This document summarizes an experiment on gamma ray spectroscopy and attenuation. Key findings include: 1) Gamma ray emission spectra were collected for isotopes 22Na, 60Co, 137Cs, and 133Ba and a mystery isotope was identified as 232Th. 2) Exponential attenuation models were tested for 137Cs and 60Co interacting with lead, aluminum, and graphite. The model was rejected for 137Cs but not for 60Co. 3) Mass attenuation coefficients were determined for the absorbing materials using photopeak photometry data from 137Cs and 60Co.

1. 1
Gamma Ray Spectroscopy
and Attenuation
Nikolas Guillemaud
Lab Partner: Choungkeat Ly
Physics 134
Professor: David Smith
Submitted: 6/23/14
Abstract:
The purpose of this experiment was to perform a spectroscopic examination of, and
identify key features in, the ɣ-ray emission spectrums for four different radioactive isotopes:
22
Na, 60
Co, 137
Cs, and 133
Ba. Furthermore, we used gamma ray spectroscopy to identify a
mystery element X. The Gaussian model for the photopeaks of these isotopes was rejected
with greater than 99% confidence for the majority of the fits as the P-values were 0.0001 .
Despite this, we were able to successfully determine which known gamma emissions the
experimental energies should correspond to. The mystery isotope was found to be 232
Th and
was contained within commercially available thorium welding rods.
Additionally, the mass attenuation coefficients of lead, aluminum, and graphite were
determined using photopeak photometry data from the elements 137
Cs at 661.657 KeV and
60
Co at 1173.237 KeV. The exponential attenuation model for the absorbing materials and
137
Cs was rejected with greater than 99% confidence  0.0001P  . This is in contrast to 60
Co
where, at this energy and activity level, the model produced P-values of
0.5254, 0.2628, and 0.9262P  for lead, aluminum, and graphite respectively. We
concluded that the exponential attenuation model could not be rejected.

2. 2
1. Introduction
1.1. Nuclear Decay and Gamma Rays
It was in the early 19th
century when Sir Ernest Rutherford first made his
breakthrough discoveries investigating radioactivity. In their 1903 paper “Radioactive
Change”, Sir Ernest Rutherford and Frederick Soddy put forth a theory for radioactive
disintegration. According to Rutherford and Soddy, a radioactive substance is
transformed into another substance in the sense that the atoms are changed from a “parent
element” to another “daughter element” (Rutherford 1903). This process causes
“emanations” or radiation to be released, the types of which Rutherford named α, β, and
ɣ (Rutherford 1912). When the unstable parent atom experiences nuclear decay, emission
of α or β radiation, it sometimes produces a daughter atom with a nucleus in an excited
state. The subsequent transition of the daughter atom, from an excited to a more stable
state, results in gamma radiation. While α and β radiations are highly energetic particles
ejected from the nucleus, ɣ radiation is photonic in nature and usually follows α and/or β
decay.
Shown below, in Fig. 1, are the decay schemes of 137
Cs, 133
Ba, 60
Co, and 22
Na
numbered (1-4) respectively. These decay schemes illustrate how ɣ-ray energies
correspond to discrete energy levels within the transition. With data on the discrete ɣ-ray
energies that are emitted, it is possible to perform ɣ-ray emission spectroscopy on the
aforementioned isotopes.

3. 3
(Images: Peterson 1996)
Figure 1: Decay schemes of: (1) 137
Cs, (2) 133
Ba, (3) 60
Co, and (4) 22
Na.
1.2. Gamma Rays Interacting with Matter
Gamma rays interact with matter through three main processes: Compton
scattering, photoelectric absorption, and pair production. The combination of these
processes is responsible for the attenuation of ɣ-rays when incident upon sufficiently
dense materials. The attenuated intensity of the ɣ-ray beam I can be expressed in terms
of the initial intensity 0I , the absorption coefficient  , and the depth of the attenuating
material x .
0
x
I I e 
 (3)

