1. health and fitness
2. disease
3. cancer

RADIONUCLIDE CONTENT OF SAND USED FOR CONSTRUCTION IN
KAKAMEGA COUNTY AND ASSOCIATED INDOOR RADON DIFFUSION
DOSES
SHIKALI N. COLLINS [B.Ed. (Sc)]
I56/CE/15221/2008
A thesis submitted in partial fulfillment of the requirements for the award of the degree of
Master of Science in the School of Pure and Applied Sciences of Kenyatta University.
August, 2013.
ii
DECLARATION
This thesis is an original work and has not been presented for the award of a degree at
any other institution of higher learning.
Shikali N. Collins
Signature: ……………………. Date: ………………
I56/CE/15221/08
Department of Physics
Kenyatta University
Nairobi, Kenya
`
Supervisors:
Dr. W.J. Ambusso
Signature ……….………….… Date ………..
Department of Physics
Kenyatta University
Nairobi, Kenya
Dr. M. K. Munji
Department of Physics
Kenyatta University
Nairobi, Kenya
Signature ………………….
Date …………..
iii
DEDICATION
This thesis is dedicated to my wife Lydia, son Dennis Ndenga and daughter Venus Irangi.
iv
ACKNOWLEDGEMENTS
I sincerely thank my supervisors Dr. Ambusso and Dr. Munji (Kenyatta University) for
their whole hearted continuous academic and moral support. Without them this study
would have been impossible. I thank the whole Kenyatta University Physics Department
for providing laboratory facilities, Internet Services for accessing scientific journals and
technical staff that have made this research successful.
Thanks to Dr. Angeyo (University of Nairobi) for providing useful literature materials,
activated charcoal canisters and IAEA standard samples. I also thank fellow Kenyatta
University Physics students particularly Tuwei A., Masinde T., Abuga V., Adero B,
Businei M. just to name but a few for their moral support and academic support.
Iam very much indebted to the National Council for Science and Technology (NCST) for
their sponsorship. The encouragement and financial support I received from NCST
through Prof. Shaukat Abdulrazak (Secretary/ CEO) is highly appreciated.
I sincerely thank my wife Lydia for encouragement, patience and all forms of support
during the research period. Sincere gratitude to all my family for their support during this
period.
Above all I thank the Almighty God for leading me this far. I confess that it is through his
grace that I have reached this far.
v
TABLE OF CONTENTS
DECLARATION ................................................................................................................ ii
DEDICATION ................................................................................................................... iii
ACKNOWLEDGEMENTS ............................................................................................... iv
LIST OF TABLES ........................................................................................................... viii
LIST OF FIGURES……………………………………………………………………..ix
ABBREVIATIONS AND ACRONYMS .......................................................................... xi
ABSTRACT ...................................................................................................................... xii
CHAPTER ONE ................................................................................................................. 1
INTRODUCTION .............................................................................................................. 1
1.1 Background to the study ............................................................................................... 1
1.1.1 Radon… ..................................................................................................................... 2
1.1.2 Modeling of radon entry in houses ........................................................................... 3
1.2 Physiographical and geological outline of Kakamega County .................................... 3
1.3 Statement of the research problem ............................................................................... 4
1.4 Objectives ..................................................................................................................... 5
1.4.1 Main Objectives ........................................................................................................ 5
1.4.2 Specific Objectives .................................................................................................... 5
1.5 Rationale of the study ................................................................................................... 6
CHAPTER TWO ................................................................................................................ 7
LITERATURE REVIEW ................................................................................................... 7
2.1 Natural radioactivity and indoor radon ......................................................................... 7
2.2 Related studies on natural radioactivity of sand used for construction and indoor
radon…… ........................................................................................................................... 7
2.2.1 Biological effects of ionizing radiation.................................................................... 10
CHAPTER THREE .......................................................................................................... 12
THEORETICAL CONCEPTS OF GAMMA RAY SPECTROMETRY AND INDOOR
RADON DIFFUSION FLUXES ...................................................................................... 12
3.1 Theoretical background to gamma radiation .............................................................. 12
3.2 Secular equilibrium ..................................................................................................... 12
3.3 Gamma Ray Spectrometry .......................................................................................... 13
3.3.1 Interaction of Gamma ray with matter ..................................................................... 13
3.3.2 Photoelectric Effect .................................................................................................. 14
vi
3.3.3 Compton Scattering ................................................................................................. 15
3.3.4 Pair production ......................................................................................................... 17
3.4 Principal mechanism of NaI(Tl) gamma ray detector................................................ 17
3.5 Indoor radon ................................................................................................................ 18
3.5.1 Radon generation ..................................................................................................... 19
3.5.2 Radon transport in sand as a building material ........................................................ 21
3.5.3 Estimation of radiation dose in dwellings ................................................................ 23
3.6 Radiation quantity and exposure units ........................................................................ 24
3.6.1 Radiation concentration ........................................................................................... 24
CHAPTER FOUR ............................................................................................................. 26
MATERIALS AND METHODS ...................................................................................... 26
4.1 Materials and Equipment used in this study ............................................................... 26
4.2 Sample collection and preparation .............................................................................. 27
4.3 Radioactivity Measurements ....................................................................................... 27
4.3.1 Energy calibration in NaI (Tl) spectrometry ............................................................ 29
4.3.2 Determination of Gamma Activities ........................................................................ 32
4.3.3 Detector counting efficiency .................................................................................... 32
4.2.4 Detection limits of the analytical system ................................................................. 33
4.3.5 Energy Resolution of the detector............................................................................ 34
4.3.6 Gamma ray spectral data analysis ............................................................................ 36
4.3.7 Analysis of Certified Reference Materials (IAEA-RGK-1, RGTh-1 and RGU-1) . 36
4.4 Activity Concentrations .............................................................................................. 36
4.5 Radiological parameters.............................................................................................. 37
4.5.1 Gamma dose rate...................................................................................................... 37
4.5.2 The Annual Effective Dose Rate (AEDR) ............................................................... 38
4.5.3 Radium Equivalent Activity .................................................................................... 38
4.5.4 External hazard index (Hex) ..................................................................................... 39
4.5.5 Gamma Index (Iγ) ..................................................................................................... 39
4.6 Modeling of radon diffusion fluxes in a room ............................................................ 40
4.6.1 Theory of modeling.................................................................................................. 40
4.6.2 The governing equations .......................................................................................... 41
4.6.3 Program Structure .................................................................................................... 43
4.7 Estimation of uncertainties ......................................................................................... 44
4.7.1 Uncertainty due to sample preparation .................................................................... 45
vii
4.7.2 Uncertainty due to Efficiency calibration ................................................................ 45
4.7.3 Uncertainty due to measurement of samples ........................................................... 45
CHAPTER FIVE .............................................................................................................. 47
RESULTS AND DISCUSSION ....................................................................................... 47
5.1 Radioactivity concentration of building sand ............................................................. 47
5.1.1 Exposure due to gamma radiation............................................................................ 50
5.1.2 External hazard index (Hex) ..................................................................................... 52
5.1.3 Gamma Index (Iγ)..................................................................................................... 52
5.1.4 Statistical analysis of 226Ra, 232Th and 40K in this study .......................................... 54
5.2 Indoor radon Model Results........................................................................................ 56
5.3 Model validation ......................................................................................................... 62
CHAPTER SIX ................................................................................................................. 65
CONCLUSIONS AND RECOMMENDATIONS ........................................................... 65
6.1 Conclusions ................................................................................................................. 65
6.2 Recommendations ....................................................................................................... 66
REFERENCES ................................................................................................................. 68
APPENDICES .................................................................................................................. 74
viii
LIST OF TABLES
Page
Table 4.1: The parameters of polynomial used for calibration of
the detector…………………………………………………..30
Table 4.2: Efficiencies of emission of K-40, Th-232and U-238 in NaI(Tl)
spectrometry……………………………………………..…..33
Table 4.3: The fit parameters for the Caesium- 137 photo peak Measured
in this work………………………………………………......35
Table 4.5: Dispersion of measured activities from certified activities
For (RGK-1, RGTh-1 and RGU-1) …………………………..36
Table 5.1: Average activity concentration of radionuclide in sand from
Old gold mining zones of Kakamega County………………..48
Table 5.2: Comparison between radium equivalent activities, indoor
Gamma Dose rates and annual effective dose in the present
Study and those reported in other countries…………………49
Table 5.3: Radium equivalent activity, external hazard indices, dose rate
and Annual effective dose …………………………………...51
Table 5.4: Comparison of hazard indices in present study and those for
Other countries………………………………………………..51
Table 5.5: Statistical summary of radionuclide…………………. ............54
Table 5.6: Limits of kurtosis for normal distribution (Taylor, 1990)…….55
Table 5.7: Limits of skewness factor for normal distribution (Taylor,
1990)…………………..…………………………………….…5
ix
LIST OF FIGURES
page
Figure 3.1: A schematic diagram illustrating Photoelectric-effect………14
Figure 3.2: Schematic diagram illustrating Compton Scattering
process………………..……………………………………....15
Figure 3.3: Radiation detection using Thallium activated Sodium Iodide
[NaI(Tl)] detector…………………………………….………18
Figure 3.4: Schematic representation of advective and Diffusive transport
of radon in sand as a porous material…………………………22
Figure 3.5: Possible uncertainties that could be considered in
determination of activity concentrations of NORM in sand
samples………...……………………………..……………….28
Figure 4.1: A map showing the sampling sites in old gold mining region
of Kakamega County…………………….…………………..28
Figure 4.2: Schematic diagram of NaI(Tl) spectrometer used To measure
radioactivity concentration…………………..……………….29
Figure 4.3: Energy calibration of NaI(Tl) detector used….…………...…31
Figure 4.4: A typical gamma ray spectrum of construction Sand
sample…………….………………………………………....31
Figure 4.5: Gaussian fitting of Caesium -137 spectrums measured in this
work…………………….…………………………………....35
Figure 4.6: A schematic chart showing the main parts of the
Program………………………………………………………44
Figure 5.1: Activity concentration and radium equivalent Activity
distribution in all the sampling sites……………..…………..50
Figure 5.2: A scatter plot of the external hazard indices and
Gamma hazard indices for different samples ……………….54
Figure 5.3: Two dimensional gridding of the model room…………..….57
Figure 5.4: Different build-up curves for the exhaling source block…….58
Figure 5.5: Radon Concentration profiles in the blocks [diffusion only]
………………………………………………………………59
x
Figure 5.6: Radon Concentration profiles in the blocks [diffusion with decay]
…………………………………………………………….....61
Figure 5.7: A comparison of concentration profiles in blocks where Radon
diffuses with and without decay……………………………..61
Figure 5.8: A comparison of measured and modeled radon concentration
………………………………………………………………63
Figure 5.9: Radon growth curve obtained by fitting measured radon
Concentration for monitoring station 1………………………63
xi
ABBREVIATIONS AND ACRONYMS
ADC
Analogue to Digital Converter
EPA
Environment Protection Agency
EFDM
Explicit Finite Difference Method
FWHM
Full Width at Half Maximum
HBRA
High Background Radiation Area
HV
High Voltage
IAEA
International Atomic Energy Agency
ICRP
International Commission on Radiological Protection
IUPAC International Union of Pure and Applied Chemistry
MCA
Multichannel Analyzer
NaI(Tl) Thallium activated sodium Iodide Detector
NCRP
National Council on Radiation Protection
NORM Naturally Occurring Radioactive Material
OECD
Organization for Economic Cooperation and Development
PM
Photomultiplier
TAP
Total Absorbed Dose
TENORM
UNSCEAR
W HO
Technologically Enhanced Naturally Occurring Radioactive Material
United Nation Scientific Committee of the Effects of Atomic Radiation
World Health Organization
xii
ABSTRACT
The greatest portion of radiation received by world‟s population comes from natural
radioactive sources. Everyone on earth receives natural radiation; some get much more
than others depending on where they live. Primordial radionuclide in building sand and
gravels from quarries are some of the sources of radiation hazards common in dwellings
and working places. In this study, activity concentrations of naturally occurring
radionuclide in mineral sand used for construction collected in old gold mining belt of
Kakamega County were measured using gamma ray spectrometry technique, [NaI(Tl)].
