I have a result, and I have to write a report.
Can you do a report for me please?
I almost write the result and I copy paste the introduction and method from multi article you
need just to make paraphrase and you need to write the rest.
I put the result in excel and method and introduction you need to paraphrase and complete
the rest.
Please make sure the report be perfect and I wrote some result but I not sure about it and
also you should complete the rest by follow the criteria. (please check Experiment2.docx)
I have change some of my result in the table1 (therefore I attached NewDataForTable1experiment2.docx).
It’s same except some number in table 1 I am not sure about my result not just in the table
all the result, so could u please check it and if wrong do the right.
I attached reference 1, but I can’t attach reference 2 as its very big file , but I can tell the
name and author here , it’s a book “radiation physics for medical physicists” by Ervin B.
Podgorsak , 3rd edition
Abstract
Introduction
1. Background
Gamma rays can penetrate through material much further than alpha or beta particles, due to
the high energy it carries and its lack of electric charge. Though this is the case, gamma
photons can get attenuated in matter, and they do so in one of three possible processes:
1) Photoelectric effect: Gamma photons can interact with electrons initially bound to an atom
to eject an electron from the atom. This effect can only take place if the gamma’s energy is
greater than the binding potential of the electron. All of the gamma’s energy is transferred
to this electron (hence, called a photoelectron); the kinetic energy of the ejected
photoelectron is the difference of energies of the incident gamma and the bound electron
potential.
2) Compton effect: Gamma photons can collide with the free electrons in a material and
scatter, imparting some of its energy to the electron. The result is a deflected photon of
longer wavelength (ie. less energetic) and an electron with additional kinetic energy due to
the collision with the photon. The energies imparted to an electron are related to the
photon’s angle of incidence, and can be calculated using the Compton Scattering formula.
3) Pair Production: Gamma photons, when in the vicinity of the Coulomb field of an atomic
nucleus, can materialize into an electron-positron pair. This phenomenon can only occur if
the energy of the gamma photon is at least twice the electron rest mass energy (1.022
MeV). On average, the kinetic energies of the electron and positron are (each) half the
excess energy of the incident gamma photon.
The attenuation coefficient of any element is a summation of the attenuation-contributions of
each of these processes; hence, the larger the coefficient, the more probability of attenuating
the gamma radiation. The relationship between attenuation and probability of penetration
without interaction is expressed via the Beer-Lambert law:
𝐼(𝑥) = 𝐼0 𝑒 −𝜇𝑥
Where
-
I is the intensity of radiation (number of counts detected at a particular thickness x within an attenuator
within a fixed time period – all count values in this experiment are values per 30 seconds)
I0is the initial intensity in the absence of any attenuating material
μ is the linear attenuation coefficient of the attenuator in question
2. Objective: (make a paraphrasing in three sentences)
1. To measure the attenuation coefficient for water and lead for 137Cs gamma radiation.
2. To use the experimentally determined attenuation coefficient for lead to estimate the
thickness of a given lead plate
3. To illustrate the difference between narrow beam and broad beam attenuation of gamma
Radiation.
Methods and Materials(Make a paraphrasing at same arrangement)
The experiment consists of two parts which are attenuation by lead, 0.662 MeV gamma-rays from 137Cs(narrow
beam and broad beam) and attenuation by water, 0.662 MeV gamma-rays from 137Cs. Every step the background
was measured, and it was usually the first step without Cs-137 source. Then, it will be recorded for three times
and obtain the average which will be subtracted from each value of the sample. Using a set-up in which the
radioactive source 137Cs was placed vertically above a NaI detector, interspaced by a few centimetres in
which we were able to insert samples of attenuators, we were able to investigate gamma attenuation. As the
detector is adjusted, counting time is 30 seconds for each sample. By recording the amount of gamma
radiation that penetrated the lead and water that were positioned between the source and detector for
varying thicknesses, we were able to determine the mass attenuation coefficients for lead.
