speak of the range of the beta ray, which is the maximum distance traveled before coming essentially to
rest.
Dean Sieglaff
Created: 22 Apr 2007
Modified:
1
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NEBRASKA WESLEYAN UNIVERSITY
SPRING 2010 - 2011
THEORY
The absorption of radiation is characterized by the equation
N  N0 exp   x  ,
(1)
where N0 is the number of particles of radiation counted during a certain time duration without any
absorber, N is the number counted during the same time with a thickness x of absorber between the source
of radiation and the detector, and  is the absorption coefficient. This equation may be cast into the linear
form
ln N   x  ln N0 .
(2)
The mass absorption coefficient m is defined as
m 

,

(3)
where  is the mass density of the absorber.
HV
TO PC
RUNNING
UCS20
SOFTWARE
USB
SPECTECH
UCS20
PREAMP
IN
SIGNAL
HV
NaI/PMT
DETECTOR
Pb SHIELD
SAMPLE
HOLDER
Figure 1. Apparatus for the study of gamma ray absorption.
Dean Sieglaff
Created: 22 Apr 2007
Modified:
2
PHYS-162 LAB
NEBRASKA WESLEYAN UNIVERSITY
SPRING 2010 - 2011
METHOD
To measure the attenuation constant for the absorption of gamma rays, a sample of radioactive material was
placed in a sample holder beneath a NaI scintillation detector and photomultiplier tube (PMT), as shown in
Figure 1, with enough room between the sample and the detector to place various thicknesses of absorbing
material. An initial pulse height spectrum was obtained using a SpecTech UCS20 multichannel analyzer
(MCA) with no absorbers. The energy peak associated with the sought radiation was identified, and the
number of counts in the peak channel was recorded. Without moving the radiation source, various
thicknesses of absorbing material were placed between the source and the detector. For each thickness
used, a new spectrum was acquired for the same amount of time as the initial measurement, and the number
of counts in the sought radiation peak, in the same channel as the initial measurement, was recorded.
HV
SPECTECH
ST360
PREAMP
IN
SIGNAL
HV
GM
DETECTOR
SAMPLE
HOLDER
Figure 2. Apparatus for the study of beta ray absorption.
To measure the range of 0.52 MeV beta rays from Cs-137 in Al, the sample was placed beneath a GeigerMueller (GM) detector, as shown in Figure 2. An initial number of counts was obtained using a SpecTech
ST360 radiation counter. Various thicknesses of Al were placed between the source and the detector. For
each thickness used, the number of counts was gathered over the same amount of time as the initial
measurement.
RESULTS
Figure 3a shows the attenuation of 0.66 MeV gamma ray photons from Cs-137 in Pb. Figure 3b shows the
same except in Al. Figure 3c shows the attenuation of 1.33 MeV gamma ray photons from Co-60 in Pb.
Dean Sieglaff
Created: 22 Apr 2007
Modified:
3
PHYS-162 LAB
NEBRASKA WESLEYAN UNIVERSITY
SPRING 2010 - 2011
These data were fit using a linear function of the form of equation (2). In each case the linear fit is shown.
Table 1 summarizes the absorption coefficients and mass absorption coefficients determined for each case.
Uncertainties are the standard error in the slope determination.
6.0
Natural Log of Counts
Natural Log of Counts
7.0
6.5
6.0
5.5
5.5
5.0
4.5
4.0
5.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Absorber Thickness (cm)
Absorber Thickness (cm)
b)
a)
Natural Log of Counts
5.3
5.2
5.1
5.0
4.9
4.8
4.7
4.6
4.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Absorber Thickness (cm)
c)
Figure 3. The attenuation of 0.66 MeV gamma ray photons in a) Pb, and b) Al. The attenuation of
1.33 MeV gamma ray photons in c) Pb.
Dean Sieglaff
Created: 22 Apr 2007
Modified:
4
PHYS-162 LAB
ENERGY OF
PHOTON
(MeV)
NEBRASKA WESLEYAN UNIVERSITY
SPRING 2010 - 2011
ABSORBER
MATERIAL
ABSORBER
DENSITY (g-cm-3)
ABSORPTION COEFFICIENT (cm-1)
MASS ABSORPTION
COEFFICIENT (cm2-g-1)
Pb
11.34
1.136 ± 0.037 (± 3.3%)
0.101 ± 0.003
Al
2.7
0.1842 ± 0.0034 (± 1.9%)
0.068 ± 0.001
Pb
11.34
0.520 ± 0.070 (± 13%)
0.046 ± 0.006
0.66
1.33
Table 1. Mass absorption coefficients and related data for the cases studied.
Figure 4a shows the attenuation of 0.52 MeV beta particles from Cs-137 in Al. A significant difficulty
arose because the gamma radiation emitted by the Cs-137 source was also detected by the GM detector.
However, each of the radiations exhibited a vastly different absorption coefficient. Therefore it was
possible to fit an attenuation curve to just the gamma ray contribution, as shown in Figure 4a. The number
of counts from the gamma rays, Ngamma, for the data that included both beta and gamma radiation was
estimated using the following formula
N gamma  exp  mx  ln  b   ,
(4)
where m is the slope and b is the intercept of the fit formula displayed in Figure 4a. For each value of x
investigated, Ngamma was computed and subtracted from the number of counts recorded, to produce a set of
corrected counts. To determine the range of beta particles in Al, those corrected count values greater than
N 0 , where N0 is the number of corrected counts obtained with no absorber, were included in a fit to
determine the attenuation of beta particles only in Al, as shown in Figure 4b. The range is defined as the
thickness of absorber required to just stop all of the beta particles. Experimentally, when the counts drop
“into the noise” for a given thickness, the definition is satisfied. The “noise” is the absolute statistical
N 0 . This noise level is marked on Figure 4b. The range is
uncertainty in the initial count value, or
therefore calculated by the following formula
x
Dean Sieglaff
Created: 22 Apr 2007
Modified:
ln