4. 4
This exponential relationship was first discovered by Soddy and Russell and discussed in
their 1909 paper, “The ɣ Rays of Uranium”.
1.2.1. Compton Scattering
In his 1923 paper, “Scattering of X-rays by Light Elements”, Compton theorized
that, as a result of a ballistic collision, some ɣ-ray photons incident on a target would
deflect at an angle and thus experience a change in momentum. This momentum is
conserved and transferred to the scattering electron as it recoils from the collision (Fig.2).
Known as the Compton effect/shift, the phenomenon is observed when a photon collides
with a free charged particle, or in the case of a bound electron, when the energy of the
incident photon is much greater than the binding energy of the electron (Chao 1930).
(Image: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/compton.html 5/18/14)
Figure 2: A depiction of Compton scattering shows an incident photon with an
initial wavelength i colliding with an electron and deflected through an angle 
with a longer wavelength f , due to the energy imparted upon the recoiling
electron.
Compton’s theory implied that the energy of the scattered photon would be equal
to that of the incident photon minus the kinetic energy imparted to the electron. Compton

5. 5
expected this energy reduction to result in a proportional reduction in frequency and
increase in wavelength (Compton 1923). He expressed the resultant wavelength f
mathematically as
(1 cos )f i
e
h
m c
     (1)
where i is the incident photon wavelength, em is the mass of the electron, c is the speed
of light, and  is the scattering angle of the photon. Recasting Eq. 1 in terms of the
incident and scattered photon energies can be done using the energy-wavelength relation
photon
hc
photonE  , thus producing Eq. 2.
2
0
1 1 (1 cos )
f eE E m c

  (2)
Solving this for the scattered energy, as a function of  and 0E , generates
 2
0
1 1 coso
e
f E
m c
E
E


 
(3)
where fE is the scattered photon energy and 0E the initial.
Compton scattering will contribute both a backscatter peak and Compton shoulder
to the spectrums of the analyzed isotopes. The energy of the backscatter peak is given by
  2 2
0 0
2
1 1 cos 1o o
e e
BS E E
m c m c
E E
E

 
  
(4)
while the energy of the Compton shoulder or limit is
2
0 0 2
1
1
1 o
e
CS BS E
m c
E E E E
 
    
 
 
(5)

6. 6
where BSE and CSE are indicative of the scattered photon and electron energies near
  . Energies vary between those values and form a “plateau” feature. The drop off in
counts or the “valley” before the photopeak is a manifestation of the maximum energy
transferable due to Compton scattering.
1.2.2. Photoelectric Absorption
It was in his 1905 paper titled, “Concerning an Heuristic Point of View Toward
the Emission and Transformation of Light”, Einstein first explained the photoelectric
effect. In general, the photoelectric effect is the property of metals to eject loosely bound
electrons from their surface by absorbing an incident photon as a complete unit of energy,
or quanta. The photon energy must be greater than or equal to the binding energy of the
electron for this process to occur; any remaining energy after electron liberation is
converted to kinetic energy of the electron (Fig. 3). The binding energy is dependent on
the work function of the material upon which the photons are incident (Einstein 1905).
Figure 3: A depiction of the photoelectric effect. The left side shows three incident
photons of differing energy incident on a metal surface. The lowest frequency

7. 7
photon fails to liberate an electron. The middle figure shows that it’s energy h
was not enough to overcome the work function  . The middle and high frequency
photons eject electrons with some kinetic energy, shown as I and II respectively in
the plot on the right.
Gamma ray photons are of high enough energy to overcome the binding energies
of the inner-shell electrons. When inner-shell electrons are ejected the vacancy must be
filled by an electron of higher energy. The drop in energy is accounted for by an X-ray
photon emission. This is known as K-shell fluorescence or XRF (Smith 2014).
Additionally, it is important to note that the photoelectric effect is completely
independent of beam intensity. Only the energies of the incident photons are important.
Einstein’s insights provided important support for the quantum theory of light.
1.2.3. Pair Production
Pair production is the conversion of a photon’s energy, after imparting momentum
to the nucleus of an atom, in to mass via Einstein’s 2
E mc . Specifically for our
experiment, a photon with energy greater than 1.022MeV, in the ɣ-ray range, can
produce a positron and electron pair within material, seen in Fig. 4 below (Smith 2014).
Each of these particles has a rest mass energy of 0.511MeV, thus
 2
2 2 0.511MeV 1.022MeVeE m c   (6)
is the minimum required energy for a ɣ-ray photon to undergo pair production.
Subsequently, the positron quickly annihilates with an electron inside the material and
produces two ɣ-ray photons with 511 KeVPPE  .