Part 1:attenuation by lead, 0.662 MeV gamma-rays from 137Cs
A. Narrow beam geometry
The count rate was recorded for a variety of thicknesses of lead absorber with collimator.
B.Board beam geometry
Use an unshielded detector, which allowed for the detected gamma radiation to originate from a much
larger beam, and a range of large surface-area lead absorbers may be
rested on the plastic stand between source and detector. Any suitable 137Cs source may be
used.
Part 2: attenuation by water, 0.662 MeV gamma-rays from 137Cs
The same process was then repeated using any convenient 137Cs source and without any collimation. The
lead plate was replaced with a container of water, and thickness of water (0-16 cm) under narrow beam
conditions. The height of the water in the container was varied (in the same manner that the thickness of
lead plates was varied), and the amount of gamma radiation that was displayed by the detector was recorded
– providing us with the data that we required to determine the count-rate build-up factor.
Results
1. Narrow Beam Geometry:
5
4.5
Ln%( Transmitted Intensity)
4
3.5
3
2.5
2
y = -0.0986x + 4.6229
1.5
1
0.5
0
0
5
10
15
20
25
30
35
Thickness of Lead (g/cm^2)
Figure 1: The intensity γ-ray decreases as thickness in lead sheet increases (narrow beam geometry)
2. Broad Beam Geometry:
5
4.5
Ln%( Transmitted Intensity)
4
3.5
3
2.5
y = -0.0965x + 4.6224
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
16
18
20
Thickness of Lead (g/cm^2
Figure 2: The intensity γ-ray decreases as thickness in lead sheet increases (broad beam geometry)
3. Attenuation by Water:
5
4.5
Ln%( Transmitted Intensity)
4
3.5
3
2.5
y = -0.0745x + 4.6077
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
16
18
Thickness of Water (cm)
Figure 3: Predicted transmitted intensity for varying thicknesses of water under narrow beam conditions
using .662 MeV of Cs-137
4. Narrow and broad beam geometriesfor any two thicknesses of lead:
The comparison the transmitted intensity for the narrow and broad beams geometries (make a graph and
discuss the result
The build-up factor can be calculated by choosing two different thicknesses such as ? g/cm2 and ? g/cm2.
5. Plot the results on the same graph as for the expected narrow beam
geometry, after again having expressed the count rates at various depths as
a percentage of the "zero depth" count rate. Determine the count-rate
build-up factor B for two different depths of water.
To calculate the linear attenuation coefficient
Narrow Beam
𝜇𝐿 = 𝜇𝑚 ∗ ρ = 0.0986 ∗ 11.36 = 1.12 𝑐𝑚−1
Broad Beam
𝜇𝐿 = 𝜇𝑚 ∗ ρ = 0.0965 ∗ 11.36 = 1.09 𝑐𝑚−1
To calculate HVT and TVT
HVL and TVT for narrow beam
𝐻𝑉𝑇 =
𝑇𝑉𝑇 =
2.303
2.303
=
= 2.05 𝑐𝑚
𝜇𝑙
1.12
0.693
0.693
=
= 0.618 𝑐𝑚
𝜇𝑙
1.12
HVL and TVT for Water
𝐻𝑉𝑇 =
𝑇𝑉𝑇 =
0.693
0.693
=
= 9.3 𝑐𝑚
𝜇𝑙
0.0745
2.303
2.303
=
= 30.91𝑐𝑚
𝜇𝑙
0.0745
THEORETICAL
OBSERVED
THEORETICAL
OBSERVED
μl(cm-1)
μm(cm2/g)
μl(cm-1)
μm(cm2/g)
TVT(cm)
HVT(cm)
TVT(cm)
HVT(cm)
LEADNARROW
1.4
0.124
1.12±0.2
0.0986±0.204
7.74
0.495
2.05±0.2
0.618±0.49
WATER
0.0895
0.0895
0.0745±0.167
0.0745±0.167
25.73
1.645
30.91±0.201
9.3±0.2
Table 1: The result of theoretical and experimental linear attenuation coefficients, mass attenuation
coefficients, half-value thicknesses (HVT), and tenth-value thicknesses (TVT) for lead and water with error.