The results of the concentrations of naturally occurring radionuclide were as follows:
226
Ra ranged from 36.79±8.89 to185.21±5.89 Bqkg-1, 232Th ranged from 51.12±2.56 to
158.92±7.95 Bqkg-1 and 40K ranged from 322.38±16.12 to 960.53±48.03 Bqkg-1. The
calculated radium equivalent activity (Raeq), the absorbed dose rate (D), and the external
hazard index (Hex) were within the international recommended values. Hence
construction sands from the study region do not pose any risk to the inhabitants in terms
of the acceptable limits. The movement of radon by diffusion from the walls of
classrooms constructed from such sand into indoor air was modeled based on radiological
parameters. The posed model predicted an ambient indoor radon concentration of 9 Bqm3
, 15.6 Bqm-3 and 28.7 Bqm-3 in three monitoring stations (classrooms) in the region. The
modeled radon concentrations were lower than measured; the model reproduced the
general trends associated with diffused indoor radon fluxes. Thus it can be helpful in
estimating radon concentrations for other similar processes such as estimating radon
concentration in caves and mines.
1
CHAPTER ONE
INTRODUCTION
1.1
Background to the study
Natural radioactivity is widespread in human immediate environment. It can originate
from terrestrial radiation, cosmic radiation or indoor radiation from building materials.
Researchers have shown that the presence of natural radioactive sources such as Radium226 (226 Ra) and Thorium-232 (232 Th), and their progenies, and Potassium-40 (40K) in
building materials result in harmful external and internal effects to occupants. The
external effect is caused by direct gamma radiation from the natural occurring
radionuclide (NORM) affecting external organs like skin. The internal effect normally
affects internal organs mainly the respiratory tract, is due to radon and its daughters
which are released from building materials (European Commission, 1999). For instance,
high concentration of radon gas has been identified to cause lung cancer among persons
exposed to high doses of radon. Good examples are people working in mines.
Indoor radon is released from the radium trapped in mineral grains of the building
materials. The gas then escapes to air because the radon diffusion length is comparable to
the thickness of the material (Rizzo et al., 2001). This contribution depends on
concentration of radium, which is generally low in materials of low activity (UNSCEAR,
1999). The harmful effects of gamma radiation from building materials and radon in
dwellings are generally well known, but information on concentration levels of radon in
dwellings and work environment in Kenya is not readily available. There is therefore a
2
need to study building materials from areas perceived to have higher concentration of
NORM with the aim of measuring and documenting their actual levels in dwellings. This
is aimed at estimating the actual risk of exposure due to ionization radiation that people
are exposed to. In this study, a theoretical model to estimate the contribution of mineral
sand used for construction to the indoor dose rate and to radon air contribution is
developed. Knowledge of the level of natural activity in mineral sand is thus important to
assess the possible radiological hazards to human health and to develop standards and
guidelines for use and management of sand used as building material.
1.1.1
Radon
Radon is a colorless odorless noble gas with atomic number 86. It is one of the decay
products of uranium and thorium decay series. It has three isotopes;
235
220
Rn and
Rn that originate from
222
Rn is considered important due to its longer life as compared to the others. The other
Th and
238
Rn,
222
U,
232
219
U decay series, respectively. In this work
isotopes of radon will be mentioned explicitly.
Radon is believed to originate from materials that are rich in uranium. Such materials are
soil, sand, rocks, gravels and many others. Since it is a gaseous product, it responds to
temperature and pressure gradients. It may succeed in escaping
out of such materials
and get mixed with air because of its relatively long life. If it escapes to a confined space
with limited ventilation, its concentration may become fairly high. Humans living in such
confined places inhale air which may be rich in radon and its daughters. The radioactive
heavy metal daughters of radon including
218
Po,
214
Pb,
214
Bi and
214
Po are short lived.
3
Thus, once inhaled; they remain in the “mucus” lining and may be lodged in lungs
(James, 1987). On decaying, they deposit large amount of energy in the surrounding
tissues, causing cancer. Several techniques can be applied for measurement of radon and
its daughters. These techniques are based on active and passive methods. The criterion
for selection is based on objective behind the measurement, available equipment, and the
costs among others.
1.1.2
Modeling of radon entry in houses
A model is a representation of a real process or system. In an effort to understand indoor
radon concentration this study focuses on radon entry into houses which depends on the
following factors: radon generation from the source; transport properties of the source;
transport properties of the interface between the source and indoor air and the driving
forces. There are three approaches applied when modeling radon entry in houses; these
are analytic modeling, lumped parameter modeling and numerical modeling (Carmen,
1992). In this study, a numerical model for estimating the contribution of mineral sand
used for building to the indoor dose rate and to the radon air concentration is developed.
Knowledge of the level of natural activity in mineral sand is thus important in assessing
the possible radiological hazards to human health and in developing standards and
guidelines for use and management of sand used as building material.
1.2
Physiographical and geological outline of Kakamega County
Kakamega county is located in Western Kenya about 30 km north of equator, 52 km
4
north of Kisumu at latitude N 00 30 – N00 0 and longitude E340 30 – E350 0. The average
elevation of kakamega is 1535m (ISRIC, 2012). It borders the indigenous Kakamega
forest on the west and has three main rivers i.e. R. Nzoia, R. Yala and R. Isiukhu flowing
across the county to Lake Victoria. The construction sand deposits are mainly found from
these rivers and they are sources of domestic water supply in the county. The underlying
rocks in this area are associated with ancient gneisses of Kavirondo and Nyanzian
systems as well as basalt, phenolites and gold – bearing quartz veins. They are referred to
as Kisumu- Kakamega- Mumias granite- greenstone complex.
The main inhabitants of this region are the Luhya. Their main economic activities include
small scale subsidence farming, large scale sugar – cane and tea growing, small scale
artisanal gold mining and small scale trading.
1.3
Statement of the research problem
There is inadequate knowledge about the levels of naturally occurring radionuclide that
result from sand used for construction in Kakamega County; though, several studies on
risks of human exposure and impact of ionizing radiations from NORM due to sand used
for construction from other places have been documented (Xinwei et al., 2006 and Cervic
et al., 2009). Similarly, there is scanty or no data and records on levels of radon in
dwellings and work places in this region. Adequate data is important for regulatory and
advisory purposes in protection of the general public from unnecessary exposure to
radiation. Thus, measuring the activity concentration of naturally occurring radionuclide
in mineral sand used for construction in this region is important for evaluation of the
5
impact of radiation on the environment and in the assessment of radiation effects on
human population (Tuo et al., 2010). This is particularly important for building materials
since most people spend 80% of their time indoors (UNSCEAR, 1999).
1.4
Objectives
1.4.1
Main Objectives
This research sets to achieve two main objectives. The first one is to measure the activity
concentration of
226
Ra,
232
Th and
40
K in mineral sand used for construction in old gold
mining belt of Kakamega County. The activity concentration values are used to assess the
external annual dose for individuals living in dwellings constructed using such sand in
this region. Secondly, the research aims to develop a theoretical model for estimation of
the contribution of mineral sand to the indoor radon dose rate.
1.4.2
Specific Objectives
The specific objectives are as follows;
i.
To determine the radioactivity concentration of naturally occurring
radionuclide present in the mineral sand used for construction in old gold
mining zones of Kakamega County.
ii.
To estimate the radiation doses that people are exposed to due to indoor
gamma radiation and indoor radon in the region.
iii.
To develop predictive models for the diffused radon concentrations fluxes in a
room, assuming that all dwellings, classrooms and other buildings in the
region are constructed using mineral sand.
6
1.5
Rationale of the study
Environmental impact due to effect of ionizing radiation from NORM in this region is
difficult to assess due to inadequate data. In this study, measured data about levels of
naturally occurring radionuclide has been provided and modeling of radon fluxes in a
room has been done. Availability of such information is helpful in understanding the
doses that people are exposed to. It is envisaged that the results of this study will be
useful to the relevant scientific committees, government and non-governmental
organizations in making decisions about mineral sand as a building materials in this
region.
7
CHAPTER TWO
LITERATURE REVIEW
2.1 Natural radioactivity and indoor radon
There has been concern about the effects of radon and gamma radiation exposure to
people especially in dwellings, schools and working places in Kenya (Mustapha et al.,
1997). Due to insufficient information about the concentrations and harmful effects of
gamma radiation and radon, many people have continued to work and leave in dwellings
unaware of the dangers posed by these radiations in their lives. Besides, remedial action
even when possible is never undertaken because of lack of sufficient and relevant
information. In this study concentration level of NORM in construction sand from old
gold mining belt of Kakamega has been measured. Radon concentration fluxes in a room
were modeled using activity concentration of
226
Ra measured from sand. The assessment
of natural radioactivity in this region is important because industrial, agricultural,
artisanal gold mining, etc have resulted in Technologically Enhanced Naturally
Occurring Radionuclide Materials (TENORM) that have elevated the levels of NORM in
the environment (Bliss, 1987; Salman and Amany, 2008). These naturally occurring
radionuclides emit ionizing radiations that cause somatic and genetic effects in human
beings.
2.2 Related studies on natural radioactivity of sand used for construction and indoor
radon
Worldwide a number of studies have been undertaken to assess the hazards posed to
8
humans due exposure to radiation from naturally occurring radionuclide in the
environment. In Pakistan, natural radioactivity and radiological hazards have been
assessed for soils and building materials in six district of Punjab Province (Faheem et al.,
2008). The annual effective dose equivalents were found to vary from 0.10 to 0.37mSv.
These results showed that the materials are safe to be used as building materials.
In Turkey, an assessment natural radioactivity of sand used for construction in the whole
country has been done (Cervic et al., 2009). The measured activity in sand samples
ranged from 17 to 97 Bq/kg, 10 to 133 Bq/kg and 16 to 955 Bq/kg for
40
226
Ra,
232
Th and
K respectively. The study showed that measured sand samples do not pose any
significant source of radiation hazard and are safe to be used as building materials.