8. 8
Figure 4: Diagram of a photon interacting with an atomic nucleus and undergoing pair
production.
2. Procedure
2.1. Experimental Setup and Equipment
We were given samples of the radioactive isotopes 137
Cs, 133
Ba, 60
Co, and 22
Na.
When these sources experienced nuclear decay they released β-particles
(electrons/positrons) and produced ɣ-ray photons of varying energies. To detect the
radiations we used a 2x2 inch NaI(Ti) crystalline scintillator coupled with a Canberra
photomultiplier tube, model 2m2/2.
The detector was mounted to a metal stand above the sample isotopes (Fig.5). The
scintillator contained a conduction-valence band gap with a large energy difference.
Within that band gap was an energy differential equal to the energy of photons found in
visible light; a manifestation of the Thallium (Ti) doping. When absorbed by the
scintillator, photons would then cause electrons within the crystal to excite in to the
higher energy conduction band. On their way back down to the valence energy, their
stable state, the electrons released photons of visible light; called scintillation light.

9. 9
Figure 5: Photograph of our experimental setup. A two point calibration reading with both the
barium and cesium samples is shown here.
The scintillation light was then fed in to the photomultiplier tube (PMT) in order
to convert scintillation photons into large pulses of electrons. When scintillation photons
entered the PMT they were incident upon a photocathode and, through the photoelectric
effect, electrons were freed from the surface (Brown 2014). The freed electrons were then
accelerated by electric potential difference through a series of electrodes, known as
dynodes. Each of the dynodes, in turn, produced multiple electrons for each incoming
electron. The process, known as photomultiplier gain, produced easily measurable signals
from the scintillator. The energy of the collected photons was then examined using
multichannel analyzer (MCA) software.
The multichannel analyzer used was the Genie 2000 Gamma Acquisition and
Analysis v.3.1 software. The MCA was used to amplify, shape, and digitize the electron

10. 10
pulses fed to it from the PMT (Brown 2013). The software placed each electron pulse
from the PMT in to a digital channel according to its amplitude. It created a histogram
(spectrum) that we could calibrate to obtain the energy and number of the photons
absorbed by the scintillator.
2.2. Data Collection
2.2.1. Gamma Ray Emission Spectra
To capture the spectrum data of 137
Cs, 133
Ba, 60
Co, and 22
Na we first positioned
the detector at a height 8.65 0.05cm above the sample. To begin, we setup the MCA to
apply a potential difference of 850V to the PMT and record the data for precisely 300s of
live time. Next, we took a two point energy calibration reading using the barium and
cesium samples simultaneously. The MCA was then calibrated accordingly with the
known photopeak energies of those isotopes. We then proceeded to collect spectrum data
for each isotope individually. A background reading was taken after completing all four
isotopes, again for 300s. All of the data collected was saved to a text file for further
analysis. Additionally, the spectrum data of an unknown isotope X was collected in this
manner but at a voltage of 880V and using a one point calibration with the photopeak
from cesium.
2.2.2. Gamma Ray Mass Attenuation
To begin, we measured the depth of all the lead, aluminum, and graphite plates
that were to be used for attenuation with a vernier caliper; recording those values in our
lab notebooks. Next, we set the detector to a height of 10.8cm above the isotope bezel in
order to accommodate the plates of attenuating material.

11. 11
To collect attenuation data for 137
Cs the voltage was set to 965V in the MCA
settings. Then a two point calibration reading was taken, again with barium and cesium
simultaneously for 300s, and the MCA calibrated as done previously but at the new
voltage. We then collected data for varying thicknesses of aluminum, graphite, and lead
up to ~1000 counts in the main photopeak channel being sure to record the live time of
the detector for each depth. Additionally, a measurement with no plates was recorded for
initial intensity 0I . Lastly, a background measurement was taken for 300s. All the count
data was saved to text files as before.
To collect attenuation data for 60
Co the voltage was set to 880V in the MCA
settings. Then a two point calibration reading was taken, this time with cesium and cobalt
simultaneously for 300s, and the MCA calibrated as done previously. We then set out to
record data for ~1000 counts in the primary photopeak channel and recorded the live
times of the detector in our notebooks. After taking data for varying thicknesses of
graphite, we realized that we needed to expedite the process. Subsequently, the data for
aluminum and lead were recorded up to ~300 counts under the main photopeak channel.
Additionally, a measurement with no plates was recorded for initial intensity 0I . Lastly, a
background measurement was taken for 300s. Again, all data was saved to text files for
later analysis.
3. Results
3.1. Gamma Ray Emission Spectra Analysis
The experimental data saved in the text files contained only the number of counts
per channel. This large amount of data required some preliminary analysis to be

