Final Year Project
2010
D. A. Lewis
Physics with Nuclear Astrophysics
Determining Levels of Naturally Occurring Radioactive Materials in
Environmental Sand samples
D. A. Lewis, Department of Physics, University of Surrey,
Guildford, GU2 7XH
Abstract
Four high resolution gamma-ray spectroscopies were carried out weekly, on a sand sample taken
from a beach in Thailand to find out what Naturally Occurring Radioactive Materials was present,
including nuclides from Uranium-238, 235 and Thorium-232 decay chains. It was found that the
activity concentration for the Uranium-238 series was 80.9 ± 12.9 Bq/Kg, the Thorium-232 series was
86.0 ± 18.6 Bq/Kg whereas the activity concentration for the Uranium-235 series was 1.19 ± 0.54
Bq/Kg. As part of all three decay series, Radon-gas is found. It was though that sealing the sand
sample would trap the Radon-gas, allowing the Radon-activity to grow into secular equilibrium with
the parent nuclide. This was not found experimentally.
Page: 2
Contents
1. Introduction
1.1. Naturally Occurring Radioactive Material (NORM)
1.2. Radon Gas
1.3. Secular Equilibrium
1.4. Airborne Radioactive Nuclides
2. Theory
2.1. Detector Theory
2.1.1. Introduction
2.1.2. Diagram
2.1.3. Detector
2.2. Radiation
2.2.1. Radiation Theory
2.2.2. Activity
2.2.3. Photoelectric effect
2.2.4. Compton Scattering
2.2.5. Pair Production
2.2.6. Internal Conversion
2.2.7. Secular Equilibrium
2.2.8. Radon Growth
3. Detector Setup and Method
3.1. Diagram
4. Results
4.1. Activity Concentration
4.2. Radon Growth
5. Conclusions
6. Acknowledgements
7. References
- Page:4
- Page:4
- Page:5
- Page:5
- Page:6
- Page : 6
- Page:6
- Page:6
- Page:7
- Page:7
Appendix
A1 Energy Calibration
-Page-20
-Page : 9
- Page:9
- Page:10
- Page:10
- Page:11
- Page:11
- Page:12
- Page:12
- Page:14
-Page: 15
-Page:15
-Page:16
-Page:17
-Page:17
-Page: 17
-Page:18
-Page:18
-Page-20
-Page-20
-Page-23
A2 Efficiency calibration
Graphs and tables
Page: 3
1. Introduction
1.1 Naturally Occurring Radioactive Material (NORM)
Naturally Occurring Radioactive Material is radiation found in the environment, which has decayed
since the formation of the Earth, or has been created with cosmic-ray nuclear reactions. Isotopes
such as Uranim-235 and 238 and Thorium-232 are amongst the most abundant sources. Isotopes
such as Uranium-238 and Uranium-235 have such large half lives that they and their radioactive
decay products can be detected using relatively simple detection methods today despite being
present when the Earth was formed.
Cosmic ray interactions with air from the Earth’s atmosphere can create cosmological radionuclides
such as Carbon-14, Hydrogen-3 and Berylium-7 which all emit radiation that adds to the total
amount of environmental radiation. As these radionuclides are airborne, they may be present in any
non-vacuum detector.
Naturally occurring radioactive material can be found in almost all types of matter and in all types of
physical states, including the bones of mammals. Most humans carry approximately 17mg of
Potassium-40, which is a radioactive nuclide with an activity of 4.4 KBq [2].
Man made radionuclides are also present in the environment and add to the natural background
radiation count. These have been created in nuclear fission power stations, nuclear weapons fallout
and nuclear reactor accidents; such as Chernobyl. Such radionuclides are Ceasium-137 and
Strontium-90. These radionuclides can be found all over the planet from nuclear weapons testing
carried out in the late fifties and sixties.
Uranium-238, Uranium-235 and Thorium-232, do not simply decay to a single, non-excited daughter
nuclides, they decay via large, complex decay chains.
The terrestrial radionuclides Uranium-238, 235 and Thorium-232, most probably created in a type-II
supernova, were amongst the elements that formed the Earth. As a result, their unique decay
fingerprints can be detected in matter across the whole planet.
The main method for detecting these terrestrial radionuclides is gamma spectroscopy; despite the
majority of radionuclides along all three decay chains emit high energy alpha particles. The problem
with trying to detect the emission of a characteristic alpha particle is the poor penetrative ability of
the alpha particle.
Instead, when the parent radionuclide decays, it decays to an excited state of the daughter
radionuclide. This in turn, emits a gamma-ray when the daughter nuclide decays to its ground state.
This gamma-ray is characteristic in its energy and can be used to identify the presence of the
daughter radionuclide and hence the parent. Gamma-rays have a very good penetrative property,
allowing much easier detection that can be carried out with relatively simple equipment.
In this project, a sand sample was taken from Thailand’s beaches for gamma-ray analysis to find
what naturally occurring radioactive material could be found. The sample was sealed into an airtight
container on the fourteenth of February 2010. The reason for the source needing to be sealed is
because of Radon gas.
Page: 4
1.2 Radon Gas
Radon gas is a gaseous radionuclide that emits alpha particles and is produced at some point, in all
three decay chains of Thorium and Uranium. In the sand sample, the presence of the Uranium and
Thorium decay chain products should all be detectable. However, if the Radon gas is allowed to
escape into the atmosphere, the decay products that follow Radon will not be contained in the
sample.
In this project, the sand sample was sealed, keeping any produced Radon gas inside of the container.
Hence, any decay products of the Radon should be contained inside the sample.
Sealing the sample to contain the Radon gas also provides a safer working environment in the
laboratory. Normal alpha emitters are relatively harmless to humans, despite their high ionising
potential. This is due to their poor penetrative properties, as alpha particles are not able to
penetrate human skin and cause damage to living cells.
However, in the case of Radon gas, if it is present in the air, a human could breathe it into his/her
lungs. This is very hazardous, as the Radon particle can then directly irradiate live tissue and cause
cancerous mutations. Radon isotopes have relatively short half lives and can decay to a non-gaseous
daughter radionuclide quickly, becoming trapped inside the person’s lungs, causing a permanent
radiation hazard.