Material
Thickness
Lead
Water
Narrow
Broad
6.55g/cm2
8.2g/cm2
6 cm
10 cm
Build-up factor
Table 2: Count-rate build-up factor B values for lead and water for their respective thicknesses
Discussion and Conclusion
The purpose of this experiment was to find out the
References
Is attachement
Abstract
Introduction
1. Background
Gamma rays can penetrate through material much further than alpha or beta particles, due to
the high energy it carries and its lack of electric charge. Though this is the case, gamma
photons can get attenuated in matter, and they do so in one of three possible processes:
1) Photoelectric effect: Gamma photons can interact with electrons initially bound to an atom
to eject an electron from the atom. This effect can only take place if the gamma’s energy is
greater than the binding potential of the electron. All of the gamma’s energy is transferred
to this electron (hence, called a photoelectron); the kinetic energy of the ejected
photoelectron is the difference of energies of the incident gamma and the bound electron
potential.
2) Compton effect: Gamma photons can collide with the free electrons in a material and
scatter, imparting some of its energy to the electron. The result is a deflected photon of
longer wavelength (ie. less energetic) and an electron with additional kinetic energy due to
the collision with the photon. The energies imparted to an electron are related to the
photon’s angle of incidence, and can be calculated using the Compton Scattering formula.
3) Pair Production: Gamma photons, when in the vicinity of the Coulomb field of an atomic
nucleus, can materialize into an electron-positron pair. This phenomenon can only occur if
the energy of the gamma photon is at least twice the electron rest mass energy (1.022
MeV). On average, the kinetic energies of the electron and positron are (each) half the
excess energy of the incident gamma photon.
The attenuation coefficient of any element is a summation of the attenuation-contributions of
each of these processes; hence, the larger the coefficient, the more probability of attenuating
the gamma radiation. The relationship between attenuation and probability of penetration
without interaction is expressed via the Beer-Lambert law:
𝐼(𝑥) = 𝐼0 𝑒 −𝜇𝑥
Where
-
I is the intensity of radiation (number of counts detected at a particular thickness x within an attenuator
within a fixed time period – all count values in this experiment are values per 30 seconds)
I0is the initial intensity in the absence of any attenuating material
μ is the linear attenuation coefficient of the attenuator in question
2. Objective: (make a paraphrasing in three sentences)
1. To measure the attenuation coefficient for water and lead for 137Cs gamma radiation.
2. To use the experimentally determined attenuation coefficient for lead to estimate the
thickness of a given lead plate
3. To illustrate the difference between narrow beam and broad beam attenuation of gamma
Radiation.
Methods and Materials(Make a paraphrasing at same arrangement)
The experiment consists of two parts which are attenuation by lead, 0.662 MeV gamma-rays from 137Cs(narrow
beam and broad beam) and attenuation by water, 0.662 MeV gamma-rays from 137Cs. Every step the background
was measured, and it was usually the first step without Cs-137 source. Then, it will be recorded for three times
and obtain the average which will be subtracted from each value of the sample. Using a set-up in which the
radioactive source 137Cs was placed vertically above a NaI detector, interspaced by a few centimetres in
which we were able to insert samples of attenuators, we were able to investigate gamma attenuation. As the
detector is adjusted, counting time is 30 seconds for each sample. By recording the amount of gamma
radiation that penetrated the lead and water that were positioned between the source and detector for
varying thicknesses, we were able to determine the mass attenuation coefficients for lead.
Part 1:attenuation by lead, 0.662 MeV gamma-rays from 137Cs
A. Narrow beam geometry
The count rate was recorded for a variety of thicknesses of lead absorber with collimator.
B.Board beam geometry
Use an unshielded detector, which allowed for the detected gamma radiation to originate from a much
larger beam, and a range of large surface-area lead absorbers may be
rested on the plastic stand between source and detector. Any suitable 137Cs source may be
used.