In Greece, measurement of indoor radon levels and natural gamma radiation in public
work places was done in north - western part of the country (Papachritodouloou et al.,
2010). They found that the radon concentration followed a log- normal distribution with
arithmetic mean of 95±5 Bq/m3, which is within the European Commission
recommendation.
In Algeria, natural radioactivity in building materials has been assessed (Amran and
Tahtat, 2001). The radium equivalent activities were below the gamma radiation dose rate
(1.5 mSvy
-1
). Therefore, the use of the materials in construction of dwellings is
considered safe for inhabitants according to Organization for Economic Cooperation and
Development (OECD, 1979).
9
In Kenya, a number of studies have been undertaken to assess the hazards of human
exposure to indoor external doses due to NORM in building materials and indoor radon.
Natural radioactivity in some building materials and the contributions to the indoor
external doses has been studied (Mustapha, 1999). It was reported that the activity
concentration of
40
K was much higher than that of
226
Ra and
232
Th which is a common
occurrence in normal geological materials.
Measurement of indoor 222Rn concentration in dwellings of Kenyatta University has been
documented (Chege, 2007). The measured average concentration during the sampling
period was found to be 188 Bq/m3. A further investigation of the effects of
meteorological parameters on indoor radon in model traditional huts has also been
undertaken in Kenyatta University (Chege et al., 2007). The radon concentration in these
huts correlated positively with rainfall, but negatively with outdoor air temperature and
wind speed. The average radon concentration reported was 170±39.6 Bqm-3 indicating
that radon might pose radiological problems in such dwellings. ICRP (1993) recommends
action levels for
222
Rn concentration of 200-600 Bqm-3. Other studies include the
investigation of radon concentration in coastal and Rift valley regions (Maina et al.,
2004). Higher concentration were reported in coastal region (43-704 Bqm-3) while Rift
valley regions reported radon concentrations of less than 100 Bqm-3.
Sarvovic and Djordjevic (2008) devised a model describing the flow of radon through
concrete. The method allowed for the calculation of radon diffusion through concrete
walls and hence estimation of indoor radon concentration.
10
None of these studies in Kenya has adequately investigated the effects of building
materials and indoor radon in old gold mining belt of Kakamega County. It is envisaged
that the results of this study will be helpful for setting limits of radionuclide concentration
in construction sand or propose a ban on use of sand from this region in case the sand
contain abnormally high activity concentrations. Furthermore none of these studies in
Kenya have attempted to determine the backward or forward variation in radiation levels.
This study introduces this aspect by developing a finite difference numerical model
which estimates the variation of indoor radon levels in a room.
2.2.1 Biological effects of ionizing radiation
Exposure to ionizing radiations can produce harmful effects on human health. Radon and
its decay products is the main producer of harmful health effect. Others include ionizing
radiation from NORM in building materials and soil. For instance lung cancer is mainly
attributed to inhalation of radon. The Environment Protection Agency (EPA) estimate
that radon may cause between 5000 – 20000 lung cancers (NCRP, 1984) in U.S.A.
Biological effect starts when molecules in living cell interact with radiation energy
through deposition and or exposure. If a large dose is delivered in a short period,
symptoms of a cute radiation injury occurs. When delivered dose is much smaller and
repeated for longer time, the biological effects may not appear for many years. These
effects can be classified as direct or indirect effects. Direct effects occur when ionizing
radiations cause excitation in the same molecule where the radiation is primarily
deposited and absorbed. While indirect effects occur when ionizing radiation is absorbed
(for example) in water molecule in human body and produces short lived chemically
11
reactive products i.e. radicals that react with other molecules in other parts of the body
(Thermod and Maille, 2003). In an effort to minimize radiation exposure to members of
the public, limits on exposure to ionizing radiation have to be set (ICRP, 1991). Hence, it
is necessary to measure radiation dose in order to monitor the effects of nuclear radiation
on biological tissue.
12
CHAPTER THREE
THEORETICAL CONCEPTS OF GAMMA RAY SPECTROMETRY AND
INDOOR RADON DIFFUSION FLUXES
3.1 Theoretical background to gamma radiation
Gamma rays are the most energetic and harmful form of electromagnetic radiation that
are produced when radioactive nuclei undergoes transitions. Gamma radiation is mostly
produced alongside other forms of radiation such as α and β. Unstable atomic nuclei
spontaneously decay to produce stable nuclides, the daughter nuclei are sometimes
produced in excited states. The subsequent decay of excited state results in emission of γrays. They can also be produced when there is positron annihilation in matter.
3.2 Secular equilibrium
The total activity of a radionuclide undergoing radioactive decay can be calculated by
considering a long lived parent decaying into a shorter lived daughter which in turn,
decays into a stable nuclide. Secular equilibrium is a condition in which the decay rates
of the parent radionuclide and that of the daughter radionuclide are equal. This is only
possible if the half-life of the parent radionuclide is longer. It should be long enough that
there is no noticeable decay during the time interval of interest. If the parent radionuclide
half-life is longer, but short enough so that there is noticeable decay of parent nuclei
during the time interval of interest, a condition of transient equilibrium is reached. When
state of secular equilibrium is reached, the activity of daughter radionuclide is determined
by the activity of the parent radionuclide.
13
3.3 Gamma Ray Spectrometry
Gamma ray spectrometry refers to the process of detection and measurement of gamma
ray energy emitted during nuclear de-excitation process. Some radioactive sources
produce gamma rays of various energies in the range 0.1 to 10 MeV. The energy
produced is characteristic of the emitting nucleus hence used to identify the type of the
radioactive nuclei. When these radiations are detected and analyzed using gamma ray
spectrometry, a gamma ray energy spectrum is produced. A detailed analysis of the
spectrum is used to identify the type and quantify gamma emitters present in the source.
3.3.1 Interaction of Gamma ray with matter
Gamma rays are photons that originate from the nuclei of a radioactive atom undergoing
decay. They have no mass and no charge. They are quanta of electromagnetic energy that
travels at the speed of light and can travel long distances in air un-attenuated. When
these photons interact with matter, free electrons are generated and as these electrons are
slowed down by matter, they create charge pairs. The photon detectors use the charge
pairs generated to determine the photon energy by measuring the quantity of charge
produced by these pairs (Debertin and Helmer, 1988). Knowledge of interactions of
gamma rays with detector matter is essential for the understanding of how the gamma
photons are detected and attenuated in the detectors. There are three main mechanisms
through which gamma photon interact with matter; photoelectric effect, Compton
scattering and pair production. These mechanisms are discussed in the preceding
subsections:
14
3.3.2 Photoelectric Effect
Figure 3.1 shows a schematic diagram of a gamma ray photon absorption by an electron
within an atom. When the incident gamma ray photon interacts with tightly bound
electron in matter, the electron absorbs the incident photon energy and is emitted as a
photoelectron. The emitted photoelectron leaves a vacancy in the shell of the atom
making the atom excited. During de-excitation, X-rays or an Auger electron is emitted. If
the absorber material is large enough, the X- rays will be absorbed in the surrounding
matter. The kinetic energy of the ejected electron is given by Eq.3.1;
Ee− = hν − Eb ,
(3.1)
where Eb is the binding energy of the photoelectron‟s original shell, hν is the incidence
gamma energy and Ee- is the kinetic energy of ejected photoelectron.
Photoelectron
E
K-Shell
hv
Incident gamma photon
Atomic Nucleus
L-Shell
Figure 3.1: Schematic diagram of gamma ray photon absorption by an electron in an
atom
Photoelectric effect is the most dominant mode of interaction of γ or x- ray photons with
15
matter for relatively low energy. Photoelectric effect is enhanced in absorber material of
high atomic number. This can be illustrated by the interaction cross section τ, described
in Eq. 3.2 (Knoll, 1989);
𝑍𝑛
𝜏 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝐸 3.5 ,
(3.2)
𝛾
where, n varies between 3 and 5 over the gamma- or x-ray photon energy of interest.
3.3.3 Compton Scattering
Figure 3.2 shows a schematic diagram illustrating Compton Scattering process in an atom
where the incidence photon energy is greater than the binding energy of the bound
electron in the atom.
E   h  Scattered photon

E  h
ss
s
s
 Recoil electron angle
Figure 3.2: Schematic diagram illustrating Compton Scattering process
In Compton Scattering the binding energy of the electron becomes less significant and
the electron is considered free. Thus Compton scattering is the process of collision
between incident gamma photon and an electron in the absorber. During the collision the
gamma photon is deflected through angle θ with respect to its original direction as shown.
16
The total incident photon energy is not deposited at the initial interaction site, but there
are series of Compton scattering events, which reduces the secondary photon energy
before the sequence ends up with photoelectric absorption event. The energy of scattered
photon is given by Eq. 3.3;
h  
h
,
h
1
m0 c 2 (1  cos  )
(3.3)
where hν is the incident gamma ray energy, m0 is rest mass of ejected electron (0.511
MeV) and θ Scattering angle.
If a head-on collision occurs, the incident gamma photon is scattered towards its direction
of origin, leading to the energy transferred to the recoil electron in a single Compton
interaction reaching a maximum value. This forms a special spectral feature known as the
„Compton Edge‟. In normal situations, all scattering angles occur in a finite sized detector
volume. Therefore, a continuum of energies is transferred to the recoil electron. The
Compton interaction cross section is given by Eq. 3.4;
  cons tan t 
Z
,
E
(3.4)
where Z is the absorber atomic number and E is the incident gamma energy (hν). The
interaction cross section increases linearly with the atomic number, Z of the absorber
atom.
17
3.3.4 Pair production
This is the process through which a gamma photon is transformed into an electronpositron pair. The process occurs close to the nuclei of the absorbing material due to high
electric field at this point. A minimum gamma ray energy of 2m0c2 (1.022Mev) is
required for any incident photon to undergo this process. Any excess energy above this
value is transferred into kinetic energy which is shared by electron-positron pair. The
electron and positron travels a few mm before losing their energy in the absorbing
medium due to collisions within the medium. As the positron slows down due to
collisions, the positron can combine with an electron from absorbing medium; this is
followed by annihilation of both particles. The annihilated particles are replaced by two
annihilation photons, each of energy m0c2 (0.511Mev) which are emitted back-to-back.
The probability of pair production, k varies approximately as the square of the atomic
number Z of the absorber material (Knoll, 1989) given in Eq. 3.5;
f k = kαZ 2 ,
(3.5)
3.4 Principal mechanism of NaI(Tl) gamma ray detector
The NaI(Tl) gamma ray detector used in this study operates on the principle of emission
of light by florescent
materials (scintillation) when illuminated by incident gamma
radiation. Figure 3.3 shows a schematic diagram of the detection system of NaI(Tl)
detector. The detector consists of a scintillation counter, a photocathode, a
photomultiplier tube and associated electronics. When the incident gamma photon enters
the scintillation counter, the photons deposit their energy in the scintillation counter
18
resulting in the elevation of detector atoms to excited states (the electrons of the atom
jump from valence band, which is generally full to empty conduction band across energy
band gap of ≈ 4eV). Eventually, the excited atoms lose their energy by emitting visible
radiation and the electrons drop back to valence band. The visible radiation hit a
photosensitive surface and photoelectrons are generated. Electrical pulses are formed by
multiplying and accelerating the photoelectrons using a photomultiplier tube.