This is a problem in places where a lot of granite is present. The decay of Uranium-235,238 and
Thorium 232 is present in granite and produce Radon gas that become trapped, causing large
amounts of radiation to build up.
1.3 Secular equilibrium
Secular equilibrium occurs in decay chains where the half-life of the parent nuclide is much greater
than that of the daughter. Secular equilibrium describes the case when the decay-rate of a parent is
the production rate of a daughter nuclide, due to the extreme half-life difference. In the case of a
large decay chain like the Thorium and Uranium series, equilibrium can be expected across all of the
chains.
So, at any point in either of the decay chains, the amount of any radionuclide being produced, once
in equilibrium, is the same at any point in the decay chain. Secular equilibrium normally takes
several half-lives to be achieved; this is the case here as these radionuclides have been present since
the formation of the Earth.
When the sand sample is sealed, it is assumed that there is no Radon gas present, as it has all
escaped into the atmosphere. Hence, no decay products should be detectable below Radon in the
decay chains. Once it is sealed, the Radon gas becomes trapped and decays to its daughter, the
radionuclides below Radon in the decay chains will then become trapped inside the sample and
become detectable.
Once sealed, the amount of Radon gas and its decay products should then ‘grow in’ to secular
equilibrium with the radionuclides above it in the decay chain. This idea was incorporated into the
project, as it was thought to be possible to see this growth of Radon after it had been sealed.
Page: 5
Weekly gamma-ray spectroscopy of the sample would be carried out to see if the amount of Radon
gas and its decay products were growing into secular equilibrium as expected.
1.4 Airborne Background Nuclides
As mentioned earlier, cosmic ray interactions can give rise to cosmological radionuclides such as
Berylium-7. Just as an aside, each spectrum was analysed to find if any Beryllium-7 was present in
the detector. [6]
2. Theory
2.1 Detector Theory
2.11 Introduction
For this project, a sand sample has been selected to undergo gamma-ray spectroscopy to find the
different types and quantities of naturally occurring radioactive materials.
All the radioactive sources that could possibly be in the sand sample decay via alpha or beta
emission, as well as gamma emission. The reason for gamma spectroscopy has been implied earlier;
gamma radiation has a much higher penetrative ability and is much more easily detected. There is a
downside to this high penetrative ability and that is a large amount of background radiation.
Naturally occurring radioactive material is found everywhere, including in the walls and building
where a detector can be housed. Any gamma radiation emitted from a source in the walls or
anything in the near vicinity, will add to the background. To deal with this issue, a suitable detector
would need to be heavily shielded from this outside gamma background.
The main method for detecting gamma radiation is by using a semiconductor detector, such as
germanium. Semiconductor detectors offer massive advantages over other types of detectors, such
as excellent resolution and the ability to detect high energy decays. Germanium detectors have
several drawbacks, which, fortunately, can be overcome. Impurities in the germanium crystals used
as the semiconductors trap electrons, reducing the detection capabilities to near nothing. This
problem can be overcome by using a germanium detector that has no impurities, often called a
Hyper-Pure germanium crystal.
Another main drawback is thermal noise. At room temperature, germanium as a semiconductor has
massive thermal noise, where electrons can easily cross the band gap. This makes germanium
detectors useless at room temperature. To overcome this, the semiconductor must be cooled using
liquid nitrogen.
The final issue with a germanium detector is poor efficiency. Due to the size of the germanium
crystal itself, and the ability of that crystal to detect ionizing radiation, the efficiency of the crystal is
very poor, with typical values of order 1% - 5%. Due to the physical properties of the germanium
crystal, the efficiency is also related to the energy of the incoming ionizing radiation. This problem
cannot be physically overcome like the others, but a calibration of the detector, to find out how the
efficiency varies with the energy of the incident radiation, can be undertaken to counteract this
problem. Once done, an efficiency variable can be factored into any calculation.
Page: 6
For this project, a high resolution Gamma spectroscopy was required, so a hyper-pure, liquid
nitrogen cooled, germanium detector was used. To overcome the problem of background gamma
detection, the germanium detector was heavily shielded with a lead casing. A schematic diagram of
a typical germanium detector can be seen below.
2.12 Diagram
Figure 2.121: Diagram of typical germanium detector (Taken from [3])
2.13 Detector
As mentioned, germanium is a suitable solid semiconductor that can be using in the detection of
gamma emissions. When formed into a solid crystal, the germanium atoms have four valance
electrons which form covalent bonds between other atoms. According to solid state physics,
electrons in atoms are formed in bands in the atom, as shown in figure [2.131].
Electrons are bound to the atom via the Coulomb force. Valence electrons require a massive amount
of energy to overcome the Coulomb force and due to this, cannot move, and hence do not conduct.
Electrons in the conduction band are further away from the nucleus which houses the protons
responsible for the Coulomb force on the electrons. This results in the Coulomb force being much
weaker on the conduction electrons, such that the binding energy of the electron via the Coulomb
force is less than the energy of the atom, allowing the electron to be freed, allowing a current to
flow.
Page: 7
Figure 2.131:: Band Gap in Semiconductors (Taken from [5])
When a semiconductor material, such as germanium, is exposed to incident gamma radiation, an
electron is excited from the valence band of an atom into the conduction band. This has two effects,
the first, we have an electron that is in the conduction band of an atom, the second,
second, a vacancy is
produced in the valance band of that atom where the electron used to be.
This vacancy hole is then filled by an electron from an adjacent atom’s valance band; this hole is
then filled by the new atoms’
atoms adjacent partner. The net effect of this process is that the hole moves
through the crystal in one direction and the excited conduction electron, the other.
The direction of the hole and the electron is dictated by a large voltage bias that is placed over the
crystal, typically of order 1000
1000 volts. The energy of the incident radiation dictates how many
electrons are excited to the conduction band. These electrons are then collected, the more the
electrons, the higher the energy of the incident radiation.
As each detector and semiconductor is
is slightly different, the amount of electrons excited to the
conduction band is unknown for certain energies of incident radiation. To overcome this, the
detector must undergo an energy calibration before any gamma spectroscopy can be completed.
