Physics Lab Report: Gamma Radiation Attenuation in Water and Lead

This physics lab report details an experiment on the attenuation of gamma radiation through lead and water. The experiment utilizes a Cs-137 radioactive source and explores both narrow and broad beam geometries. The procedure involves measuring count rates with varying thicknesses of lead and water to determine linear and mass attenuation coefficients. The results are presented graphically and analyzed to calculate the unknown thickness of a lead plate and compare the attenuation characteristics between narrow and broad beam configurations. Additionally, the report investigates the attenuation of Co-60, half value layer, tenth value layer and build-up factors, concluding with a comparison of the attenuation factors and the impact of different materials on gamma radiation.

Running head: PHYSICS
PHYSICS
Name of Student
Institution Affiliation

PHYSICS 2
INTRODUCTION
Photons of gamma radiation interact electromagnetically with matter. Interaction
takes either absorption or scattering processes (Korun, Vodenik, & Zorko, 2016). Absorption
involves disappearance of photon with transfer of its full energy to secondary particles or to
the atoms of the materials while scattering is when the photon propagates in a different
direction without disappearing. Compton scattering, photoelectric effect, electron-positron
pair production and attenuation coefficient are the various kinds of the interaction processes
(Stalter & Howarth, 2016). This experiment focuses on measurement of attenuation
coefficient of water and lead and the result used to approximate a given lead plate’s
thickness. Finally, distinction between broad beam and narrow beam attenuations is noted.
PROCEDURE
Collimators, a cylinder of water, Nal detector, 82Pb samples and a 60Co radioactive
source were the components used in this experiment. At the onset, background radiation of
the radioactive source was measured for every 30 second interval. Thereafter, the radioactive
source –with a 10 cm approximate interspacing- was vertically placed above the detector.
With the collimators between the two, count rate was calculated for zero thickness of lead
absorber and then seven other different thicknesses used and their corresponding count rates
computed. After which, the mass and linear attenuation coefficients were analytically
determined.
The above procedure was repeated for the case of broad beam geometry; however,
with the collimators removed and the lead absorber replaced with a water cylinder of water
heights in the range (0-18 cm). A series of gamma radiation count rates were then measured
and recorded as in results. Finally, these results were then analysed to verify their conformity
with the desired objectives.

PHYSICS 3
RESULT:
Part 1: Attenuation by lead, 0.662 Mev γ-rays from 137Cs
(a) Narrow beam geometry

PHYSICS 4
0 2 4 6 8 10 12 14 16
0
500
1000
1500
2000
2500
f(x) = 2287.44699814178 exp( − 0.0977504623395981 x )
R² = 0.997207243100617
Narrow beam of Cs 137 in Pb absorbed
Thickness of Pb (g/cm2 )
Count
Figure 1: Showing Count against of Pb (g/cm2) for narrow beam of Cs 137 in Pb absorbed
(b) Broad beam geometry
0 2 4 6 8 10 12 14 16 18 20
0
20
40
60
80
100
120
Attenuation of Cs 137 in narrow and broad beam geometry
Broad Beam
Narrow Beam
Thickness of Pb (g/cm2)
% Attenuation
Figure 2: Showing % attenuation against thickness of Pb (g/cm2) for Cs 137 in narrow and
broad beam geometry

PHYSICS 5
Part 2: Attenuation by water, 0.662 Mev γ-rays from 137Cs
Broad beam geometry:
0 2 4 6 8 10 12 14 16 18 20
0
500
1000
1500
2000
2500
3000
f(x) = 2527.07032706231 exp( − 0.0695632451334494 x )
R² = 0.996640990013922
Cs137 attenuation due to water in Broad Beam
Geometry
Thickness of water (cm)
Counts
Figure 3: Showing counts against thickness of water (cm) for 137 attenuation due to water in
broad beam Geometry

PHYSICS 6
0 2 4 6 8 10 12 14 16 18 20
0
20
40
60
80
100
120
Water attenuation between broad beam and
narrow beam geometry for Cs 137
Measured (Broad Beam) Calculated (Narrow Beam)
Thickness of water (cm)
% Attenuation
Figure 4: Showing % attenuation against thickness of water (cm) for water attenuation
between broad beam and narrow beam geometry for Cs 137
Part 3:
Analysis:
Part 1: Lead attenuation