12. 12
meaningful. First, the background counts were subtracted from the sample counts for
every channel in the spectrum of each isotope. This required that their respective errors,
iN from Poisson statistics where iN is the number of counts in a given channel, be
added in quadrature. The corrected counts per channel, for the range of channels that
contained a feature of interest, were then fit with a Gaussian function combined with a
linear background; utilizing the new error f i ibN N   . Here, ibN is the number of
counts from the background spectrum.
The Gaussian fits produced the mean channel mCh of the spectral feature peaks,
with error mCh . This was done for each peak of interest using Gnuplot. Table 1 provides
the mean channel, the determined energies dE , and their corresponding errors.
A two point energy calibration was done manually, for each spectrum, using the
saved calibration data. To determine the energies from the mean channel of a spectral
feature, the two point calibration was performed using the linear relationship
 
 
 
1
2 1 1
2 1
m
d
Ch Ch
E E E E
Ch Ch

  

(7)
where dE is the energy to be determined from the mean channel mCh . Furthermore, 1E
and 1Ch correspond to one point in the calibration, while 2E and 2Ch correspond to the
second. The energies 1E and 2E are the known photopeak energies for the chosen
calibration elements. The calibration channels 1Ch and 2Ch along with their
corresponding channel errors were also obtained through Gaussian fitting. The error for
each energy dE was obtained via the “bump up and down” method; utilizing the Gnuplot

13. 13
generated errors of both the calibration peaks ( 1Ch and 2Ch ) and the peaks of interest (
mCh ). This method of error estimation produced slightly differing values for high-side
and low-side error.
Table 1: This table presents results of the fitting done in Gnuplot for spectroscopic analysis,
including the mean channel values mCh and the energy determinations dE , along with their
corresponding errors, for features of interest in the spectrums of the five radioactive isotopes.
Figures 8-12 are the background corrected gamma emission spectrums for each isotope
plotted and labeled with the determined energies for each peak of interest.
Isotope Peak # Reduced χ2 P-value Chm σ Chm Ed (KeV) σ Ed Low (KeV) σ Ed High (KeV)
137
Cs 1 1.98 0.0093 17.5003 0.0222 27.088 0.302 0.302
2 9.33 < 0.0001 92.6177 0.2945 207.540 1.072 1.073
3 5.36 < 0.0001 283.7550 0.0464 666.702 0.772 0.773
133
Ba 1 96.56 < 0.0001 16.9630 0.0432 25.797 0.351 0.352
2 90.22 < 0.0001 40.3407 0.1226 81.957 0.578 0.579
3 3.76 < 0.0001 74.2026 0.1413 163.302 0.676 0.676
4 2.99 < 0.0001 133.3910 0.7268 305.488 2.173 2.176
5 8.69 < 0.0001 157.8600 0.0827 364.269 0.665 0.665
60
Co 1 4.16 < 0.0001 104.5900 0.4404 236.300 1.441 1.443
2 1.31 0.0394 490.9780 0.1345 1164.506 1.305 1.306
3 1.85 < 0.0001 556.0090 0.1649 1320.727 1.478 1.480
22
Na 1 5.82 < 0.0001 86.8846 0.8612 193.767 2.423 2.427
2 1.73 0.0006 221.1160 0.0891 516.226 0.778 0.779
3 1.08 0.3062 531.7200 0.3669 1262.379 1.926 1.928
X 1 2.37 < 0.0001 39.1838 0.3386 70.825 0.762 0.765
2 2.99 < 0.0001 136.5370 0.3890 246.793 1.228 1.233
3 1.28 0.0952 324.7510 0.5926 586.993 2.321 2.331
4 1.82 < 0.0001 507.3220 1.7680 916.993 5.145 5.167

14. 14
Figure 8: Plot of cesium spectrum.
Figure 9: Plot of barium spectrum.

15. 15
Figure 10: Plot of cobalt spectrum.
Figure 11: Plot of sodium spectrum.