An energy calibration simply tells the detector the value of the energy of the incident radiation from
a known source. The detector registers this to the number of electrons actually detected from the
radiation. This process was required for my project and is described
descri
in the appendix,, along with the
efficiency calibration.
calibration
Once an energy calibration was completed, the efficiency calibration was undertaken, and found
that,, although still very low, there is a definite peak in the efficiency of the germanium detector used
for this project around 175 keV.
Page: 8
2.2 Radiation Theory
2.21 Radiation
Unstable particles decay to stable states by the emission of energy, either in the form of an
electromagnetic gamma wave, or via particle expulsion such as beta particles and neutrinos or alpha
particles.
The nuclides that will be considered in this report decay via alpha, beta and gamma emission, alpha
particles are Helium-4 nuclides and gamma-rays are electro-magnetic phenomena. There are three
types of beta-decay each very different.
For the Uranium and Thorium decay chains, the only processes that can occur are alpha-decay, beta
minus decay and gamma-decay. However my sample may contain other nuclides.
Alpha particles have very poor penetrative properties and can be stopped by a thin sheet of paper.
This makes detection of alpha particles very difficult as the detector must be flush against the
sample and the sample must not be hindered by anything. Gamma-rays have massive penetrative
properties compared to both alphas and betas, requiring several inches of lead to stop them.
Unstable particles that decay via the expulsion of small particles don’t always decay straight to the
ground state of a daughter nuclide. When a radioactive nuclide decays via an alpha emission or a
beta, the daughter nuclide can be left in an excited state. These excited states are quantised,
meaning they have specific characteristic energy values dictated by quantum mechanical factors.
The daughter nuclide rapidly decays via the emission of a gamma-ray from the excited nuclear state
to the ground state.
Most daughter nuclides have very complex nuclear structures which depend on the parity and
angular momentum of the state. When a parent nuclide decays to the daughter, it can be left in any
one of these excited states, which in turn will decay to the ground state emitting at least one
gamma-ray.
Each nuclear state in the daughter nuclide has a certain probability of being obtained when decay
occurs. These probabilities are calculated using quantum mechanical selection rules and are called
branching ratios.
This adds a level of difficulty when trying to determine the activity of a sample as we now need to
take into account the probability of that characteristic gamma-ray being emitted.
As the energy levels in the daughter are quantised, and hence unique, the emission of the gammaray is characteristic of the daughter nuclide. This is an extremely important point without which this
project would not work. As the gamma-ray is characteristic, once detected, we can determine the
daughter nuclide it was emitted from.
Due to excellent penetrative properties of gamma-rays, this gives us an extremely powerful tool to
find what constituents are inside a sample via these gamma-ray fingerprints.
The number of radioactive particles dN decaying in a time period dt is proportional to the number of
radioactive nuclei present can be expressed as,
Page: 9
ߣ= −
ቀ݀ܰൗ݀‫ݐ‬ቁ
{2.211}
ܰ
Where, λ = Decay constant and N is the number of particles at time t.
If we integrate this equation, we obtain the exponential law of radioactive decay, one of the most
fundamental and important equations to this report.
ܰሺ‫ݐ‬ሻ = ܰ଴ ݁ ି ߣ‫{ ݐ‬2.212}
Where N0 is the constant of integration and represents the number of particles before disintegration
started, it is found from the boundary condition that none of the particles have decayed at a t=0.
We also need to define what is meant by the term activity. It is defined as the rate, at which decays
occur in a sample and can be expressed as,
‫ܣ‬ሺ‫ݐ‬ሻ = ߣܰ {2.213}
4.22 Activity concentration
The activity concentration of a radionuclide in a sample, literally means the amount of specific
activity of a radionuclide per kilogram of sample, it is given by,
‫=ܣ‬
Where,
ܰ
∈ ‫ܫ‬ఊ ‫ݐ‬௦ ‫ܯ‬
ሼ2.221ሽ ሾଷሿ
A is the activity concentration in Becquerels per kilogram
N is the number of counts obtained for a specific gamma-ray energy photo-peak
ϵ is the detector efficiency at the photo-peak energy
ts is the live time of the sample spectrum collection in seconds
M is the dry mass of the measured sample in kilograms
Iϒ is the Branching Ratio of the ϒ-line corresponding to the peak energy.
When a gamma-ray is produced, there are three main interactions that the radiation can undergo,
unless it is detected. These three processes are; Compton Scattering, Pair-Production and
Photoelectric Absorption.
4.23 Photoelectric Effect
The photoelectric effect is a gamma-ray phenomenon that can cause low energy counts on a gamma
spectrum. The photoelectric effect describes the process of a gamma-ray being absorbed by an
atomic electron, normally a k-shell electron. This photoelectron is then ejected from the atom with
kinetic energy equal to,
ܶ௘ = ‫ܧ‬ఊ − ‫{ ܤ‬2.231}[ସ]
Where,
Te = Kinetic energy of ejected electron
Eϒ = Incident gamma-ray energy
B = Binding energy
Page: 10
The ejected photoelectron leaves a vacancy in the electron shell it was ejected from. All matter will
try to re-arrange itself to be in the lowest energy state possible; hence an outer shell electron will
drop down to the vacancy left by the photoelectron.
This de-excitation of an outer electron causes the release of a characteristic X-ray, as the energy
levels in an atom’s electron structure are quantised. These characteristic X-rays are of order 100 keV
and can be detected on gamma spectra.
There is a process that competes with this; the Auger process. This is where the characteristic X-ray
does not escape the atom when an electron de-excites, instead, the X-ray is absorbed by an outer
electron. If this energy is greater that the outer electron’s binding energy, the electron is then
ejected and is called an Auger electron.
2.24 Compton scattering
Compton Scattering is analogous to the photoelectric effect. Both effects involve considering the
implications of a gamma-ray imparting its energy on atomic electrons. The main difference is that
the photoelectric effect gives the electron all of its energy, whereas the Compton Effect describes a
case when only a fraction of a gamma-ray’s energy is given to an electron.