N0  b
m

5.53  11.2
 0.89  mm ,
6.29  mm 1
(5)
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SPRING 2010 - 2011
where m and b are the slope and intercept displayed in Figure 4b.
12
Natural Log of Counts
Natural Log of Counts
12
11
10
y = -0.0551x + 8.3542
9
8
7
y = -6.2889x + 11.147
11
10
9
8
7
6
5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Absorber Thickness (mm)
a)
0
0.2
0.4
0.6
0.8
1
Absorber Thickness (mm)
b)
Figure 4. a) The attenuation of 0.52 MeV beta rays and 0.66 MeV gamma rays in Al. A linear fit is
made to the gamma attenuation. b) Same as a) except with the estimated gamma counts subtracted
from the data. A linear fit is made to the beta attenuation.
DISCUSSION
It is seen that the mass absorption coefficients associated with the same gamma attenuation, from Table 1,
are similar even for materials with vastly different densities. It is seen also that the mass absorption
coefficient, in the same material, associated with a higher energy photon is less than that for a lower energy
photon. This is expected since the higher energy photons are “harder to stop.” The uncertainty in the mass
absorption coefficient measured for 1.33 MeV gamma ray photons could be lowered by obtaining a source
of higher activity. It is possible to compare the reported value of the range of beta particles to theory that
predicts an energy loss rate in matter of K = 2 MeV/(cm2/g) for relativistic charged particles1. If E is the
photon energy, then the reciprocal mass absorption coefficient would be E/K. But this is equal to x where
 is the mass density and x is the range. Therefore we have
x

1 E
cm3 
0.52  MeV


  0.096  cm  0.96  mm ,
 K 2.7  g  2  MeV  cm 2  g 1 
(6)
in excellent agreement with equation (5).
Dean Sieglaff
Created: 22 Apr 2007
Modified:
6
PHYS-162 LAB
NEBRASKA WESLEYAN UNIVERSITY
SPRING 2010 - 2011
CONCLUSION
The mass absorption coefficients in Pb for 0.66 MeV and 1.33 MeV gamma ray photons, and that in Al for
0.66 MeV gamma ray photons, were measured. The range in Al for 0.52 MeV beta rays was determined.
1
Melissinos, Experiments in Modern Physics, Academic Press, 1966, p.161.
Dean Sieglaff
Created: 22 Apr 2007
Modified:
7