Figure 3.3: Radiation detection using Thallium activated sodium Iodide [NaI(Tl)]
detector
3.5 Indoor radon
The main factors considered in determination of radon and progeny activities in
dwellings include geology, climate, building materials, design and construction
(especially single or multi-storey), building age, barometric pressure effects and lifestyle
of the residents (Mudd, 2008). In this study, building sand contribute to gamma dose rate
19
through inhalation of radon and external irradiation by NORM in buildings constructed
from such sand (Rizzo et al., 2001). Thus, the measurement of the radionuclide
concentrations of sand was used to evaluate both indoor radon concentration and gamma
dose rate. Indoor radon in dwellings can be studied in three levels; radon generation,
transport and distribution inside dwellings via airflows.
3.5.1 Radon generation
In dwellings indoor radon originate from presence of trace elements of
238
U in soil and
building materials. Depending on the properties of building material, radon can be
transferred through the building material and enter the dwelling space. Building materials
such as sand in this case can generate radon by the decay of radium minerals in their
components. The radon generated in building materials depends on the age of the
building material, relative humidity, type and amount of building material (Michel van
der Pal, 2003). The rate of radon generation is proportional to the amount of radium in
the sand as a building material. Not all the radon generated is available for transport, part
of it remain in the solid matrix of the sand. The ratio of the amount of radon that becomes
available for transport to the total amount of radon generated is called emanation
coefficient, η. The emanation coefficient is determined using Eq. 3.6;
η
=
amount of radon available for transport
total amount of radon generated
(3.6)
The rate at which radon atoms decay is also proportional to the number of radon atoms.
Thus the total rate of change of the number of radon atoms per unit time due to
20
generation and decay is described by Eq. 3.7:
dN Rn
 Rn N Rn  Ra N Ra ,
dt
(3.7)
where:
NRa
Number of radium atoms;
NRn
Number of decaying radon atoms;
λRa
Radium decay constant (3.6× 10-12 s-1);
λRn
Radon decay constant (2.1×10-6 s-1).
The first term on the right hand side of Eq. 3.7 describes the loss of radon due to decay
and the second term describes the amount of radon atoms gained by generation from
radium. The activity (number of atoms decaying per second) is calculated from the
number of atoms and the decay constant. Hence, activity for radium and radon
respectively are given by Eq. 3.8a and 3.8b.
ARa  Ra N Ra
,
(3.8a)
ARn  Rn N Rn ,
(3.8b)
Where ARa and ARn is radium activity (Bq) and radon activity (Bq) respectively.
The radon activity concentration is expressed as activity of radon per unit volume, while
radium activity concentration is expressed as the activity per unit mass as given by Eq.
3.9a and 3.9b.
C Rn 
ARn
,
V
C Ra 
ARa
,
Ms
(3.9a)
(3.9b)
21
where CRn is radon activity concentration (Bqm-3), CRa is radium activity concentration
(Bqkg-1), V is volume (m3) and ms is the mass of the sample (kg).
The rate of change in radon activity concentration can be written as described in Eq.3.10.
dC
  Rm C   Rn  b C Ra
dt
,
(3.10)
where 𝜌𝑏 is the bulk density (kgm-3).
The decay constant of radium is not explicitly present in Eq. 3.10 as it is included in the
radium activity concentration. Thus we get the following expressions for the decay and
generation of radon:
js = ηλRn ρb CRa ,
(3.11a)
jb = βλRn ,
(3.11b)
where β , is the partition corrected porosity.
The Eq. 3.11a and 3.11b shows that the radium concentration, the partition corrected
porosity, the emanation coefficient and the density of the sand are material properties
required to describe the generation of radon in sand as a porous building material.
3.5.2 Radon transport in sand as a building material
To gain insight on the mechanisms that play major roles in the transport of radon in sand
as a building material, we considered the sand to be porous and isotropic. Two
mechanisms were assumed to play a role;
a) Radon can be transported due to differences in radon concentration (diffusive
transport). This mode is considered one of the main processes for exhalation of
radon atoms in sand as a building material from the walls in houses.
22
b) Radon can be transported by the flow of air (advective transport). Advection is
not limited to exchange of air between open spaces but can also be the flow
through porous media such as building sand (Fig. 3.4). Thus porous concrete
fabricated from sand can act as sources of advective radon. Advective transport is
also an important mechanism for entry of radon from soil to the crawl space and
further to the living space.
where ∆C= change in radon concentration and ∆P= change in Pressure
Figure 3.4: Schematic representation of advective and diffusive transport of radon,
respectively, in sand as a porous building material
In this study diffusive transport of radon in sand as a building material will be considered
important. To describe the diffusive transport of radon in porous sand we relate it to the
diffusion transport in air. The transport of radon through air is described by Fick‟s law of
diffusion as shown in Eq. 3.12.
𝑗 = −𝐷𝑚 𝛻𝐶𝑎 ,
(3.12)
23
where; 𝑗 is flux (Bqm-2s-1), Dm is molecular diffusion coefficient (m2s-1) and 𝛻𝐶𝑎 is
radon concentration gradient (Bqm-4). The left hand side of Eq. 3.12 describes the amount
of radon that is transported per surface area per unit time. The term on the right hand side
gives the driving force, 𝛻𝐶𝑎 and the negative sign describe the effect of the driving force
on the flux. The law assumes a mixture of ideal gases and very low radon concentration.
For porous media like building sand the Eq. 3.12 is modified as given by Eq. 3.13.
𝑗𝑑,𝑎 = −𝐷𝑏 𝛻𝐶𝑎
(3.13)
where; 𝑗𝑑,𝑎 is flux of radon as a result of diffusion in the air–phase (Bqm-2s-1) and Db is
bulk diffusion coefficient of porous sand (m2s-1). It is assumed all pores in the sand are
oriented in same direction as applied concentration gradient.
3.5.3 Estimation of radiation dose in dwellings
In principle, it is possible to evaluate the indoor radon concentration provided the radon
sources and airflows are given. In practice, this is not possible, due to many timedependent and unknown parameters. Thus we make many assumptions to simplify the
description. Several models have been documented to describe the entry of radon in
dwellings (Rodgers et al.,1991), but in this study we consider a model that aims at
estimating the radiation dose in dwellings based on building plans rather than actual
measurements. Thus the building plans can be adjusted to meet the radiation
requirements prior to the building of the dwellings. In this model, the radiation dose in
dwellings is considered to be the sum of contribution of gamma radiation and the
contribution of alpha radiation from radon and its decay products.
The assessment of the behavior of indoor radon will depend on the mass-balance between
24
the entry rate and the removal rate in living room. For a given entry rate, the
accumulation of radon in a room will depend on the room volume, ventilation rate and
inter-zone flows (Carmen,1992).
3.6 Radiation quantity and exposure units
Ionizing radiation is measured in terms of the strength of the radiation source, energy of
the radiation, level of radiation in the environment and the radiation dose or amount of
radiation energy absorbed by the human body (Nemangwele, 2005). When ionising
radiation interacts with human body, the body tissue absorb the radiation energy. The
amount of energy absorbed per unit mass of tissue is known as absorbed dose. It is
expressed in units called the Gray (Gy). One Gray is equivalent to one joule radiation
energy absorbed per kilogram of tissue (Mudd, 2008). Equal doses of all types of ionising
radiation are not equally harmful. In order to compare effects of radiation, an equivalent
dose in unit of Sievert (Sv) is required which allows for differing biological effects of
alpha, beta and gamma radiation (Allisy- Roberts, 2005).
Dose equivalent (Sv) = Absorbed dose (Gy) × Radiation weighting factor (WR)
3.6.1 Radiation concentration
The amount of radioactive material is expressed by mass or activity. The activity in
Bequerrel (Bq) is the rate at which radioactive atoms decays per second. For radon,
potential alpha energy concentration (PAEC) is expressed in Working Level (WL).
Potential alpha energy concentration (PAEC) is a measure of the total alpha energy per
25
volume emmitted by a radon atom as it undergoes complete decay. A PAEC of 1 WL is
approximately the PAEC of radon progeny in radioactive equilibrium with radon
concentration of 3700 Bq/m3 (Nazaroff and Nero,1988).
26
CHAPTER FOUR
MATERIALS AND METHODS
4.1 Materials and Equipment used in this study
The following materials and equipment were used in this study:
a) Garmin GPS supplied by Titan Avionics Limited, Nairobi.
b) 1.0 Liter marinelli beakers manufactured by Nuclear Technology Services,
Roswell.
c) Metallic buckets and 1mm wire mesh sieve manufactured by Jua Kali artisans,
Kakamega.
d) Hot air oven manufactured by Omega Oven limited, Nairobi.
e) 76mm×76mm Thallium activated Sodium Iodide [NaI(Tl)] detector manufactured
by Oxford Instruments Inc. Tennessee.
f) PCA-P software manufactured by Nuclear Measurements Group, Tennessee.
g) Oxford win-MCA and Assayer Software version 3.80 manufactured by American
Nuclear Systems, Inc. Ork Ridge.
h) Microsoft professional C++ software supplied by Specicom Technologies,
Nairobi.
i) Standard IAEA reference Samples, preparation and certification of IAEA Gamma
Spectrometry Reference material, Vienna.
j) Dell D620 Computer laptop supplied by Stewan Computer Garage Limited,
Nairobi.
27
4.2 Sample collection and preparation
In this survey, the construction sand samples were collected along the main rivers in the
old gold mining region of Kakamega county i.e. R. Yala and R. Isiukhu. The most
suitable sampling approach that was employed involved a combination of grid sampling
and systematic random sampling. The distance between neighboring grid centres was
approximately 1 km. All sampling points were selected randomly within a particular grid.
Figure 4.1 shows a map of the sampling sites. From the grids, 19 sampling positions S1S19 were randomly identified. A total of 38 construction sand samples were collected,
two from each sampling site. The collected samples weight was approximately between
1.5 kg and 2.0 kg. The exact positions for the sampling sites were recorded using hand
held Garmin GPS (Global Position System, model number 12).
Each collected sand sample was crushed to fine powder, thoroughly mixed to ensure
homogeneity and placed in a drying oven at a temperature of 110 0C for 24 hours to
ensure that any significant moisture was removed. To obtain uniform particle sizes, a 1×1
mm meshed sieve was used. Accurate weights of 500±1 g of each sample was taken and
stored in sealed plastic bags for four weeks prior to counting. This was meant for the
samples to achieve a secular equilibrium between Radium-226 and its short lived decay
products.
4.3 Radioactivity Measurements
Radioactivity measurements in this work was done by a shielded 76mm × 76mm NaI(Tl)
detector coupled to a computer based MCA. The detector was used to determine the
28
concentration of 226Ra,
232
Th and 40K in the construction sand samples. The detector was
shielded by 15cm thick lead on all four sides and 10cm thick on top to reduce the
gamma-ray background.
Figure 4.1: A map showing the sampling sites in old gold mining region of Kakamega
County.