The electron being given energy is recoiled by a scattering angle φ, and the gamma-ray photon is
scattered with a reduced energy at an angle θ.
Figure: 2.241 [Taken from [3]]
The gamma-ray being ejected can have a range of energies depending on the energy of the incident
photon and the scattering angle. Meaning that the energy of the scattered gamma photon could
have any value within a certain range, given by,
‫ܧ‬ఊᇱ =
‫ܧ‬ఊ
{2.241}[ସ]
‫ܧ‬ఊ
1 + ൬ ଶ ൰ (1 − ܿ‫)ߠݏ݋‬
݉ܿ
The maximum value of the scattered gamma-photon can range between the energy of the incident
gamma-photon and mc2 / 2 = 0.25 MeV.
2.25 Pair Production
Pair production is another gamma-decay phenomenon whereby an electron-positron pair is created
from the energy of the incident gamma-ray photon. This electron-positron pair, once created,
Page: 11
annihilates to create back-to-back photons with energy equal to the rest mass energy, 511 keV, of
the electron and positron.
Due to energy conservation, the incident gamma-ray must have energy of at least twice the electron
rest mass, 1.022MeV, indicating that this process only comes into consideration for relatively high
energy gamma-rays.
It can be seen that the probability of the above three processes occurring is related to the energy of
the incident gamma radiation. Their dominance according to the incident gamma-ray energy and the
proton number of the material being subjected, can be summarised in the below figure. [2.242]
Figure: 2.242 [Taken from [4]]
2.26 Internal Conversion
When decay takes place between a parent and a daughter nuclide, the excited state of the daughter
can be populated. This is normally followed by the emission of a gamma-ray as the daughter deexcites to its nuclear ground state. However, there is another process that competes with gamma
emission; Internal Conversion.
Internal Conversion is a different process which allows the de-excitation of a daughter nuclide. This
is achieved by the daughter nuclide transferring all of its energy to an atomic electron, which is then
emitted from the atom, causing ionisation. This is different from beta-decay in the fact that there is
no change in the number of protons or neutrons. It is often associated with the two-step process,
the photoelectric effect, where a photon of energy ‘hf’ knocks an atomic electron of the atom.
Internal conversion is a single step process; here the energy is transferred atomically to an atomic
electron.
The kinetic energy of the ejected electron can be found simply by considering the energies involved,
and must equal to the amount of energy given to it by the de-excitation, minus the electron’s
binding energy.
Page: 12
௘ ∆ 2.261ሾସሿ
Where,
Te = Kinetic energy of ejected electron
∆E = De-excitation
excitation energy
B = Binding energy
As the binding energies of the internal electrons are quantised as well as the de-excitation
de excitation energy,
the electron kinetic energy must also be discrete and quantised, rather than continuous like
electrons
ctrons emitted from beta-decay.
2.27 Secular equilibrium
Secular equilibrium can only happen if the half life of the parent
p
nuclide is much greater than that of
the daughter nuclides in the decay chain. In this project, this is the case for all three decay chains.
Following
lowing the derivation found on page
p
171 of [4], the ratio of the activities of a parent and daughter
nuclide in secular equilibrium can be expressed as
ଶ ≅ ଶ
1 ିሺఒమିఒభ 2.271
ଶ ଵ
This process can be seen on the below figure which shows the Growth of I-132
132 from Te-132.
Te
Figure 2.271:
.271: Secular equilibrium of I-132
I
from Te-132 [taken from [4]]
4]]
But what happens in the case of large decay chains where we have more than three generations, like
the Uranium and Thorium decay chains considered in this report?
If we consider a decay chain of n generations, we
we can make a general expression,
expression as each generation
is created by the parent
௡ ሺ௡ିଵሻ ሺ௡ିଵሻ ௡ ௡ Page: 13
2.272
The Bateman equations provide a solution for this integration, expressing the activity of a specific
generation as,
௡ୀଵ
‫ܣ‬௡ = ܰ଴ ෍ ܿ௜ ݁ ିఒభ௧
௜ୀଵ
{2.273}
= ܰ଴ ൫ܿଵ ݁ ିఒభ௧ + ܿଶ ݁ ିఒమ௧ + ܿ௡ ݁ ିఒ೙௧ ൯
{2.274}
Where,
ܿ௠ =
ߣଵ ߣଶ ߣଷ … . . ߣ௡
ሺߣଵ − ߣ௠ ሻሺߣଶ − ߣ௠ ሻ … . ሺߣ௡ − ߣ௠ ሻ
{2.275}
When considering equation {2.275}, we omit the term on the bottom when n=m, as this would be
zero making the term infinite.
2.28 Radon Growth
A theoretical growth curve can be calculated for each of the three decay chains using equation
{2.271}. This is based on the assumption that the decay chain is in secular equilibrium up to Radon
gas and, hence, all the nuclides between the parent and Radon are decaying at the same rate as the
parent itself. This theoretical secular equilibrium growth curve can then be used as a comparison to
the actually recorded growth curve in the results section.
The theoretical curve for the growth of Radon-222 into secular equilibrium with the Uranium-238
decay chain can be seen in the appendix as graph {A3}. It can be seen that the activity of the Radon
reached equilibrium after about 1000 hours, about 50 days. The date of the sealing of the sample
was the 14th of February; the first reading was taken five days later on the 19th of February.
After this five day period the sample was counted for two days, meaning the Radon should already
be over halfway to secular equilibrium. The graph has been annotated to show where the four
different gamma-ray spectroscopes took place.
The theoretical equilibrium curves for the decay of Uranium-235 to Radon-219 and Thorium-232 to
Radon-220 can also be calculated. But, due to the massively small half-lives of the Radon isotopes
compared to the parent isotopes, the Radon isotopes grow into secular equilibrium within a few
minutes. Due to the period of sealing before the first measurement, the Radon gas from these
isotopes will already be in secular equilibrium. So, the growth curve from the Uranium-238 decay
should be the only one obtainable from the data.
A copy of the FORTRAN code used to create these three graphs is shown in the appendix.