Part 2: attenuation by water, 0.662 MeV gamma-rays from 137Cs
The same process was then repeated using any convenient 137Cs source and without any collimation. The
lead plate was replaced with a container of water, and thickness of water (0-16 cm) under narrow beam
conditions. The height of the water in the container was varied (in the same manner that the thickness of
lead plates was varied), and the amount of gamma radiation that was displayed by the detector was recorded
– providing us with the data that we required to determine the count-rate build-up factor.
Results
1. Narrow Beam Geometry:
5
4.5
Ln%( Transmitted Intensity)
4
3.5
3
2.5
2
y = -0.0986x + 4.6229
1.5
1
0.5
0
0
5
10
15
20
25
30
35
Thickness of Lead (g/cm^2)
Figure 1: The intensity γ-ray decreases as thickness in lead sheet increases (narrow beam geometry)
2. Broad Beam Geometry:
5
4.5
Ln%( Transmitted Intensity)
4
3.5
3
2.5
y = -0.0965x + 4.6224
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
16
18
20
Thickness of Lead (g/cm^2
Figure 2: The intensity γ-ray decreases as thickness in lead sheet increases (broad beam geometry)
3. Attenuation by Water:
5
4.5
Ln%( Transmitted Intensity)
4
3.5
3
2.5
y = -0.0745x + 4.6077
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
16
18
Thickness of Water (cm)
Figure 3: Predicted transmitted intensity for varying thicknesses of water under narrow beam conditions
using .662 MeV of Cs-137
4. Narrow and broad beam geometriesfor any two thicknesses of lead:
The comparison the transmitted intensity for the narrow and broad beams geometries (make a graph and
discuss the result
The build-up factor can be calculated by choosing two different thicknesses such as ? g/cm2 and ? g/cm2.
5. Plot the results on the same graph as for the expected narrow beam
geometry, after again having expressed the count rates at various depths as
a percentage of the "zero depth" count rate. Determine the count-rate
build-up factor B for two different depths of water.
6. Using the lead plate of unknown thickness as the ‘only’ absorber measure
the count rate and hence determine its thickness
The unknown thickness which you can selected one of the ones I measured to be the unknown from narrow
beam in excel and put chart and use the number of counts to estimate the thickness.
To calculate the linear attenuation coefficient
Narrow Beam
𝜇𝐿 = 𝜇𝑚 ∗ ρ = 0.0986 ∗ 11.36 = 1.12 𝑐𝑚−1
Broad Beam
𝜇𝐿 = 𝜇𝑚 ∗ ρ = 0.0965 ∗ 11.36 = 1.09 𝑐𝑚−1
To calculate HVT and TVT
HVL and TVT for narrow beam
𝐻𝑉𝑇 =
𝑇𝑉𝑇 =
2.303
2.303
=
= 2.05 𝑐𝑚
𝜇𝑙
1.12
0.693
0.693
=
= 0.618 𝑐𝑚
𝜇𝑙
1.12
HVL and TVT for Water
𝐻𝑉𝑇 =
𝑇𝑉𝑇 =
0.693
0.693
=
= 9.3 𝑐𝑚
𝜇𝑙
0.0745
2.303
2.303
=
= 30.91𝑐𝑚
𝜇𝑙
0.0745
THEORETICAL
OBSERVED
THEORETICAL
OBSERVED
μl(cm-1)
μm(cm2/g)
μl(cm-1)
μm(cm2/g)
TVT(cm)
HVT(cm)
TVT(cm)
HVT(cm)
LEADNARROW
1.27
0.124
1.12±0.118
0.0986±0.204
1.81
0.545
2.05±0.132
0.618±0.86
WATER
0.0895
0.0895
0.0745±0.167
0.0745±0.167
25.73
1.645
30.91±0.201
9.3±0.2
Table 1: The result of theoretical and experimental linear attenuation coefficients, mass attenuation
coefficients, half-value thicknesses (HVT), and tenth-value thicknesses (TVT) for lead and water with error.