29
The samples in sealed marinelli beakers were placed on the detector and counted for
30000 seconds. The same sample‟s and reference‟s geometry was used to determine the
peak area to minimize uncertainties due to measurements (Turhan et al., 2008).
Background counts were taken under the same conditions of sample measurements and
subtracted in order to get net counts for the sample.
At the end of the counting period, the spectrum recorded was displayed on the screen of
the MCA with the horizontal axis representing the photon energy (channel number) while
the vertical axis representing the photons recorded per channel (intensity). This gave the
information regarding the type and the concentration of the radionuclide present in the
sample.
4.3.1 Energy calibration in NaI (Tl) spectrometry
The purpose of energy calibration of the NaI(Tl) gamma ray spectrometer was to obtain a
relationship between peak position in the spectrum against the corresponding gamma ray
energy. Energy calibration was done at the start of every measurement to cater for
changes in weather, vibrations and heating up of the detector. Energy calibration involved
measuring sources that emits gamma rays of known energy and comparing the measured
peaks with energy. In this work, International Atomic Energy Agency (IAEA) certified
reference materials ( a standard soil of known radioactivity, soil -6, Uranium ore sample,
RGU1 and a thorium ore sample RGTh1) were used and calibration done in the energy
range of 350 keV to 3000 keV. The following energy peaks were used:
214
Pb (1125 keV) and
214
214
Bi (609 keV),
Bi (1765 keV) which correspond to uranium activity;
228
Ac
30
(911.2 keV), 208Tl (583 keV) and 208Tl (2615 keV) which correspond to thorium activity;
and
40
K (1460 keV) which correspond to potassium activity. The peak positions were
used to deduce the energy-channel relationship.
The photon energy was represented as a function of channel number using a second order
polynomial of the form shown in Eq. 4.1 (Debertin and Helmer, 1988);
E  E0  B(channel .no.)  A(channel .no.) 2 ,
(4.1)
Where A, B and E0 are constants. The polynomial was generated by Least Square fit to
the calibration points using micro cal origin software. Figure 4.3 shows a graphical
representation of the calibration parameters. The fit parameters are tabulated in Table 4.1.
Table 4.1: The fit parameters of the polynomial used for calibration obtained by fitting a
second order polynomial
Fit parameter
Fitted Value
A
-77.8614
B
3.50
E0
2.3715E-4
31
Figure 4.3: Energy calibration of the NaI (Tl) detector used
Several spectra for all samples were recorded and stored. Figure 4.4 shows a sample
spectrum curve for construction sand sample collected from Site S9 from old gold mining
Tl -2615 keV
208
214
0.1
Bi -1765 keV
K -1460 keV
40
Bi- 609 keV
214
0.2
228
Intensity (c/s)
0.3
Ac -911 keV
zones of Kakamega County on the spectrometer.
0.0
500
1000
1500
2000
Energy (KeV)
Figure 4.4: A gamma ray spectrum of construction sand sample
2500
3000
32
4.3.2 Determination of Gamma Activities
In determination of the γ activities of the NORM in the samples, the focus was placed on
the identification of three regions of interest (ROI) in the spectrum, which were centered
on the three characteristic photo-peaks, at approximate 1460 keV (40K), 1765 keV (214Bi)
and 2615 keV (208Tl). These were used to evaluate activity levels of 40K, 226Ra and 232Th
series, respectively (Suresh et al, 2010).
The process was as follows:
i.
Every sample was counted for 30,000s on a calibrated NaI(Tl) spectrometer
and its spectrum recorded and stored in text files of a PC based MCA.
ii.
Average Background count was subtracted from the sample count to obtain
the net count. (Two background readings were taken at the end of two weeks
for 30,000s each).
iii.
The activity concentration of the sample was then calculated as explained in
section 4.4.
4.3.3 Detector counting efficiency
The performance of the detector was determined by relating the amount of radiation
emitted by the source to the amount of radiation measured by the detector (Mustapha,
1999). The relationship is as shown in Eq. 4.2.
𝜀𝑖 =
𝐼𝑠 −𝐼𝑏
𝜌𝑐 𝑚 𝑠
,
(4.2)
where, 𝜀𝑖 is the efficiency of the detector corresponding to the radionuclide of interest in
33
RGMIX-2., Is is the intensity of the radionuclide of interest in RGMIX-2., Ib is the
background intensity of the radionuclide of interest in distilled water, ρ is the photon
emission probability of the radionuclide of interest in RGMIX-2. and ms is the mass of
the sample RGMIX-2.
The gamma lines emission probabilities ρ of the IAEA reference material RGMIX-2
used in equation 4.2 were as follows: ρ=0.11 at 1460 keV, 0.161 at 1765keV and 0.36 at
2615 keV (IAEA, 1992). The calculated efficiencies corresponding to the three
radionuclides are given in the Table 4.2.
Table 4.2: Efficiencies of emission of K-40, Th-232and Ra-226 in NaI(Tl) spectrometry
Radionuclide Intensity of
radionuclide
of interest
in RGMIX2, Is (c/s)
K-40
U-238
Th-232
1.926
0.057
0.243
Background
Is-Ib
intensity of
(c/s)
radionuclide
of interest
in
water,
Ib(c/s)
1.066
0.860
0.018
0.039
0.115
0.128
Emission
probability,
(ρ)
Concentration Efficiency,
(Bq/kg)
(ε)
(10-3%)
0.110
0.161
0.360
5400
1260
1160
8
11
17
The measured efficiency values are in line with values obtained by other researchers
(Knoll, 2000). Thus the detection efficiency was good.
4.2.4 Detection limits of the analytical system
The detection limits of the detector were computed using the Eq. 4.3 (Mustapha, 1999);
34
LD 
 2.71
I 
 4.65 b 

ms i   T
T 
1
,
(4.3)
where, T is the counting time (30000s) of the detector. Other symbols are defined by
equation 4.2. The detection limits for 40K, 232Th and 226Ra were found to be 93.5 BqKg-1,
40.76 BqKg-1 and 33.86 BqKg-1 respectively. The detection limits are above the natural
background activity concentration levels.
4.3.5 Energy Resolution of the detector
The ability of the detector to distinguish two close lying photo peaks was determined by
Gaussian fitting of radioactive ceasium-137 photo peak as shown in figure 4.5. The peak
shape for the detector is usually a Gaussian distribution.
3
Measured spectrum
Gaussian fitting
Intensity (c/s)
2
1
0
550
600
650
700
750
800
Energy keV)
Figure 4.5: Gaussian fitting of ceasium-137 spectrum measured in this work
35
The Gaussian model equation applied during fitting is shown by Eq. 4.4
  2( x  x0 ) 
y  y0 
exp 

w2



w
2
A
2
(4.4)
where y0 is the base line offset, A is the area under curve, x0 is the centre of the peak and
w is the width of the curve at half height. The fit parameters used are given in table 4.3.
Table 4.3: The fit parameters for the Caesium- 137 photo-peak measured in this work
Parameter
Description
Fitted value
y0
Vertical shift of peak
0.03673±0.0042
xc
Centroid of peak
661.67±0.1069
W
Full width at half maximum
46.54±0.2454
A
Area of the peak
134.588±0.7482
The detector resolution was 7.03% obtained from equation 4.5;
R
FWHM
 100% ,
XC
(4.5)
where R is the resolution, FWHM is full width at a half maximum and Xc is the Caesium
centroid peak energy. Wang (2003) reports the best resolution achievable to be 7% for
the 662 keV gamma ray from Cs-137 for a 76mm×76mm NaI(Tl) detector which is in
good agreement with the resolution determined in this work.
36
4.3.6 Gamma ray spectral data analysis
The naturally occurring radionuclide
226
Ra,
232
Th and
40
K in the collected samples were
detected and quantified by the method of comparison given in section 4.4.
4.3.7 Analysis of Certified Reference Materials (IAEA-RGK-1, RGTh-1 and RGU-1)
For quality assurance in the measurement of radionuclide using NaI(Tl) detector,
dispersion (Ai)disp of measured activity values (Ai)m from the certified values (Ai)c was
calculated using Eq. 4.6 and recorded in table 4.4.
 Ai disp 
 Ai m   Ai c
 100%
 Ai c
(4.6)
Table 4.4: Dispersion of measured activities from certified activities for (RGK-1, RGTh1 and RGU-1)
RGU-1
RGTh-1
RGK-1
Measured value (Bq/kg)
5360
3379
12886
Certified value (Bq/kg)
4900
3280
13400
Dispersion (%)
9.39
3.02
-3.84
It was found out that the performance of the detector was good since the dispersion value
was within ± 10 % as recommended by IAEA, 1987.
4.4 Activity Concentrations
The specific activity for each detected radionuclide in the
232
Th and
226
Ra decay series
37
and 40K was determined using the Eq. 4.7.
As .M s AR .M R

,
Is
IR
(4.7)
where, AS is the activity of the radionuclide in the sample, MS, is the mass of the sample
to be analyzed, IS is the intensity of the radionuclide in the sample to be analyzed, AR is
the activity of the radionuclide in the reference sample, MR is the mass of the reference
sample, IR is the intensity of the radionuclide in the reference sample.
4.5 Radiological parameters
4.5.1 Gamma dose rate
The gamma dose rate (D) in the indoor air 1m above the ground was calculated using Eq.
4.8, (Faheem et al., 2008):
𝐷=
𝑥
𝐴𝑥 × 𝐶𝑥 ,
where Ax (Bqkg-1) is the mean activity of
(4.8)
226
Ra,
232
Th or
40
K and Cx (nGyh-1/Bqkg-1)
are the corresponding dose conversion coefficients which transform the specific activities
into absorbed dose. The conversion factors with respect to building sand used in this
study are 0.462, 0.604 and 0.0417 for 226Ra, 232Th and 40K respectively. These conversion
coefficients were determined by Monte Carlo simulation assuming a standard room
(4m×5m×2.8m) model (UNSCEAR 1993, 2000). In determination of the conversion
coefficient; it is assumed that all the decay products of
226
Ra and 232Th are in radioactive
38
equilibrium. The published permissible dose rate is 55 nGyh-1 (UNSCEAR, 1993).
4.5.2 The Annual Effective Dose Rate (AEDR)
In order to estimate the annual effective dose rate in air due to construction sand, the
conversion coefficient from absorbed dose in air to effective dose received by an adult
must be considered. This value is 0.7 SVGy-1 (UNSCEAR 1993, 2000) for environmental
exposure to gamma rays of moderate energy. For indoor measurements, the occupancy
factor of 0.8 is considered. Thus the annual effective dose rate equivalence in this work
was calculated using Eq. 4.9 below.
𝐴𝐸𝐷𝑅
𝑚𝑆𝑣
𝑦
= 𝐷(
𝑛𝐺𝑦
ℎ
ℎ
𝑆𝑣
) × 8760(𝑦 ) × 0.8 × 0.7(𝐺𝑦 ) × 10−6
(4.9)
The world average AEDE from outdoor or indoor terrestrial gamma ray radiation is 0.460
µSv/y.