Due to some of the high energy gamma-rays being produced by some of the constituents of the sand
sample being tested, Pair-Production could be occurring in the sample producing back-to-back
511keV photons. The one and only characteristic gamma-ray energy emitted from a Radon-222
decay to Polonium-218 is 510keV. Although we are using a high resolution gamma detector, it will
not be able to distinguish between these two values.
Page: 14
This problem can be overcome by considering that the rate of Pair-Production should not be
increasing, so any increase in counts should be due to the growth of the Radon-222 into secular
equilibrium. However, if the emissions due to Pair-Production are massive compared to the Radon222 emissions, then the growth of Radon-222 into secular equilibrium will not be found as it will be
overshadowed by Pair-Production.
3 Detector Setup and Method
Once an energy and efficiency calibration had been completed, the analysis of my sand sample could
begin. Firstly, the sand sample needed to be weighed in order to calculate the activity concentration.
The sand sample was in a special container called a Marinelli beaker, a chemically resistant
polypropylene container. The sand sample had been dried to remove any water, so that the weight
of the sample was from solid material only. The sample was weighed along with an empty beaker to
find the weight of the sample on its own. This was 1010.20 grams.
The sand sample was the placed inside the lead shielding of the Germanium detector seen on figure
{3.11}. The high voltage bias was set to 3000 volts on the amplifier seen below in figure {3.12}. Once
the sample was inside the lead shielding, it was locked in and the detector was set to count for 48
hours. This was deemed, from experience of my PhD supervisor, enough time to collect meaningful
spectra.
3.1 Diagram
Figure 3.11 Liquid Nitrogen Dewar and Lead Shielding [2]
Figure 3.12: Bias Voltage and Amplifier Rack
This process was set to be a weekly event, to ensure that the detection of the increase of Radon gas
would be done on a consistent time scale, but due to the availability of the laboratory, four spectra
were obtained on the following dates.
14th February 2010,
26th February 2010,
Page: 15
10th March 2010
19th March 2010
A further gamma analysis was undertaken on a sample of de-ionised water. This will not emit any
radiation; hence, any counts obtained from this analysis will be purely from background sources.
This is essential, as the spectra obtained from the sand sample can now have the background
spectra removed, so that the sand sample spectrum is purely representative of the radiation emitted
from it alone.
4 Results
The spectra obtained from the gamma-ray analysis of the sand sample can be found in the appendix
as graphs [A4-A7] and the background count as graph [A8]. Each spectrum proved to be very similar,
which is expected as the contents had not changed apart from the possible increase of Radon gas
and its decay products.
Each spectrum has a Compton Continuum and Compton edge present from the Compton scattering
effect, plus many different energy decay peaks from the sand sample. Low energy X-rays from
internal conversion and the photoelectric effect were seen in the spectra, and a high count near 511
keV, could indicate a large Pair-Production count.
A table has been included to show the main emission energies found from naturally occurring
radioactive material, and what radio-isotope the emission corresponds to and from what decay
chain, if any, it is from.
As for the growth of Radon gas into secular equilibrium, we are interested in a 510 keV peak,
unfortunately, there is no real growth seen. The peak remained almost constant for all four different
readings; approximately 0.013 counts per second.
Figure 4.1 Decay data from NORM [Taken from [2]]
Page: 16
4.1 Activity Concentration
From equation {2.221}, the activity concentration of each possible nuclide in each series was found;
these were then summed to find the total series specific activity. Only one individual background
decay was found, Potassium-40. This can be seen in table [T1] in the appendix.
It was found that the activity concentration for the Uranium-238 series was 80.9 ± 12.9 Bq/Kg, the
Thorium-232 series was 86.0 ± 18.6 Bq/Kg whereas the activity concentration for the Uranium-235
series was 1.19 ± 0.5 Bq/Kg.
The activity concentration for the Uranium-235 series was based on three decays being detected.
This is primarily due to the very low abundance of Uranium-235, as only 0.7% of a sample of
Uranium is Uranium-235. However, two of the three possible decays counted from Uranium-235 are
substantially close to two decays from Uranium-238, where the difference is un-resolvable; this is
highlighted in orange and yellow on Table [T1]. Due to this, their presence could not be included in
the total activity.
Two emission energies, one from the Uranium-238 and one from the Thorium-232 series were very
close to each other, marked red on the results table, they could not be included in the calculation.
The activity concentration for Radon-222 is massive in comparison, and is omitted from the activity
concentration total, as this count is obviously aided by the 511 keV annihilation energies. This
proved very problematic for the calculation of Radon-gas growth, as the only gamma emission from
this decay is one of the emitted results.
4.2 Radon Growth
The growth of Radon-222 from the Uranium-238 decay chain can be seen in graph [A9]. It is quite
clear that the latter three data points could be sitting on the growth curve see in graph [A3].
However, the first data point suggests that the Radon gas has not grown in; instead it has been in
secular equilibrium before this project was undertaken.
5 Conclusions
From the results, it can be deduced that the activity concentration is much higher for the Thorium232 series than the other two Uranium series. The ability to find any isotopes in the Uranium-235
series was poor due to its very low abundance. Looking at the spectrum, one would think that there
would be masses of Uranium-235 due to the high count for 185.6 keV, one of Uranium-235’s gamma
emission energies.
Unfortunately the large peak around this energy can be attributed to Uranium-238, as in its decay
chain, when Radium-226 decays to Radon-222, it emits a 186.21 keV gamma-ray and the difference
between the energies is un-resolvable and is counted as the same. Also, the germanium detector has
peak efficiency around this energy, so despite initial thoughts of a high Uranium-235 count, the
realisation is that there isn’t much activity in the sample due to Uranium-235.
Due to this point the 185.70 keV Uranium-235 emissions were not included in the activity
concentration summation, yielding a low value for this decay chain; however, a comparatively low
activity concentration is expected for Uranium-235 due to its low abundance.
Page: 17
As for the Radon growth, unfortunately, the data points did not show conclusively the growth of
Radon gas. Possibly if a measurement had been made closer to the time of sealing and more
frequently, this may have been picked up. It may have been due to the Radon gas being trapped
inside the sand sample even when the sample was not sealed. If this experiment was to be
repeated, I would suggest stirring the sand sample in a ventilated area to ensure that any Radon gas
is able to escape before sealing.