16. 16
Figure 12: Plot of unknown element X spectrum.
3.2. Gamma Ray Mass Attenuation Coefficients
The photopeaks in the spectrums of 137
Cs and 60
Co were first fit as above, using a
Gaussian in conjunction with a linear background. The fit was repeated for each depth of
lead, aluminum, and graphite, as well as in the absence of any attenuating material. The
Gaussian fitting generated a value for the net area under the photopeak along with its
error. The net area under the Gaussian fit represents the total number of photons
collected for a specific peak aN . The intensity of the beam of ɣ-rays is proportional to
the number of photons emitted per second a
a
N
a tn  , where at is the elapsed live time of
the detector. Equation 3 can now be written as 0
ax
an n e 
 , where 0n is the number of
photons per second with no attenuating material present. Furthermore, to fit the

17. 17
exponential model and obtain the mass absorption coefficients for the different
materials, Eq. 3 can be manipulated to the form
 m axa
o
n
e
n
 
 . (8)
When fit in this form, the mass absorption coefficient m

  , where  is the density
of the material. The density values, and the accepted ranges for the mass attenuation
coefficients, come from the National Institute of Standards and Technology (Hubbell
2004). The densities of the materials are 3
11.35 g/cmPb  , 3
2.699 g/cmAl  , and
3
1.700 g/cmC  .
The error was calculated in the following way. For the Gaussian fits, and the
linear background fits, the simple iN iN  was used as the error bars. The error on the
fitted Gaussian area aN was then used to calculate Na
a an t

  . After subtracting the
background counts per second, the actual error associated with an became
   
2 2
af a abn n n    . Here, Nab
ab abn t

  is the error on the number of counts per
second contributed by the background. Next, the error on the ratio of counts a
o
n
n was
determined using
   
2 2
/
n naf o
a o a on n n n
 
   . (9)
This was error used when the exponential attenuation model was fit to the data. After
fitting, the error on the mass absorption coefficient m was generated by Gnuplot. The
results of the preceding fits and calculations are presented in below in Table 2.

18. 18
Table 2: This table presents the results of the fitting from Gnuplot, including: the net area aN ,
the ratio of intensities a
o
n
n , and the mass attenuation coefficients m , along with their respective
errors. Note that the depth error increases with the number plates but remained miniscule enough
to neglect.
Figures 13-18 show the mass attenuation model fits for both elements and all three materials.
Isotope Material
xa (cm)
(±0.002 -
0.018)
Gauss Fit
Reduced
χ2
Gauss Fit
P-value
Area Na
(counts)
σ Na
ta (s)
(± 0.001)
na / no (σ na)/no
μm
(cm2
/g)
σ μm
(cm2
/g)
137
Cs Lead 0.0000 1.45 0.0002 52699.6 302.3 81.78 1.0000 0.0081 0.0864 0.0069
Peak 3 0.3627 4.10 < 0.0001 51968.6 504.7 105.06 0.7666 0.0113
661.7 KeV 1.0244 4.66 < 0.0001 50452.3 585.9 229.81 0.3379 0.0130 Reduced χ2 P-value
1.7013 4.74 < 0.0001 47891.2 619.3 480.05 0.1513 0.0143 11.8300 < 0.0001
2.9764 4.19 < 0.0001 41217.1 625.9 1877.08 0.0300 0.0186
Aluminum 0.0000 1.45 0.0002 52699.6 302.3 81.78 1.0000 0.0081 0.0583 0.0058
0.7254 1.32 0.0029 52089.1 284.8 84.34 0.9582 0.0079
1.4092 2.09 < 0.0001 50832.5 368.9 96.30 0.8184 0.0093 Reduced χ2 P-value
2.0744 2.28 < 0.0001 47095.0 377.4 100.85 0.7235 0.0099 19.6900 < 0.0001
4.6614 4.45 < 0.0001 45851.7 569.8 166.50 0.4249 0.0137
9.7706 9.25 < 0.0001 41825.1 901.5 431.61 0.1468 0.0223
Graphite 0.0000 1.45 0.0002 52699.6 302.3 81.78 1.0000 0.0081 0.0715 0.0049
1.5065 1.82 < 0.0001 51498.2 331.4 89.53 0.8922 0.0086
3.0043 2.07 < 0.0001 50958.9 371.4 113.99 0.6924 0.0093 Reduced χ2 P-value
4.4999 3.20 < 0.0001 48483.0 470.4 135.13 0.5549 0.0113 13.8200 < 0.0001
5.9962 2.74 < 0.0001 49704.1 448.5 165.80 0.4630 0.0107
60
Co Lead 0.0000 1.54 0.0014 42389.9 700.0 593.06 1.0000 0.0237 0.0596 0.0039
Peak 2 0.3627 1.40 0.0062 14363.6 335.8 261.67 0.7629 0.0290
1173.2 KeV 1.0244 0.76 0.9416 13026.7 416.2 328.01 0.5458 0.0364 Reduced χ2 P-value
1.7013 1.29 0.0309 12255.7 880.2 653.25 0.2462 0.0745 0.7990 0.5254
2.9764 1.14 0.1847 10291.5 403.2 1129.81 0.1082 0.0479
Aluminum 0.0000 1.54 0.0014 42389.9 700.0 593.06 1.0000 0.0237 0.0544 0.0035
0.7254 1.36 0.0130 12027.0 320.6 175.01 0.9606 0.0316
1.4092 1.20 0.0966 11871.6 257.9 195.61 0.8458 0.0276 Reduced χ2 P-value
2.0744 1.65 < 0.0001 11894.7 294.3 222.36 0.7429 0.0301 1.2900 0.2628
4.6614 0.96 0.5824 11160.0 274.0 310.16 0.4925 0.0302
5.1092 1.46 0.0021 10739.0 276.1 337.44 0.4330 0.0377
Graphite 0.0000 1.54 0.0014 42389.9 700.0 593.06 1.0000 0.0237 0.0614 0.0015
1.4956 1.46 0.0052 40003.5 845.4 639.64 0.8722 0.0272
2.9934 1.72 < 0.0001 41454.1 788.1 779.46 0.7384 0.0256 Reduced χ2 P-value
4.4999 1.45 0.0052 39790.4 738.3 871.74 0.6306 0.0254 0.222 0.9262
5.9962 1.46 0.0052 38863.4 802.0 1029.13 0.5179 0.0271
Model Fit
Model Fit
Model Fit
Model Fit
Model Fit
Model Fit