4.5.3 Radium Equivalent Activity
Radium equivalent activity (Raeq) was used to assess hazards associated with construction
sand since it was found to contain
assuming that 370 Bq/kg of
226
226
Ra,
232
Th and
Ra, or 260 Bq/kg of
40
K in Bq/kg. It was determined by
232
Th or 4810 Bq/kg of
40
K produce
same gamma dose rate. The Radium equivalent activities, Raeq in Bq/kg in sand samples
were calculated using Eq. 4.10:
39
Raeq = AK × 0.0077 + ARa + (ATh × 1.43),
(4.10)
where 𝐴𝐾 , 𝐴𝑅𝑎 and 𝐴𝑇ℎ are activity concentration for 40K, 226Ra and 232Th respectively.
Maximal admissible Raeq is 370 Bq/kg to keep the external dose below 1.5 mSvy-1.
4.5.4 External hazard index (Hex)
To limit the radiation dose to permissible dose equivalent limit of 1 mSvy-1, the external
hazard index (Hex) was calculated using Eq. 4.11:
H ex 
ARa ATh
A

 K 1
370 259 4810
(4.11)
The Eq. 4.11 is obtained from the expression for radium equivalent activity through the
supposition that its maximum allowed value corresponds to the upper limit of radium
equivalent activity (370 BqKg-1) so that the external annual dose rate does not exceed 1.5
mGy (Tufail et al., 2007).
4.5.5 Gamma Index (Iγ)
Gamma index is a criterion for assessment of the radiological suitability of a building
material. It has been defined by European Commission (EC, 1999) as;
I 
ARa ATh
A

 K ,
300 200 3000
(4.12)
40
Values of index Iγ ≤2 corresponds to a dose rate criterion of 0.3 mSvy-1, whereas 2<Iγ≤6
corresponds to a dose rate criterion of 1 mSvy-1 (Anjos et al., 2005).
4.6 Modeling of radon diffusion fluxes in a room
4.6.1 Theory of modeling
Modeling is a method of describing and simplifying a process that one tries to understand
(Paul et al., 2008). The model proposed in this work is used to estimate and predict the
concentration of indoor radon emitted from the walls in dwellings constructed from sand.
This will assist in the formulation of effective control strategies to reduce emission of
indoor radon. This model assumes that;
i.
Radon is not released from materials inside the room,
ii.
radon is homogeneously mixed with room air,
iii.
and it does not react with any substance or disappear by any process other than
physical decay.
In this study, finite difference numerical methods are employed to solve equations that
govern the transport of radon in a room. Due to the complex nature of the model, a
computer code was developed to solve the equations using numerical methods.
Numerical methods yield approximate solution to the governing equation through
discretisation of space and time (Munene, 2007). Numerical models can relax the rigid
idealized conditions of analytic models; hence they are more realistic for simulating field
conditions.
In this model, radon concentration values are mapped on a fixed grid as will be described
latter in section 5.2. The finite difference numerical method is applied to calculate the
41
concentration variation over time and in space. The finite difference method is based on
the principle that any complex function [f(x)] can be approximated with a simple linear
function for a small increment of independent variable (x) which could be space or time.
There are three categories of finite difference numerical methods i.e. explicit, implicit
and Crank-Nicholson method. In this work explicit finite difference method was used
since it has the advantage of calculating the concentration at grid i at time t+∆t, using
only known concentration at time t. The numerical schemes for solving the transport
equation were to meet convergence conditions, correctly model the conservation,
dissipation and dispersion properties of the governing equations (Celia et al., 1990).
4.6.2 The governing equations
In this model the concentration of indoor radon, C at time t and space r = (x,y) in a room
is calculated by solving the transport expression given by Eq. 4.13. The equation
describes the change in radon concentration due to creation, decay, ventilation and
diffusion; i.e. it takes into account the formation of new radon atoms as well as removal
due to decay, ventilation and diffusion during the transport process. Radon diffusion
occurs when radon atoms migrate due to concentration gradients as is described by Fick‟s
law, which relates the concentration gradient to the flux.
C S
q
   Rn C  v (C  C0 ) 
t V
V
,
(4.13)
where C is the concentration of radon (Bqm-3), the first term on the right-hand side
42
represents the source, second represents the decay, third represents advection and the last
term represents diffusion.
There are two main processes that govern radon transport in living space of buildings i.e.
diffusion and advection. Advection is not considered in this study, its role depends on
pressure changes that tend to average out for a closed room (Speelman et al., 2009). Thus
the transport equation reduces to Eq. 4.14 shown below;
C S
q
   Rn C 
t V
V
,
(4.14)
The explicit finite difference method is used to solve Eq. 4.14. In difference form, the Eq.
4.14 is transformed to Eq. 4.15.
𝑆
𝐷
𝐶𝑗𝑛+1 = 𝐶𝑗𝑛 + 𝑉 ∆𝑡 − 𝜆𝑅𝑛 ∆𝑡𝐶𝑗𝑛 + 𝑉 ∆𝑡
𝐶𝑗𝑛+1 −2𝐶𝑗𝑛 +𝐶𝑗𝑛−1
(∆𝑥)2
,
(4.15)
where indexes j and n refer to the discrete position and times determined by step lengths
∆x and ∆t for the coordinates x and time t respectively. Using a small enough value of
∆t and ∆x, the truncation error can be reduced until the accuracy achieved is within the
error tolerance (Andersen, 1995). To compute the numerical solution of Eq. 4.15 a
computer code was developed in which all the parameters had to be transferred to the
code in a manner that it would recognize each and every part of the equations to be used
(Ambusso, 2007).
43
4.6.3 Program Structure
The computer program that simulates the radon transport in a room has the following
parts; the data that defines the physical properties of the room and the source, the
procedures or codes that process the data and the results that indicate the changes that
have taken place in the room. The main parts of the program are represented by the
schematic chart shown in figure 4.6.
Figure 4.6: Schematic chart showing the main parts of the program
44
4.7 Estimation of uncertainties
One of the main aim of this study is to determine the activity concentration of
232
Th (and their decay progeny) and
40
226
Ra,
K in building sand from old gold mining belt of
Kakamega County. The activity concentration are deduced indirectly by the comparison
method, as discussed in section 4.4. The
uncertainties of the parameters in the
determination of activity concentration by comparisson method can be statistical
(random) or systematical. The uncertainty, u, characterizes the range around the final
value x where the unknown true value is expected to lie, usually written as x ±u.
Identifying sources of uncerntaity in gamma ray spectrometry involving the sand samples
in this study is an essential step for determining high quality results. The sources of
uncertainty can be classified according to their origin as shown in figure 4.7. Some of the
uncertainties are quantifiable before the start of the measurements such as uncertainties
due to nuclear data or energy and efficiency calibrations. While others are quantified
directly from the measurements.
Sources of uncertainty
Sample
preparation
Energy and
efficiency
calibration
Measurement of
test samples
Nuclear
data
Figure 4.7: Possible uncertainties that could be considered in determination of activity
concentrations of 226Ra and 232Th (and their progeny) and 40K in sand samples
45
4.7.1 Uncertainty due to sample preparation
During sand preparation process, the sand samples were dried and sieved in order to
achieve uniform distribution of radionuclides and then stored in air/gas tight containers.
One source of uncertainty in such case is the mass of the sample. This was estimated
from the precision of weighing balance used (±0.01g).
4.7.2 Uncertainty due to Efficiency calibration
Efficiency calibration was aimed at deriving a relationship between absolute full energy
peak efficiency of gamma ray spectroscopy system and the energy (Huda Al- Sulaiti,
2011). The uncertainty associated with the number of counts in peaks; along with the
uncertainty in the nuclear data contribute to the combined uncertainty of the efficiency
calibration.
4.7.3 Uncertainty due to measurement of samples
The most important uncertainties in the final combined uncertainty are those originating
from measurements. These uncertainties may arise due; to differences in counting
geometries of the samples and standards, random coincides, decay time effects, dead time
effects and due to counting statistics.
In summary, the activity concentration distribution of
226
Ra, 232Th and 40K in the earth‟s
crust is variable and the same applies to the sand samples drawn in the study region. In
this study, γ-ray activities due to
226
Ra,
232
Th and
40
K were measured in building sand
samples. This involved crushing, drying and sealing of samples in marinnelli beakers.
The samples together with standard samples obtained from IAEA were stored for more
46
than four weeks to achieve secular equilibrium between
226
Ra and its short lived decay
products. The activity measurements were performed using PC based NaI(Tl) gamma ray
spectrometer. The detector was shielded to reduce the background. The combined
uncertainty of the activity concentrations was calculated by applying Gauss error
propagation law. The proposed model was meant to predict the transport and distribution
of indoor radon in living rooms in the study region. This was accomplished by solving
the transport equation using explicit finite difference numerical method.
47
CHAPTER FIVE
RESULTS AND DISCUSSION
5.1
Radioactivity concentration of building sand
The building sand used to construct houses/buildings in the study area was assumed to
come from various streams in the region. The two main sources of sand deposits along
the river banks are Rivers Yala and Isiukhu. The specific gamma ray activity
concentrations of radionuclide 40K,
226
Ra and
232
Th were calculated in Bq/kg by method
of comparison and recorded in Table 5.1. The minimum activities of 226Ra, 232Th and 40K
recorded were 36.79±5.89 Bq/kg, 51.12±2.56 Bq/kg and 322.38±16.12 Bq/kg and the
maximum values were 185.21±5.89 Bq/kg, 158.92±7.95 Bq/kg and 960.53±48.03 Bq/kg.
The average concentrations of
226
Ra,
232
Th and 40K in samples were 128.05±8.89 Bq/kg,
98.37±6.41 Bq/kg and 756.39±35.99 Bq/kg respectively. It is observed that the activity
concentrations are above the world‟s accepted average values of 33 Bq/kg for
226
Ra, 45
Bq/kg for 232Th and 420Bq/kg for 40K as reported in UNSCEAR (2000).
A summary of the activity concentration in sands from old gold mining zones of
Kakamega County compared with other parts of the world are presented in Table 5.2.
These high levels of natural radionuclide concentration in this region might have resulted
from artisanal gold mining. During gold mining concealed radioactive rich igneous rocks,
sand stones, monazites and quartzite are exposed to the agents of weathering and
dispersed in the region. Gold extraction processes might have enhanced the transport of
Uranium and thorium minerals as sediments in river beds. The continuous application of
phosphate fertilizers in the sugar cane, tea and maize plantations as TENORM has also
48
contributed to the high concentration levels in some parts of the old gold mining zones
(Sangura, 2012). The uncertainties in the specific activities of individual samples in Table
5.1 include uncertainties in gamma emission probability, detector efficiency, peak area
and sample weight (Malik et al., 2011).