It is unfortunate that the only emission of Radon-222 is 511 keV as this energy is also very close to
the annihilation energy caused by Pair-Production and the gamma emission of Ti-208. Due to these
factors, as mentioned in the theory section, the Radon growth could be overshadowed by these two
emissions, and the growth curve may be missed.
Despite initial considerations, no man-made isotopes including Ceasium-137, were detected in the
sample, nor were there any airborne Beryllium-7 nuclides found in any of the spectrums including
the background count. There was however a strong Potassium-40 background count, possibly due to
emission from the laboratory walls, as potassium is known to be abundant in building materials.
6 Acknowledgements
I would like to thank Professor Paddy Regan for arranging the project and aiding me throughout. I
would also like to thank my PhD supervisor, Doendara Malain, who helped with all aspects of work
including the experimental arrangement. I would also like to thank Professor David Bradley for his
help during the mid-semester interview.
7 References
1. Edgardo Browne & Richard B. Firestone, Table of radioactive Isotopes, Wiley and Sons, 1996
2. Doendara Malain, Measurements of NORM in Environmental Samples, MSc Dissertation,
Unpublished, University of Surrey, 2007
3. Martin P. Mubaiwa, Measurements of Naturally Occurring Radioactive materials in
Environmental Samples, MSc Dissertation, Unpublished, 2008
4. Kenneth S. Krane, Introductory Nuclear Physics, John Wiley and Sons, 1988
5. www.knowledgerush.com/kr/encyclopedia/Band_gap/ [Accessed 5 May 2010]
6. C.A. Huh, L.G .Liu, Precision measurements of the half-live of some electron-capture decay
nuclides, Journal of Radioanalytical and nuclear chemistry, Vol 246, No.1 (2000)229-231,
1999
7. G.Heusser, Low-radioactivity Background Techniques, Max-Planck Institute, 1995 available at
www.annualreviews.org/aronline [Accessed 5 May 2010]
8. Fatma M. Elmenshaz, Measurements of NORM in Environments Samples, MSc Dissertation,
Unpublished, University of Surrey, 2009
9. DAVID A. BRADLEY & CARLYLE ROBERTS, Forward, Appl. Radiat. lsot. Vol. 49, No. 3, pp. 147148, 1998, 1997 Elsevier Science Ltd
10. RONALD L. KATHREN, NORM Sources and Their Origins, Appl. Radiat. lsot. Vol. 49, No. 3, pp.
149-168, 1998, 1997 Elsevier Science Ltd
Page: 18
11. Stuart Hunt and Associates Ltd, A Brief Discussion about Naturally Occurring Materials
(NORM)[online], USA:SHA, 2002. Available from:
http://www.stuarthunt.com/Downloads/Docs/NormText.pdf [Accessed 10 May 2010]
12. MEHDI SOHRABI, The State-of-the-art on Worldwide Studies in some Environments with
Elevated Naturally Occurring Radioactive Materials (NORM), Appl. Radiat. lsot. Vol. 49, No. 3,
pp. 169 188, 1998, 1997 Elsevier Science Ltd
13. Gregory J. White, Arthur S. Rood, Radon emanation from NORM-contaminated pipe scale
and soil at petroleum industry sites, Journal of Environmental Radioactivity 54 (2001)
401±413, 17 July 2000
14. U.S. Environmental Protection Agency, Radiation Information: Cesium [online], USA: EPA,
2007. Available from: http://www.epa.gov/radiation/radionuclides/cesium.htm [Accessed
24th April 2009]
15. Keenan A, High-Purity Germanium Detectors [online], 2006. Available from:
http://www.phys.jyu.fi/research/gamma/publications/akthesis/node40.html [Accessed 22 March
2010]
Page: 19
Appendix
A1 Energy Calibration
The detector works on a system of channels, where if one electron is excited, a count is registered to
channel one, if two are exited, a count is registered to channel two. An energy calibration simply
tells the detector what energy a channel represents.
An energy calibration requires a known source, by which I mean a source whose emission energies
are well known and documented. The source used for the calibration was S313.PH, a source of
Europium-152. This was chosen as it is a reference source, whose activity and emission energies are
known, and has many different emission energies, that cover a large range, this is essential to obtain
a good calibration. A good energy calibration is imperative as a poor calibration will lead to
problems in the analysis of real life results.
The reference source was placed inside the germanium detector, with the lead shield closed to
reduce any background readings. The detector was set to count for twenty minutes, which, due to
the activity of the source, was deemed enough time to get an accurate calibration. Once the
counting was completed, I was presented with a spectrum of counts.
Next, the known emission energies from the source were matched up to the emissions counted
during the calibration. The values of the energies for these emissions were inputted into the
detector. As mentioned in the detector theory, the energy of the incident gamma radiation is
linearly related to the number of electrons excited into the conduction band. This means that
calibration should be linear, i.e. a 200 keV count should be twice as far away from a 0 keV count as a
100 keV count.
The accuracy of the calibration can be checked, by plotting the channel number vs. the energy value
assigned to it from the calibration. As mentioned, this should follow a linear plot, and the accuracy
can be gauged from how close the points fit to a line of best fit. There are only a certain number of
points, as Europium-152 has only nine gamma emissions, so the accuracy cannot be improved by
taking more data points.
As it can be seen in graph [A1], the data points fit perfectly, with negligible error to a linear line of
best fit. This provided evidence that the calibration was of great accuracy, and this calibration would
ensure accurate results for the future gamma spectroscopy’s that would be undertaken.
A2 Efficiency Calibration
The efficiency of a germanium detector, due to several facts, is inherently low. It is known that the
efficiency of a germanium detector is dependent on the energy of the incoming gamma-photon. This
is primarily due to the behaviour of the semi-conductor crystal; higher value energies can excite
more electrons in the semi-conductor yielding a higher probability of detection.
An efficiency calibration requires the amount of known gamma emission to be compared to the
amount detected, according to equation {E1}. For this to be completed, reference sources of known
activity and emission energies, will be placed into the detector for a set time. The number of counts
Page: 20
the detector should measure, for specific energies, can be calculated. This is then compared to the
number of actual counts the detector measures for specific energies.