Material
Thickness
Lead
Water
Narrow
Broad
6.55g/cm2
8.2g/cm2
6 cm
10 cm
Build-up factor
Table 2: Count-rate build-up factor B values for lead and water for their respective thicknesses
The error =observed- theoretical/theoretical= ±number
Discussion and Conclusion
The purpose of this experiment was to find out the
References
Is attachment
Narrow beam
Background count over 30 seconds
33
19
26
Average
Lead thickness (g/cm^2)
0
0.97
3.43
6.55
10.7
13.4
17.91
23.33
32.05
Integral narrow beam(Count over 30 seconds)
1
2
Average
2621
2578
2599.5
2385
2404
2394.5
1989
1964
1976.5
1464
1339
1401.5
909
933
921
736
731
733.5
466
441
453.5
297
298
297.5
131
143
137
(I/Io)%
100
92.03419
75.79172
53.44861
34.77754
27.49174
16.61162
10.54983
4.313192
In %(I/Io)
4.605170186
4.522160189
4.327989096
3.978720647
3.548971785
3.313885696
2.810102355
2.356110206
1.461678268
5
4.5
4
Ln%( Transmitted Intensity)
subtract BG
2573.5
2368.5
1950.5
1375.5
895
707.5
427.5
271.5
111
3.5
3
2.5
2
1.5
1
0.5
0
0
5
10
y = -0.0986x + 4.6229
10
15
20
Thickness of Lead (g/cm^2
25
30
35
Broad beam
Background count over 30 seconds
46
35
Average
40.5
Lead thickness (g/cm^2)
0
1.89
3.79
6.23
7.2
8.2
9.2
10.2
17.7
Integral of Broad beam (Count over 30 seconds)
1
2
Average
8613
8312
8462.5
7077
7302
7189.5
6033
6083
6058
4738
4789
4763.5
4261
4337
4299
3905
4090
3997.5
3557
3561
3559
3175
3266
3220.5
1567
1603
1585
subtract BG
8422
7149
6017.5
4723
4258.5
3957
3518.5
3180
1544.5
5
4.5
In %(I/Io)
4.605170186
4.441295343
4.268994747
4.026767047
3.923239842
3.849809019
3.732357619
3.631204053
2.90902309
4
Ln%( Transmitted Intensity)
(I/Io)%
100
84.88483
71.44977
56.07932
50.564
46.98409
41.77749
37.75825
18.33887
3.5
3
2.5
2
y = -0.0965x + 4.6224
1.5
1
0.5
0
0
2
4
6
8
10
12
Thickness of Lead (g/cm^2
12
s of Lead (g/cm^2
14
16
18
20
Water
Background count over 30 seconds
161
154
Average
157.5
Water thickness (g/cm^2)
0
2
4
6
8
10
12
14
16
Integral of water(Count over 30 seconds)
1
2
Average
4306
4377
4341.5
3671
3717
3694
3341
3357
3349
2940
2803
2871.5
2456
2414
2435
2158
2168
2163
1854
1890
1872
1622
1643
1632.5
1399
1451
1425
subtract BG
4184
3536.5
3191.5
2714
2277.5
2005.5
1714.5
1475
1267.5
In %(I/Io)
4.605170186
4.437039997
4.334393485
4.172326021
3.996980809
3.869795865
3.713023952
3.562560449
3.410948916
5
4.5
4
Ln%( Transmitted Intensity)
(I/Io)%
100
84.52437859
76.27868069
64.86615679
54.43355641
47.93260038
40.97753346
35.25334608
30.29397706
3.5
3
2.5
y = -0.0745x + 4.6077
2
1.5
1
0.5
0
0
2
4
6
Thickness of Water (g
45x + 4.6077
8
10
Thickness of Water (g/cm^2
12
14
16
18
Narrow beam
Average
Background count over 30 seconds
33
19
26
Lead thickness (g/cm^2) 1
0
0.97
3.43
6.55
10.7
13.4
17.91
23.33
32.05
Integral narrow beam(Count over 30 seconds)
2
Average
2621
2578
2385
2404
1989
1964
1464
1339
909
933
736
731
466
441
297
298
131
143
Broad beam
Background count over 30 seconds
46
35
Average
40.5
Lead thickness (g/cm^2)
0
1.89
3.79
6.23
7.2
8.2
9.2
10.2
17.7
Integral of Broad beam (Count over 30 seconds)
1
2
Average
8613
8312
8462.5
7077
7302
7189.5
6033
6083
6058
4738
4789
4763.5
4261
4337
4299
3905
4090
3997.5
3557
3561
3559
3175
3266
3220.5
1567
1603
1585
2599.5
2394.5
1976.5