19. 19
Figure 13: Plot of the ɣ-ray attenuation as function of material depth for cesium and lead.
Figure 14: Plot of the ɣ-ray attenuation as function of material depth for cesium and aluminum.

20. 20
Figure 15: Plot of the ɣ-ray attenuation as function of material depth for cesium and graphite.
Figure 16: Plot of the ɣ-ray attenuation as function of material depth for cobalt and lead.

21. 21
Figure 17: Plot of the ɣ-ray attenuation as function of material depth for cobalt and aluminum.
Figure 18: Plot of the ɣ-ray attenuation as function of material depth for cobalt and graphite.

22. 22
4. Discussion
4.1. Gamma Ray Spectrum Analysis
As can be seen in Table 1, the P-values indicate that the Gaussian model for the
peaks of interest can be rejected with a degree of confidence better than 90% in most
cases. This is caused by two main reasons. First, the 2
 values are dependent upon the
number of counts and shapes of the peaks. Higher count data produces lower relative
error, so data taken for longer periods of time, or more active sources, required “tighter”
fits. This is especially apparent for large peaks. Second, some peaks actually consist of
multiple energy level contributions. This distorted a few of the expected Gaussian
shapes, by broadening or adding a degree of “lumpiness” to the peaks through
combining counts, and contributed to the degradation of fits.
These considerations were important while identifying features in the gamma ray
spectra. It implies that the accepted energies of the peaks, from NIST (Hubbell 2004),
may fall outside the error ranges of the Gaussian determined energies. Additionally, we
noted some slight thermal drift between the calibration and spectra data in the MCA;
even after operating for hours. To minimize the effect, a period of time was allowed for
“warm up” whenever the equipment had to be powered on, or the voltage changed.
4.1.1. Cesium-137
The cesium spectrum in Fig. 8 has four distinct features. Peak 1 was found to
have energy of 1 27.09 0.03 KeVdE   and is due to the Ba Kα x-ray fluorescence, which
has an energy 32.194 KeVXRFE  . Peak 2 had a determined energy of
2 207.54 1.07 KeVdE   and, using Eq. 4 and the energy of Peak 3, this peak was

23. 23
determined to be the Compton backscatter where 3 184.71 KeVBSE  . The Compton
shoulder is easily identified in the same manner with Eq.5. Peak 3 is on the far right of
the spectrum. Using the decay scheme from Fig. 1, we found Peak 3 to be the primary
photopeak. Comparing the photopeak’s determined energy of 3 666.70 0.30 KeVdE  
to its known value of 3 661.657 KeVE  generated a Z-score of 6.47Z  . This means it is
over six standard deviations above the accepted value. These values are not in agreement. The
discrepancy is attributed to thermal drift as well having performed independent Gaussian fits for
the calibration and spectra data of this peak, leading to differing mCh values.
4.1.2. Barium-133
The barium spectrum in Fig. 9 has five features of interest that the decay scheme
in Fig.1 helped to identify. Peak 1 was found to have energy of 1 25.80 0.35 KeVdE  
and corresponds to the Cs Kα x-ray fluorescence photon energy of 30.973 KeVXRFE  .
Peak 2 was determined to have an energy of 2 81.96 0.58 KeVdE   . The decay scheme
suggests this peak corresponds to a gamma photon with energy of 2 80.997 KeVE  .
Comparing these two values generated a 1.66Z  . Peak 3 was proof of a photon energy
near 3 163.30 0.68 KeVdE   and was expected to have the value 3 160.613 KeVE 
 3.95Z  . Lastly, Peaks 4 and 5 were found to have energies of
4 305.49 2.17 KeVdE   and 5 364.27 0.67 KeVdE   respectively. It is important to
note that these two peaks had significant distorting overlap. With this in mind, they lend
themselves to identifying as the gamma rays with energies of 4 302.853 KeVE 