The efficiency of the germanium detector is defined simply as the ratio between the number of
detected gammas and the number of emitted gammas.
‫ܥ‬௣
ܰఊ
∈=
{‫ܧ‬1}
Where,
‫ܥ‬௣ = ܰ‫ݐ ݊݅ ݁݉݅ݐ ݐ݅݊ݑ ݎ݁݌ ݏݐ݊ݑ݋ܥ ݂݋ ݎܾ݁݉ݑ‬ℎ݁ ‫݌‬ℎ‫ ݋ݐ݋‬− ‫ݎ݋ݐܿ݁ݐ݁݀ ݉݋ݎ݂ ݇ܽ݁݌‬
ܰఊ = ܶℎ݁‫݁݉݅ݐ ݐ݅݊ݑ ݎ݁݌ ݁ܿݎݑ݋ݏ ݕܾ ݀݁ݐݐ݅݉݉݁ ݏ݉݉ܽܩ ݂݋ ݎܾ݁݉ݑ݊ ݈ܽܿ݅ݐ݁ݎ݋‬, ݃݅‫;ݕܾ ݊݁ݒ‬
ܰఊ = ‫ܣ‬௦ ‫ܫ‬ఊ ൫‫ܧ‬ఊ ൯ {‫ܧ‬2}
Where,
‫ܣ‬௦ = ܶℎ݁ ‫ݐ ݂݋ ݕݐ݅ݒ݅ݐܿܣ‬ℎ݁ ‫݁ܿݎݑ݋ݏ‬
‫ܫ‬ఊ ൫‫ܧ‬ఊ ൯ = ‫ܿ݊ܽݎܾ( ݊݋݅ݐܽݎ݃ݎ݁ݐ݊݅ݏ݅݀ ݎ݁݌ ݕݎ݁݊݁ ݂ܿ݅݅ܿ݁݌ݏ ݂݋ ݏ݊݋݅ݏ݅݉݉݁ ݂݋ ݊݋݅ݐܿܽݎܨ‬ℎ݅݊݃ ܴܽ‫)݋݅ݐ‬
The activity of a source A, after an elapsed time ∆t, with a half life, ‫ݐ‬ଵൗ is found from the original
ଶ
activity ‫ܣ‬଴ by,
∆୲
ିቆ௧ ቇ
భൗ
‫ܣ ≡ ܣ‬଴ 2
మ
{‫ܧ‬3}
Europium-152 has many different decay energies and an efficiency calibration could be attempted
using this nuclide only. However, Europium-152 does not have any low energy gamma-emissions
that could be used from comparison. Due to this fact, a calibration was completed with a Europium,
Thorium and a special sealed reference source that contained a mixed of reference radionuclides
with known activities.
Nuclide
UniS Number
A (KBq)
Activity Date
Half Life,
(yrs)
Calc. Date
Eu-152
Th-232
NG3
S313.PH
S314.PH
S312.PH
3.02
1.08
Various
20/02/2009
01/02/2009
01/02/2009
13.512[1]
1.4 x 1010[1]
Various
18/03/2010
18/03/2010
18/03/2010
o
Elapsed
Time,
(yrs)
1.1534
1.1534
1.1534
Activity, A
(kBq)
2.84
1.08
Various
We need to look at the branching ratios for each of the specific emissions in the mixed reference,
Thorium-232 and Europium-152 source to determine the efficiency. With the branching ratios, and
the activity of the specific nuclides, we can calculate the expected number of counts, and use that to
find the efficiency from the actual number of recorded counts.
Page: 21
Source
NG3 Mixed
Nuclide
‫ܧ‬ఊ (KeV)
Activity (KBq)
‫ܫ‬ఊ (B.R.)
ܰఊ
Detected
Counts Per
second
Efficiency %
Error
%
Cadneum-109
88
7.95
0.045
360
4.5
1.24
0.004
Cobalt-57
122
0.434
0.855
369
36
9.74
0.029
Mercury-203
279
0.00164
0.815
1.31
0.062
4.73
0.019
Tin-113
392
0.158
0.648
102
2.1
2.05
0.199
Strontium-85
514
0.0217
0.985
21.9
0.44
1.06
0.025
Ceasium-137
662
2.61
0.851
2220
20
0.90
0.001
Cobalt-60
1333
2.68
1.0
2680
15
0.56
0.001
0.0027
2.88
0.018
0.62
121.8
0.284
806
15
1.85
244.7
0.075
214
3.7
1.73
344.3
0.266
755
11
1.46
443.9
0.031
88.9
0.95
1.07
0.130
369
2.6
0.704
867.4
0.042
119
0.77
0.642
964
0.145
412
2.8
0.679
1112.1
0.136
386
2.5
0.646
1408
0.208
591
3.5
0.592
Thorium-232
Europium-152
63.8
778.9
1.08
2.84
0.187
0.001859
0.003455
0.001456
0.005344
0.000901
0.001409
0.003212
0.001358
0.001293
The results were plotted on the graph [A2]. A line of best fit, obeying a power law was fitted to the
decaying section of the efficiency calibration points, where a linear line of best fit was fitted to the
first two low energy points. Error bars were placed on the points but are too small to be visible, with
the exception of the Thorium-232 gamma emission, which had a very large error.
The results of the energy calibration are quite clear, the efficiency of the detector does vary with the
energy of the incident radiation, with a peak around 200 keV. Using this calibration, a factor
dependent on the incident energy can be factored into the activity concentration calculations.
Page: 22
Appendix - Graphs and Tables
Graph [A1]
Page: 23
Graph [A2]
2.4
Energy Calibration
2.2
2
Percentage Efficiency (%)
1.8
y = 32.492x-0.563
1.6
1.4
1.2
1
y = 0.0387x - 1.8447
0.8
0.6
0.4
0.2
0
0
50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500
Gamma-Ray Energy (keV)
Error bars are displayed, but are too small to be visible for all but one measurement.