1401.5
921
733.5
453.5
297.5
137
subtract BG
2573.5
2368.5
1950.5
1375.5
895
707.5
427.5
271.5
111
subtract BG
8422
7149
6017.5
4723
4258.5
3957
3518.5
3180
1544.5
(I/Io)%
100
92.03419468
75.79172333
53.44861084
34.77754031
27.49174276
16.61161842
10.54983486
4.313192151
In %(I/Io)
4.605170186
4.522160189
4.327989096
3.978720647
3.548971785
3.313885696
2.810102355
2.356110206
1.461678268
(I/Io)%
100
84.88482546
71.4497744
56.07931608
50.56399905
46.98408929
41.77748753
37.7582522
18.33887438
In %(I/Io)
4.605170186
4.441295343
4.268994747
4.026767047
3.923239842
3.849809019
3.732357619
3.631204053
2.90902309
PCN113 Radiation Physics
PRACTICAL 2
Semester 1 - 2012
ATTENUATION of Gamma RADIATION
Aim:
1.
To measure the attenuation coefficient for water and lead for 137Cs gamma radiation.
2.
To use the experimentally determined attenuation coefficient for lead to estimate the
thickness of a given lead plate
3.
To illustrate the difference between narrow beam and broad beam attenuation of gamma
radiation.
Procedure:
Part 1 - Attenuation by lead, 0.662 MeV (-rays from 137Cs
(a)
Narrow beam geometry
C
Record the count rate for a variety of thicknesses of lead absorber. Plot the percentage
of the transmitted intensity vs thickness and hence determine the linear attenuation
coefficient and also the mass attenuation coefficient.
C
Using the lead plate of unknown thickness as the ‘only’ absorber measure the count rate
and hence determine its thickness (include estimates of precision). Clearly explain the
method you used to determine this thickness.
(b)
Broad beam geometry
Use an unshielded detector and a range of large surface-area lead absorbers may be
rested on the plastic stand between source and detector. Any suitable 137Cs source (eg.
10-100 :Ci) may be used. Plot the results on the same graph as used for Part (1) (a)
and determine B for two thicknesses of lead.
Part 2 - Attenuation by water, 0.662 MeV (-rays from
137
Cs
Broad beam geometry
Plot the expected % transmitted intensity vs thickness of water (0-18 cm) under narrow
beam conditions; using the quoted value of the attenuation coefficient for 662 keV
photons in water.
The experiment is repeated using any convenient 137Cs source (eg. 100 :Ci) and
without any collimation. Water in a large tank is used as an absorber. Plot the results
on the same graph as for the expected narrow beam geometry, after again having
expressed the count rates at various depths as a percentage of the "zero depth" count
rate. Determine the count-rate build-up factor B for two different depths of water.
Analysis:
Tabulate the results for the linear and mass attenuation coefficients for lead using narrow beam
conditions. From the attenuation coefficients calculate the half-value thickness (HVT) and the
tenth-value thickness (TVT) in cm for water and lead and 137Cs radiation (assume narrow beam
conditions). Determine the HVT values (in cm) from the experimental results. Tabulate the
results. Compare the measured values with the quoted values of the attenuation coefficients.
Also tabulate values of the count-rate build-up factor B for two thicknesses of water and lead.
Comment on all results.
Purchase answer to see full
attachment