24. 24
 2.17Z  and 5 356.017 KeVE   12.32Z  . Overall, the Z-scores here indicate that
the energy values are again not in agreement.
4.1.3. Cobalt-60
The cobalt gamma emission spectrum is presented in Fig.10 and contains four
features of interest. Peak 1 was found to have energy of 1 236.30 1.44 KeVdE   . Using
Eq. 4 once again, this peak was determined to be the Compton backscatter. The
backscatter energy from Peak 2 was expected to be 2 209.53 KeVBSE  and the Compton
backscatter from Peak 3 was predicted to have 3 214.08 KeVBSE  . This overlapping
backscatter not only increased the energy of the combined peak, it also distorted the
Gaussian shape. Additionally, observing that this peak has a number of counts near that
of the two photopeaks further supports the identification of Peak 1 as the combined
Compton backscatter. As before, the Compton shoulder is also easily identified using Eq.
5.
Peak 2 is the first photopeak in cobalt and, according to its decay scheme, should
have an energy of 2 1173.237 KeVE  . Comparing that value to its determined energy
2 1164.51 1.31 KeVdE   generated a 6.66Z   . Peak 3 is the second photopeak of
cobalt with a known energy of 3 1332.501 KeVE  , compared to its determined energy of
3 1320.73 1.48 KeVdE   resulted in a 7.95Z   . The determined energies of the two
photopeaks fall more than six sigma below the expected values in both cases. A double
Gaussian fit, with linear background, should serve to reduce energy differences in future
analysis.

25. 25
4.1.4. Sodium-22
The sodium gamma emission spectrum can be seen in Fig.11 and contains four
peaks of interest. Peak 1 was found to have energy of 1 193.77 2.42 KeVdE   . Using
Eq. 4 as previously done, this peak was determined to be the Compton backscatter. The
backscatter energy from Peak 3 was predicted to be 3 212.49 KeVBSE  . The Gaussian
shape of this peak is very distorted and noisy so it not surprising that the determined
energy was quite different from the expected. The second peak, Peak 2, is a result of pair
production. With a determined energy of 2 516.23 0.78 KeVdE   the correlation with
Eq.6 was apparent. The annihilation of a pair produced positron causes two gamma ray
photons, each with 511 KeVPPE  , to be released. This dominant peak indicated that
pair production readily occured as a result of sodium gamma radiation.
To the right of the Compton shoulder is Peak 3. It is the primary photopeak of
sodium and should have an energy of 3 1274.53 KeVE  according to its decay scheme.
Comparing that value to its determined energy 3 1262.38 1.93 KeVdE   generated a
6.30Z   . Well below an acceptable agreement score. Note that this peak appears to be
broadened and, as a result, has a flattened peak which made Gaussian fitting difficult.
4.1.5. Mystery Element X
The emission spectrum for mystery element X is displayed in Fig.12. Peaks 1, 2,
3, and 4 were found to have energies of 1 70.83 0.76 KeVdE   ,
2 246.79 1.23 KeVdE   , 3 586.99 2.32 KeVdE   4 916.99 5.17 KeVdE   ,
respectively. Further research using the aforementioned energy levels, the fact that it is a
low activity source, and that it is commercially available, led us to conclude the mystery