Page: 24
Graph [A3]
Page: 25
Pb-212 238.5 keV
Graph [A4]
2500
19th February 2010 Gamma-Ray Spectrum
Pb-214 295.5 keV
2000
Pb-213 352.51 keV
Radium-226 186.1 KeV
Ti-208 2614.5 keV
Number of Counts
1500
Ti-208 583.48 keV
K-40 1460.06 keV
1000
Bi-214 609.55 keV
Ac-228 911.10 keV
Ac-228 968.81 keV
Bi-214 1120.00 keV
Bi-214 1764.5 keV
500
Compton Continuum
0
0 100 200 300 400 500 600 700 800 900 10001100120013001400150016001700180019002000210022002300240025002600270028002900300031003200
-500
Energy (KeV)
Ac-228 463.1 keV
Rn-222 510.10 keV 511 keV
Annihilation
Bi-212 727.2 keV
X-rays
Page: 26
Graph [A5]
2500
26th February 2010 Gamma-Ray Spectrum
2000
Number of Counts
1500
1000
500
0
0 100 200 300 400 500 600 700 800 900 10001100120013001400150016001700180019002000210022002300240025002600270028002900300031003200
-500
Energy (KeV)
Page: 27
Graph [A6]
2500
10th March 2010 Gamma-Ray Spectrum
2000
Number of Counts
1500
1000
500
0
0 100 200 300 400 500 600 700 800 900 10001100120013001400150016001700180019002000210022002300240025002600270028002900300031003200
-500
Energy (KeV)
Page: 28
Graph [A7]
2500
19th March 2010 Gamma-Ray Spectrum
2000
Number of Counts
1500
1000
500
0
0 100 200 300 400 500 600 700 800 900 10001100120013001400150016001700180019002000210022002300240025002600270028002900300031003200
-500
Energy (KeV)
Page: 29
Graph [A7]
250
Background Count Gamma-Ray Spectrum
200
Annihilation 511KeV
Pair Production
Potassium-40 1460.8 KeV
Ti-208 2614.5 KeV
Number of Counts
150
Ti-208 583.2KeV
100
50
0
0
-50
100 200 300 400 500 600 700 800 900 10001100120013001400150016001700180019002000210022002300240025002600270028002900300031003200
Energy (KeV)
Page: 30
Table [T1]
Series
Uranium-238
Nuclide
Energy (keV)
Activity
(Bq)
% error
Error
(Bq)
Branching Ratio
Detector Efficiency
Activity Concentration
(Bq/kg)
Error
(Bq/kg)
Th-234
62.86
0.0019
42.6
0.00081
0.03
0.006
9.39
4.00
Th-234
92.37
0.0041
9.6
0.00039
0.02
0.016
10.34
0.99
Th-235
92.79
0.0041
9.6
0.00039
0.02
0.016
10.38
1.00
pa-233
1001.03
0.0004
55.0
0.0002
0.01
0.007
6.20
3.41
Bi-214
1238.11
0.0013
20.3
0.00026
0.06
0.006
3.67
0.75
Bi-214
1764.5
0.0031
6.6
0.0002
0.15
0.005
4.19
0.28
Pb-214
295
0.0110
4.8
0.00053
0.18
0.043
1.38
0.07
Rn-222
511
0.0130
4.8
0.00062
0.001
0.010
1728.03
82.95
Ra-226
186.1
0.0094
8.2
0.00077
0.04
0.017
14.98
1.23
Bi-214
610.07
0.0140
3.2
0.00045
0.45
0.009
3.49
0.11
lead-213
352.51
0.0200
3.2
0.00064
0.35
0.012
4.68
0.15
lead-214
241.99
0.0090
8.2
0.00074
0.07
0.015
8.38
0.69
Bi-214
1120
0.0036
6.3
0.00023
0.15
0.006
3.85
0.24
Ac-228
911.2
0.0099
3.3
0.00033
0.26
0.007
5.37
0.18
Ac-228
968.97
0.0058
4.7
0.00027
0.16
0.007
5.32
0.25
Ac-228
338.49
0.0088
6.9
0.00061
0.11
0.012
6.26
0.43
Th-228
215.98
0.0004
153.9
0.00054
0.00
0.016
8.57
13.19
Rn-220
549.76
0.0002
60.8
0.00012
0.00
0.009
17.54
10.67
Bi-212
727.33
0.0031
12.6
0.00039
0.07
0.008
5.81
0.73
lead-212
238
0.0440
1.7
0.00075
0.43
0.015
6.68
0.11
Ra-224
240.99
0.0090
8.2
0.00074
0.04
0.015
14.52
1.19
Bi-212
1620.5
0.0005
36.2
0.00018
0.01
0.005
6.49
2.35
Bi-212
785.37
0.0007
27.4
0.0002
0.01
0.008
8.64
2.37
Ti-208
510.77
0.0130
4.8
0.00062
0.08
0.010
16.15
0.78
Ti-208
583.48
0.0130
3.5
0.00046
0.30
0.009
4.66
0.16
Thorium-232
Page: 31
Average Activity
(Bq/kg)
Total Activity (Bq/Kg)
Total Activity Error (Bq/Kg)
6.74
80.94
12.91
7.91
86.04
18.62
Uranium-235
Single Decays
Pb-212
300.09
0.0027
17.3
0.00047
0.03
0.013
6.16
1.07
Ti-208
2610.4
0.0067
3.7
0.00025
0.36
0.004
4.76
0.18
U-235
185.72
0.0094
8.2
0.00077
0.57
0.017
0.94
0.08
Ps-231
300.07
0.0027
17.3
0.00047
0.02
0.013
8.18
1.42
Ra-223
154.21
0.0013
45.4
0.00059
0.06
0.019
1.19
0.54
K-40
1460.06
0.0063
4.5
0.00028
0.11
0.005
10.74
0.48
Page: 32
1.19
1.19
0.54
10.74
0.48
0.48
Graph [A9]
1.20E+00
Radon Growth
Normalised Activity (Bq)
1.00E+00
8.00E-01
6.00E-01
4.00E-01
2.00E-01
0.00E+00
0
100
200
300
400
500
Time from Sealing (Hours)
Page: 33
600
700
800
900
1000
Secular Equilibrium Growth Curve FORTRN code
Page: 34