PHYSICS 7
By plotting the Ln(I/Io) vs thickness of Pb, a straight line regression with intercept forced to
0 the slope can be used to determine the linear attenuation coefficient of lead for 662 keV.
0 2 4 6 8 10 12 14 16
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0 f(x) = − 0.0977504623395981 x + 0.024986432237465
R² = 0.997207243100617
Narrow beam of Cs 137 in Pb absorbed
Ln(I/Io) vs t
Series2
Linear (Series2)
thickness of Pb (g/cm2)
Axis Title
Figure 5: Showing counts against thickness of Pb
It can be seen from Figure () that the linear attenuation coefficient is
= 0.095 0.02 cm-1
The mass attenuation coefficient can be calculated by dividing by the mass density of Pb
which is 11. 3 g /cm3 (reference)
μ
ρ =0.085 ±0.0002cm-1

PHYSICS 8
The unknown thickness of Pb can be calculate from the measured count rate, using the
following equation:
ln I
IO
=−μ t
ln 1184
2231 =−0.095 t
t ¿ 6.669
to calculate ∆t:
∆ t
t = Δ μ
μ + Δ I
I
∆ t=¿ ) x 6.669
∆ t=0.3
The thickness of Pb absorber for the unknown thickness is calculated to be:
t = 6.7 0.3 g/cm2
Narrow Beam Vs Broad Beam Geometry for Pb attenuation of Cs 137

PHYSICS 9
0 2 4 6 8 10 12 14 16 18 20
0
20
40
60
80
100
120
Attenuation of Cs 137 in narrow and broad beam
geometry
Broad Beam
Narrow Beam
Thickness of Pb (g/cm2)
% Attenuation
Figure 6: Showing % attenuation against thickness of Pb (g/cm2)
Determining the linear attenuation coefficient between narrow beam and broad beam
geometry, the ln(I/Io) graph is plotted against the thickness of Pb absorber. The linear
regression was used to determine the slope of the graph and forcing the intercept to zero.
0 2 4 6 8 10 12 14 16 18 20
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0 f(x) = − 0.095555756691766 xf(x) = − 0.0947997231105143 x
Attenuation of Cs 137 in narrow and broad beam
geometry
Broad Beam
Linear (Broad Beam)
Narrow Beam
Linear (Narrow Beam)
Thickness of Pb (g/cm2)
% Attenuation

PHYSICS 10
Figure 7: Showing % Attenuation against thickness of Pb (g/cm2) for Cs 137 narrow and
broad beam geometry
The linear attenuation coefficients are given by:
Broad beam μ = 0.0948 cm-1 and for narrow beam geometry μ = 0.0956 cm-1.
The linear attenuation coefficient for narrow beam is marginally larger than broad beam
conditions however, the differences is within measurement uncertainty.
Build up Factor:
The attenuation of intensity of count rate was calculated for two depths of lead 10 cm and 15
cm.

PHYSICS 11
Lead cm Broad Beam(%) Predicted(narrow) Build up Factor for Lead for Cs137
0 100 100
10 38.9 38.4 1.0112157
15 24.2 23.6 1.0264983
Part 2: Attenuation of Cs 137 in water
0 2 4 6 8 10 12 14 16 18 20
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0 f(x) = − 0.0713649009674301 x
Attenuation of Cs 137 of water in Broad Beam
ln(I/Io) vs water depth
water depth (cm)
Ln(I/Io)
Figure 8: Showing Ln(l/lo) against water depth (cm)

PHYSICS 12
0 2 4 6 8 10 12 14 16 18 20
-1.8
-1.4
-1
-0.6
-0.2 f(x) = − 0.0713649009674301 x
Attenuation of Cs 137 of water in Broad
Beam
ln(I/Io) vs water depth
Broad
Linear (Broad)
narrow
Linear (narrow)
water depth (cm)
Ln(I/Io)
Figure 9: Showing Ln (l/lo) against water depth (cm) for attenuation of 137 of water in
broad beam
The narrow beam geometry is more readily attenuated compared to broad beam geometry.
The linear attenuation coefficient for broad beam is 0.071 0.001 cm-1 compared to linear
attenuation coefficient of narrow beam geometry of 0.085 cm-1.
Build up Factor
The attenuation of intensity of count rate was calculated for two depths of water 5 cm and 10
cm.
Water cm Broad Beam (%) Predicted(narrow) Build up Factor for Water for