Table 5.1: Mean Specific γ –ray activity of 226Ra, 232Th and 40K in the sand samples
(n=2)
SITE
LOCATION
LATITUDE
LONGITUDE
226
232
40
S1
Shikhombelo
0.24223
34.70618
121.02±6.05
97.27±4.86
879.86±43.99
S2
Mukhonje
0.25406
34.72791
185.21±9.26
80.48±4.02
960.53±48.03
S3
Shieywe
0.27461
34.77672
107.92±5.40
87.28±4.36
812.68±40.63
S4
Mwibatsilu
0.24204
34.65198
89.45±4.47
62.53±3.13
821.89±41.10
S5
Kakamega
0.25396
34.75005
74.05±3.70
89.92±4.50
753.77±37.69
S6
Ematsayi
0.27671
34.62762
150.45±7.52
51.12±2.56
815.86±40.79
S7
Esalasala
0.29726
34.67118
155.29±7.76
95.05±4.75
322.38±16.12
S8
Eshibakala
0.26686
34.63300
36.76±1.84
82.11±4.11
760.00±38.00
S9
Imbale
0.22936
34.64335
163.38±8.17
75.90±3.70
696.11±34.81
S10
Mukulusu
0.29210
34.82379
118.48±5.92
96.15±4.81
485.36±24.29
S11
Shirulu
0.17712
34.79537
177.17±8.86
92.12±4.61
618.78±30.94
S12
Litambiza
0.16035
34.74432
138.02±6.90
84.90±4.25
877.98±43.90
S13
Shikokho
0.16993
34.71121
183.87±9.91
91.32±4.57
854.26±42.71
S14
Mwitabakha
0.16528
34.72227
99.98±5.00
100.69±5.03
648.13±32.41
S15
Lwanungu
0.17364
34.78089
115.10±5.76
158.92±7.95
725.21±36.26
S16
Isulu
0.17091
34.69703
108.55±5.43
142.28±7.11
778.95±38.95
S17
Bushiangala
0.16877
34.67945
113.26±5.66
147.15±7.36
762.68±38.13
S18
Ikonjero
0.15966
34.64159
143.14±7.46
105.15±5.26
914.99±45.75
S19
Iguhu
0.16097
34.74722
151.80±7.68
128.76±6.44
881.32±44.07
Maximum
185.21±5.89
158.92±7.95
960.53±48.03
Minimum
36.79±2.03
51.12±2.56
322.38±16.12
Average
128.05±8.89
98.37±6.41
756.39±35.99
Ra (Bq/kg)
Th (Bq/kg)
K (Bq/kg)
49
Table 5.2: Average activity concentration of radionuclide in sand from old gold mining
zones of Kakamega County compared to other parts of the world
Country
226
Ra (Bqkg-1)
232
Th (Bqkg-1)
40
K (Bqkg-1)
References
Turkey
44
26
441
Cervic et al.,2009
Netherlands
8
11
200
Ackers et al.,1985
India
44
64
456
Kumar et al.,1999
China
23
36
891
Xinnwei and xiaolan, 2008
Zambia
24
26
714
Hayumbu et al.,1995
Kenya
11
5
802
Mustapha et al., 1999
Present study
128
98
756
Figure 5.1 shows the specific activities distribution of
226
Ra,
232
Th,
40
K and Raeq in all
the sampling sites in the study area. From figure 5.1, highest concentration values of
226
Ra,
232
Th and
40
K were reported from sites S13, S15 and S2 respectively. This is
attributed to presence of radioactive rich igneous bed rocks in the region. Gold mining, an
economic activity common in this region, has enhanced the breakdown and dispersal of
these rocks as sand sediments. The highest concentration value of
40
K recorded was at
site S2. This was attributed to continuous application of fertilizers rich in potassium in tea
plantations along the slopes of River Isiukhu.
50
Ra-226
Th-232
K-40
Ra(eq)
Activity Concentration (Bq/kg)
1000
800
756.39
600
400
321.67
200
128.05
98.37
0
S2
S4
S6
S8
S10 S12 S14 S16 S18
Sampling Sites
Figure 5.1: Activity concentration and radium equivalent activity distribution in all the
sampling sites
5.1.1 Exposure due to gamma radiation
The distribution of 226Ra, 232Th and 40K is not uniform in the sand samples, thus Radium
equivalent activity (Raeq) was introduced, which represents weighted sum of specific
activities of
226
Ra,
232
Th and
40
K. Exposure due to gamma radiation in terms of Radium
equivalent activity originating from building sand in the study region was calculated and
51
the results obtained are shown in Table 5.3. Based on finding in table 5.3, the Radium
equivalent activity in the studied samples ranged from 121.43 Bq/kg at sampling site S5
(Kakamega) to 397.62 Bq/kg at sampling site S19 (Iguhu) with a mean value of
321.67±12.4 Bq/kg. The indoor dose rates ranged from 99.6 nGyh-1 to 186.84 nGh-1 with
a mean value of 151.76±5.65 nGh-1. The calculated values for annual effective dose in
the present study ranged from 0.488 mSvy-1 to 0.916 mSvy-1. The mean value was found
to be 0.744±0.02mSvy-1. For comparison purposes, data published by other researchers
for some regions is given in table 5.4. From table 5.3, the average radium equivalent
activity obtained is lower than the recommended limit of 370 Bqkg-1 although this value
is higher than the values reported in other regions.
Table 5.3: Radium equivalent activity, external hazard index, dose rate and annual
effective dose for sand samples in this work
Site no.
Raeq(Bqkg-1)
Dose Rate (nGyh-1)
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
S17
S18
S19
321.71
367.53
289.62
236.40
121.43
280.66
313.78
207.37
320.64
289.94
352.21
320.88
374.25
289.33
393.12
366.53
377.07
357.55
397.62
Maximum
Minimum
Mean
397.62
121.43
321.67±12.4
152.95
175.47
137.88
114.31
119.95
135.13
144.31
99.60
151.58
134.73
162.86
153.00
177.20
135.75
182.20
171.03
175.57
169.51
186.83
Annual Effective
Dose (mSvy-1)
0.75
0.86
0.68
0.56
0.74
0.66
0.71
0.49
0.74
0.66
0.81
0.75
0.86
0.67
0.89
0.83
0.86
0.83
0.92
External
Hazard index
0.88
1.01
0.79
0.65
0.70
0.77
0.85
0.57
0.87
0.79
0.96
0.88
1.02
0.79
1.07
1.00
1.03
0.98
1.09
186.84
99.6
151.76±5.65
0.92
0.48
0.74±0.02
1.09
0.57
0.88±0.03
52
Table 5.4: Comparison between the radium equivalent activities, indoor gamma dose
rates and annual effective dose in the present study and those reported in other countries
Country
Turkey
Radium Equivalent activities
Dose in air
Annual effective Dose
(Raeq) Bq/kg
(nGyh-1)
(mSvy-1)
112
104
0.51
(Cervic et al. ,2009)
Northern Pakistan
143.8
0.20
(Malik et al., 2011)
-------
Kenya
66
0.24
152
0.74
(Mustapha et al., 1997)
------
This study
321.7
5.1.2 External hazard index (Hex)
The calculated values of external hazard index (Hex) for the sand samples in this study
ranged from 0.57 to 1.09 with a mean value of 0.883±0.03 as shown in table 5.5. This
average value is lower than unity; therefore, according to European Commission on
Radiation Protection report (1999), sand from old gold mining zones in Kakamega
County is safe and can be used as construction material without posing any significant
radiological threat to the general public.
5.1.3 Gamma Index (Iγ)
From the indices calculated, it was found that none of the sand from the study region
posed significant exposure hazard as shown in table 5.5. The gamma index was estimated
using Eq. 4.12. The distribution of values of the gamma index for mineral sand analyzed
53
in this work is presented in table 5.5. The scatter plot of external hazard index and
gamma index as shown in figure 5.2 indicates that the sand from site S8 have the least
risk of the exposure hazard while sand from site S19 has the highest. The entire values of
indexes Iγ are < 2.0. Therefore, the annual effective dose delivered by the building made
of such sand is smaller than the annual effective dose constraint of 0.3 mSv, hence the
sand can be exempted from all restrictions concerning radioactivity (Tufail et al., 2007).
Table 5.5: The hazard indices of the sand samples collected from old gold mining zones
of Kakamega
Sampling sites
S1
S2
S3
S4
S5
S6
S7
S8
S9
S10
S11
S12
S13
S14
S15
S16
S17
S18
S19
Maximum
Minimum
Mean
Raeq (Bq/kg)
321.71
367.53
289.62
236.40
121.43
280.66
313.78
207.38
320.65
289.95
352.22
320.89
374.26
289.34
393.12
366.54
377.07
357.55
397.62
397.62
207.38
321.67±12.4
Hazard indices
External hazard
(Hex)
0.88560
1.01099
0.79762
0.65406
0.70371
0.77361
0.85371
0.57438
0.87934
0.79236
0.96316
0.88336
1.02713
0.79373
1.07544
1.00467
1.03282
0.98308
1.09064
1.0906
0.5744
0.883±0.03
Gamma index (Iγ)
1.183
1.340
1.067
0.885
0.948
1.029
1.100
0.786
1.156
1.037
1.257
1.177
1.354
1.053
1.420
1.333
1.368
1.308
1.444
1.44
0.79
1.17±0.19
54
external hazard index
Gamma index
1.6
1.5
1.4
Hazard indices
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0
2
4
6
8
10
12
14
16
18
20
Sampling sites
Figure 5.2: A scatter plot of the external hazard indexes and gamma hazard indexes for different
sampling sites in this study
5.1.4 Statistical analysis of 226Ra, 232Th and 40K in this study
The activity concentrations of
226
Ra,
232
Th and
40
K in this study were compared using
Statistical Product and Service Solution (SPSS) computer software (version 11.5) for the
determination of ordinary statistics. The computed statistics are shown in table 5.6. From
the table, the positive value of the skewness coefficient for
232
Th indicates that its
distribution is asymmetric with right tail longer than the left tail. However, the low
kurtosis coefficient for
226
Ra suggests that the distribution is close to normal. According
to Taylor (1990), the distribution of 226Ra, 232Th and 40K is within the normal distribution
limits as shown in table 5.7.
55
Table 5.6: Statistical summary of radionuclide in this work
226
232
Ra
40
Th
K
Mean conc. (Bqkg-1)
128.05
98.37
756.35
Standard deviation
38.74
27.92
154.68
Skewness coefficient
-0.478
0.778
-1.443
Kurtosis coefficient
0.220
0.356
0.469
Table 5.7: Limits for kurtosis for normal distribution (Taylor, 1990)
Size of the sample
5%
1%
5
-1.058-1.058
-1.342-1.342
10
-0.950-0.950
-1.397-1.397
15
-0.862-0.862
-1.275-1.275
20
-0.777-0.777
-1.152-1.152
25
-0.771-0.771
-1.061-1.061
30
-0.661-0.661
-0.982-0.982
35
-0.621-0.621
-0.921-0.921
40
-0.587-0.587
-0.869-0.869
45
-0.558-0.558
-0.825-0.825
50
-0.533-0.533
-0.787-0.787
100
-0.389-0.389
-0.567-0.567
200
-0.280-0.280
-0.403-0.403
1000
-0.127-0.127
-0.180-0.180
5000
-0.057-0.057
-0.081-0.081
56
Table 5.8: Limits of skewness factor for normal distribution (Taylor, 1990)
Size of sample
5%
1%
200
-0.49-0.57
-0.63-0.98
400
-0.36-0.41
-0.48-0.67
600
-0.30-0.34
-0.40-0.54
800
-0.26-0.29
-0.35-0.46
1000
-0.24-0.26
-0.32-0.41
5.2 Indoor radon Model Results
The model room was divided into discrete blocks of equal dimensions during the
gridding process as shown in figure 5.3. The blocks dimensions can be varied. The
program then distributes the radon emitted from a source within a room to all the blocks
depending on prevailing conditions. Before radon was exhaled, the concentration in all
the blocks including the source equal to zero. However, within the first 150 hours the
concentration in the room rose to 9 Bq/m3. As the time increased more radon was exhaled
into neighboring blocks as shown by the different build up curves for exhaling source
block (Fig. 4). From the curves, the radon atoms exhaled from the walls (sources) in a
model room increases exponentially until radioactive secular equilibrium is reached.