26. 26
isotope was in fact thorium, more specifically 232
Th. This is a daughter isotope of 232
U.
Furthermore, the thorium came in the form of commercial welding rods. The decay chain
of this isotope includes: 212
Pb, 208
Ti, and 228
Ac. These correspond to Peaks 2, 3, and 4
respectively. The accepted values for the gamma rays emitted by the preceding
metastable states are 2 238.632 KeVE  , 3 583.200 KeVE  , and 4 911.204 KeVE  in
the same order. Their respective Z-scores are: 6.18Z  , 1.64Z  , and 1.12Z  . While
these Z-scores inspired some confidence, there was definite room for improvement. This
source was not very active so a longer data collection time would have better defined the
peaks. Additionally, several peaks consist of counts from more than one emission energy.
Peak 1 remains undetermined but is assumed to have been an x-ray emission.
4.2. Mass Attenuation Coefficients
The mass attenuation coefficients for lead, aluminum, and graphite were
determined using the gamma ray photopeak energies of 661.657 KeV and 1173.237 KeV
from 137
Cs and 60
Co, respectively.
For 137
Cs, the mass attenuation coefficients were determined to be:
2
0.0864 0.0069 cm
gPb   ,
2
0.0583 0.0058 cm
gAl   , and
2
0.0715 0.0049 cm
gGraphite   . These coefficients, obtained by fitting Eq.8 to the
attenuation data (Figs. 13-15), all have very high values of 2
 . Subsequently, they have
low P-values which suggest the exponential model should be rejected with over 99%
confidence (see Table 2). As previously pointed out, the high activity of this source
generated very low relative errors for the fit to adhere to; causing the 2
 values to be

27. 27
abnormally high. A shorter count time would increase the relative error bars for the
exponential fit and change the level of confidence for rejection.
The 60
Co mass attenuation coefficients were determine to be:
2
0.0596 0.0039 cm
gPb   ,
2
0.0544 0.0035 cm
gAl   , and
2
0.0614 0.0015 cm
gGraphite   . The plots that determined these values can be seen in
Figs. 16-18. With 60
Co being a less active source, and the reduction in time for data
collection, the exponential model had an easier time fitting the data. This resulted in the
model not being rejected for this isotope, as determined from the P-values in Table 2.
The exact, accepted values for the mass attenuation coefficients of lead,
aluminum, and graphite were difficult to find for specific energies. Rather, NIST lists a
table of energies that can be used to determine values between which the coefficients
should fall (Hubbell 2004). For energies between 600 800 KeV the attenuation
coefficient of lead lies between
2 2
0.1248 to 0.0887cm cm
g gPb  . Similarly,
2 2
0.07802 to 0.06841cm cm
g gAl  and
2 2
0.08058 to 0.07076cm cm
g gGraphite  . The
determined coefficients for lead and graphite lie just within the above values, using
calculated errors, while the determined coefficient for aluminum falls just outside the
predicted range. This does not mean the determined values are in agreement with any
known values, but does serve to verify that they are reasonable.
At energies between 1000 1250 KeV the coefficients become:
2 2
0.07102 to 0.05876cm cm
g gPb  ,
2 2
0.06146 to 0.05496cm cm
g gAl  , and
2 2
0.06361 to 0.05690cm cm
g gGraphite  . Here, all of the determined coefficients lie
within the above ranges. Any future analysis would be more complete with exact mass

28. 28
attenuation values for lead, aluminum, and graphite at the specific photopeak energies of
661.657 KeV and 1173.237 KeV .

29. 29
5. References
1. Brown, G. Physics 134 Lab Manual (2014).
2. Compton, Arthur. A Quantum Theory of the Scattering of X-rays by Light Elements.
Physical Review, 21, pp 483-502. (1923).
3. Chao, C. Y. Scattering of hard γ-rays. Physical Review, 36 (10). pp. 1519-1522. (1930).
4. Einstein, A. Concerning an Heuristic Point of View Toward the Emission and
Transdormation of Light. Annalen der Physik 17 (6): 132–148 (1905).
5. Hubbell, J.H. and S.M. Seltzer. Tables of X-Ray Mass Attenuation Coefficients and Mass
Energy-Absorption Coefficients. (Version 1.4). National Institute of Standards and
Technology, Gaithersburg, MD. 2004. Online. http://physics.nist.gov/xaamdi (Accessed:
6/20/14)
6. Peterson, R. Experimental ɣ Ray Spectroscopy an Investigations of Environmental
Radioactivity. Spectrum Techniques (1996).
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Magazine 5, 576-5910. (1903).
8. Rutherford, E. The origin of β and γ rays from radioactive substances.
Philosophical Magazine 24, 453-462. (1912).
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10. Soddy, F. and Alexander Russell. The ɣ Rays of Uranium. Nature, Volume 80, Issue
2053, pp. 7-8 (1909).