57
49
50
51
52
53
54
55
42
43
44
45
46
47
48
35
36
37
38
39
40
41
28
29
30
31
32
33
34
21
22
23
24
25
26
27
14
15
16
17
18
19
20
7
8
9
10
11
12
13
0
1
2
3
4
5
6
Figure 5.3: Two dimensional gridding of the model room
The exhalation rate E0 from the source is described by Eq. 5.1:
E0 
C  V
,
S (1  e t )
(5.1)
where C is net concentration (Bq/m3), λ is decay constant (h-1), V is effective air volume
(m3) and S is source surface area (m2).
58
14
12
Leakage
Activity
10
Curve 3
Curve 2
Curve 1
Leakage and backdiffusion
8
6
4
2
0
0
2000
4000
6000
8000
10000
Growth Time
Figure 5.4: Different build up curves for the exhaling source block
The above equation is valid if there is no leakage of radon into or out of the walls, and if
there is no back diffusion effect. If there is leakage and back diffusion, the decay constant
is modified by replacing it with an effective decay constant (λeff). The resulting effective
decay constant is described by Eq. 5.2.
λeff =λ+λa+λb,
(5.2)
where λa and λb are leakage and back diffusion time decay constants.
Thus if the exhalation is depressed due to back diffusion and/or leakage, the equilibrium
value will be lower than the maximum expected as depicted by curve 1 and curve 2 of
figure 5.4.
59
Figure 5.5 show radon concentration profiles in the blocks assuming that the radon atoms
diffused into the room without undergoing radioactive decay. From the profiles, blocks
that are adjacent to the source (any block on the periphery, for instance block 55) receive
radon atoms radially and symmetrically by diffusion; hence have high peak concentration
in the build up phase.
0.05
0.045
0.04
Radon COnc, (kBq/m3)
0.035
0.03
NDBlnum10
0.025
NDBlnum24
0.02
NDBlnum38
0.015
NDBlnum44
0.01
0.005
0
-0.005
0
1000
2000
3000
4000
5000
6000
Time (minutes)
Figure 5.5: Radon concentration profiles in the blocks (diffusion only)
From figure 5.5, during the build up phase, blocks that are further away from the source
have a lower peak radon concentration than those that are adjacent. This process is
similar to a chemical diffusion; radon atoms migrate from the source due to concentration
60
gradient without loss until the room achieves uniform concentration (36 Bq/m3). The
peak concentration in the blocks widens and flattens as the blocks distance increases
further from the source. This is attributed to increase in mixing of radon atoms with air
molecules as the distance and time increases which results in dilution of radon „puff‟ as it
moves away from the source. The sharpness and the value of the peaks decrease further
away from the source block because the front blocks are receiving the radon atoms from
most of the blocks behind them. The peaks in the profiles results from blocks receiving
more radon atoms than they are losing but this changes after sometime when they lose
more radon than they receive.
After build up phase, the radon concentration in the blocks diminishes slowly with time
and in all profiles the concentration converges at same equilibrium concentration
(36Bq/m3) at late time. This shows that with time the concentration becomes uniform
throughout the room. This confirms that diffusion process dominates. Similar
observations are noted when radon gas from the source decay as it is transported in the
room space except the equilibrium concentration in the room is greatly reduced
(5.46Bq/m3) and the sharpness of the peaks in the profiles is increased. This is because
decay involves loss of radon atoms. Thus, the rate at which the blocks loose radon atoms
is higher than in the previous case. In this case, the radon concentration within a block
starts from zero to a maximum value and then reduces to equilibrium concentration at late
times. Figures 5.6 and 5.7 illustrate these features in the concentration profiles.
61
0.04
0.035
Radon COnc, (kBq/m3)
0.03
0.025
Blnum10
0.02
Blnum24
0.015
Blnum38
0.01
Blnum44
0.005
0
-0.005
0
1000
2000
3000
4000
5000
6000
Time (minutes)
Figure 5.6: Radon concentration profiles in the blocks (diffusion with decay)
0.05
0.045
Radon COnc, (kBq/m3)
0.04
0.035
Blnum10
0.03
Blnum24
Blnum38
0.025
Blnum44
0.02
NDBlnum10
0.015
NDBlnum24
0.01
NDBlnum38
0.005
NDBlnum44
0
-0.005 0
1000
2000
3000
4000
5000
6000
Time (minutes)
Figure 5.7: A comparison of concentration profiles in blocks where radon diffuses with
and without decay
62
5.3 Model validation
For the purpose of validating the model, the indoor radon concentrations measured at
some selected classrooms (monitoring stations) were used for comparison with the model
data. The field data measurements for indoor radon were carried out using activated
charcoal canisters, US Environmental Protection Agency (EPA) type. Measurements
were taken for a period of 2-5 days in a week. After the exposure, the cans were sealed
and reweighed. The gamma rays emitted by 214Pb (295 and 352 keV) and 214Bi (609 keV)
following the attainment of secular equilibrium between radon and its short lived decay
products were counted on a 76mmx76mm NaI(Tl) detector. Figure 5.8 shows a
comparison of the measured and modeled radon concentration in this work.
In general the model underestimated all the concentrations compared to measured values
when using charcoal canister (EPA). This can be attributed to a number of factors. The
most significant factor was that the model did not include other sources of radon such as
radon entry from the soil and the flooring material. These local sources contribute a
significant portion of radon in the indoor atmosphere. Despite the disparity between the
measured and modeled values, the model reproduced the general trends associated with
diffused radon fluxes as illustrated by figure 5.9. Therefore, the proposed model can
serve as a tool for predicting indoor radon concentration in projects that require the
assessment of impact of radiological pollution.
63
45
Radon conc. [Bq/m3]
40
35
30
25
20
modeled
15
measured
10
5
0
1
2
3
monitoring stations
Figure 5.8: A comparison of measured and modeled radon concentration
Figure 5.9: Radon growth curve obtained by fitting measured radon concentration for
monitoring station 1.
64
In summary, the suitability of a material to be used for building purposes is evaluated
basing on the radium equivalent activity and hazard indices. In this study, the average
value of radium equivalent activity in the sand samples is less than the limited value of
370 BqKg-1. The external hazard indices determined in this work are less than unity.
Therefore, it can be concluded that building sand sampled do not pose a major source of
radiation hazard. A predictive model has been developed for estimation of indoor radon
diffusion fluxes in living rooms in the study region. The modeled radon concentrations
are in good agreement with the measured values using activated charcoal canisters.
65
CHAPTER SIX
CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusions
Activity levels of natural radionuclide of uranium, thorium and potassium in
construction sand sampled from old gold mining zones of Kakamega County, a suspected
High Background Radiation Area (HBRA), was measured using NaI (Tl) gamma ray
spectrometry. The radiological effects on humans due the natural radiations from sand
were also estimated by use of radiological parameters. The measured mean activity
concentration levels of
226
Ra,
232
Th and
40
K was found to be 128.05±8.89 Bqkg-1,
98.37±6.41 Bqkg-1 and 756.39±35.99 Bqkg-1 respectively. These levels were found to be
higher than worldwide accepted average values of 33, 45 and 420 Bqkg-1 for 226Ra, 232Th
and 40K respectively. The activity levels in NORM in this region are high due to artisanal
gold mining. The mining activities have been found to influence the activity
concentration of radionuclide in sand due to the introduction and interaction of rocks
from different profiles to the earth surface.
The calculated hazard indices: radium equivalent activity and external hazard was found
to range from (207.38 to 397.62) Bqkg-1 and 0.57-1.09 respectively. This indicates that
construction sand from old gold mining zone are fit to be used as building material and so
do not pose any risk to the inhabitants in terms of the acceptable limits. The indoor
absorbed dose rate ranged from (99.6- 186.84) nGyh-1 which is above the world average
of 60 nGyh-1 (UNSCEAR, 2008). The effective dose rate for the indoor radiation ranged
from (0.48-0.92) mSvy-1. These values are above the world average 0.07 mSvy-1,
66
however all the indoor dose rates are below the accepted limit of 1 mSvy-1.
A deterministic model was developed using the mass conservation law, taking into
account diffusion, sources and sinks (decay) of radon atoms in indoor air. Differential
equations that govern the transport of radon were set up; discretized and solved
numerically using developed computer codes. Experimental data for indoor radon
concentration measurement using passive detectors was obtained and compared with
simulated results. The simulations show that with some modifications, the model can be
used by policy makers to pass legislations on the quality of indoor air in terms of radon
concentration.
6.2 Recommendations
Other than building sand, there are several natural and artificial building materials that
may contribute to radiation exposure. These include bricks, cement, clay paints, ballast
and stones. Thus it is essential to assess the contribution of each of these building
materials to external and internal dose rate to minimize the risk of exposure to high doses
to the occupants in the dwellings. To avoid risks of prolonged exposure to indoor radon
in this region, people are advised to ventilate their houses properly, not to build
residential houses on mining tailings, and seal the walls and floors well to prevent radon
entry into the living room from soil, building materials and to spend little time indoors as
compared to outdoors.
67
An epidemiological study on effects of radiation on the artisanal gold miners is also
recommended. This will help to ascertain the percentage of miners who are likely to
suffer from cancer related diseases. The transport equation with advection term should be
solved implicitly and in three dimensions to eliminate the instability problem during the
simulations.
68
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74
APPENDICES
APPENDIX I
Comparison of International Radon Action Levels (European Commission, 1998)
International Radon Action Levels
Existing Dwellings (Bq/m3) New Buildings (Bq/m3)
EU
400
200
ICRP
200-600
WHO
800
200
Canada
800
800
Finland
400
200
Czech Republic
400
200
Germany
250
250
Ireland
200
200
Norway
400
200
Sweden
400
200
SpainSwitzerland 400
185
United Kingdom
1000
400
200
200
1
APPENDIX II
222
Rn Decay series (Dumont et al., 1988)
Decay by product
Half-life
222
Alpha particle
3.82 days
218
Alpha particle
3.05 minutes
214
Beta particle and gamma radiation
26.8 minutes
214
Beta particle and gamma radiation
19.7 minutes
214
Alpha particle
0.000003 minutes
Rn
Po
Pb
Bi
Po
1