Attenuation And Build Up Factor-Physics-Lab Report, Exercises of Physics

This is lab report for Physics course. It was submitted to Dr. Urmila Bhansi at All India Institute of Medical Sciences. It includes: Electromagnetic, Waves, Simple, Scattering, Rayleigh, Attenuation, Coefficient, Photoelectric, Effect

Typology: Exercises

2011/2012

Uploaded on 07/14/2012

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Introduction
Electromagnetic waves like gamma rays and X-rays when pass through material medium, loses
energy. The energy loss can be through photo-electric effect, through Compton scattering,
through pair production or through Rayleigh scattering. All these channels of energy loss are
dominant at certain energies. Gamma rays are the most energetic in nature because they arise
from nuclear transitions. They can pass through very large thicknesses and can damage the living
tissues. Thus protection is required against them because these rays can be very harmful if the
body is exposed to a high dose of them in research labs and nuclear reactors. The protection
could be provided by material in which the energy loss of these rays is maximum. The loss is
determined by the attenuation coefficient of the material. The attenuation coefficient has
contribution coming from all of the above discussed processes. Lets discuss all of them briefly.
Simple Scattering (Rayleigh Scattering).
Rayleigh scattering (named after Lord Rayleigh) is the elastic scattering of light or other
electromagnetic radiation by particles much smaller than the wavelength of the light. It can occur
when light travels in transparent solids and liquids, but is most prominently seen in gases.
The incident photon energy is much less than the binding energy of the electron in an atom. The
photon is scattered without change of energy. But Raleigh scattering is important for low energy
photons and high Z material. It is the common practice to ignore the Rayleigh scattering in
shielding calculation.
Photoelectric Effect
The photoelectric effect, in which the photon disappears, is an interaction between a photon and
a tightly bound electron whose binding energy is equal to or less than the energy of the photon.
The primary ionizing particle resulting from this interaction is the photoelectron, whose energy is
given by as
EPhotoelectron = h f − φ.
The photoelectron dissipates its energy in the absorbing medium mainly by excitation and
ionization. The binding energy φ is transferred to the absorber by means of the fluorescent
radiation that follows the initial interaction. These low-energy photons are absorbed by outer
electrons or in other photoelectric interactions not far from their points of origin. The
photoelectric effect is favored by low-energy photons and high-atomic-numbered absorbers. The
cross section for this reaction varies approximately as Z4λ3 (Z4/E 3). It is this very strong
dependence of photoelectric absorption on the atomic number Z that makes lead such a good
material for shielding against X-rays. For very low-atomic-numbered absorbers, the photoelectric
effect is relatively unimportant. The following fig. depicts the process
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Introduction

Electromagnetic waves like gamma rays and X-rays when pass through material medium, loses

energy. The energy loss can be through photo-electric effect, through Compton scattering,

through pair production or through Rayleigh scattering. All these channels of energy loss are

dominant at certain energies. Gamma rays are the most energetic in nature because they arise

from nuclear transitions. They can pass through very large thicknesses and can damage the living

tissues. Thus protection is required against them because these rays can be very harmful if the

body is exposed to a high dose of them in research labs and nuclear reactors. The protection

could be provided by material in which the energy loss of these rays is maximum. The loss is

determined by the attenuation coefficient of the material. The attenuation coefficient has

contribution coming from all of the above discussed processes. Lets discuss all of them briefly.

Simple Scattering (Rayleigh Scattering).

Rayleigh scattering (named after Lord Rayleigh) is the elastic scattering of light or other

electromagnetic radiation by particles much smaller than the wavelength of the light. It can occur

when light travels in transparent solids and liquids, but is most prominently seen in gases.

The incident photon energy is much less than the binding energy of the electron in an atom. The

photon is scattered without change of energy. But Raleigh scattering is important for low energy

photons and high Z material. It is the common practice to ignore the Rayleigh scattering in

shielding calculation.

Photoelectric Effect

The photoelectric effect, in which the photon disappears, is an interaction between a photon and

a tightly bound electron whose binding energy is equal to or less than the energy of the photon.

The primary ionizing particle resulting from this interaction is the photoelectron, whose energy is

given by as

EPhotoelectron = h f − φ.

The photoelectron dissipates its energy in the absorbing medium mainly by excitation and

ionization. The binding energy φ is transferred to the absorber by means of the fluorescent

radiation that follows the initial interaction. These low-energy photons are absorbed by outer

electrons or in other photoelectric interactions not far from their points of origin. The

photoelectric effect is favored by low-energy photons and high-atomic-numbered absorbers. The

cross section for this reaction varies approximately as Z4λ3 (Z4/E 3). It is this very strong

dependence of photoelectric absorption on the atomic number Z that makes lead such a good

material for shielding against X-rays. For very low-atomic-numbered absorbers, the photoelectric

effect is relatively unimportant. The following fig. depicts the process

Compton Scattering

If the photon energy is much greater than the electron binding energy and only part of this is

given up during the interaction with an outer valence electron (the binding of the valance

electrons is relatively weak, hence the free). The photon is scattered with reduced energy and the

energy of the electron is dissipated through ionization. The energy needed for this process is

greater than for the photoelectric effect. This shows that the change in wavelength following a

scattering event depends only on the scattering angle; it neither depends on the energy of the

incident photon nor on the nature of the scatterer. The Compton electron dissipates its kinetic

energy in the same manner as a beta particle and is one of the primary ionizing particles

produced by gamma radiation (photons).

Due to the presence of these processes, the total attenuation coefficient can be writer

mathematically as

μ = ζ + δc + k

Where ζ, δc and k are the photoelectric, Compton scattering and pair production probabilities

respectively.

Suppose an intensity Io of photons enters a medium characterized by attenuation coefficient μ,

then the intensity I after traveling a distance x is given by the exponential decaying function.

I(x) = Ioexp(-μx)

Or this can be written as

ln (I(x)) = ln (Io) - μx

which is the equation of straight line and its slope is μ.

For a thick shield material, photons suffer multiple collisions and may reach the observation

point. In this case some of the photons will be also counted in addition to Uncollided intensity.

The effect of these scattered radiation photons is included by the mean which called Build Up

Factor.

Build up factor = B = (uncollided intensity + collided intensity.)/uncollided intensity.

This build up factor should be incorporated in the intensity equation for correction, thus

I(x) = BIoexp(-μx)

Build in factor depend on following factors

1. Shield material

2. Material Thickness

3. Geometry

4. Energy of the Gamma rays

5. Gamma rays Detector

6. Atomic number (Z) of the material

And from experiments we know that

1. Cross section for the Photoelectric effect is directly proportional to Z

n

Where n (which is a function of energy) varies from 4 to 5.

2. Cross section for Compton effect is directly proportional to Z

3.Cross section for Pair Production is directly proportional to Z^2.

Materials with higher Atomic number (Z) are more effective in attenuation of Gamma rays. The

cross section ( Photoelectric effect, Compton effect, Pair Production) also vary with Gamma rays

energy. So the total attenuation coefficient is also energy dependent.

There are following formulae normally used for Build up factors

1. B(μx)= 1+kμx

Which is called Linear Formula

2. B(μx)=1+aexp(-b μx)

Where a, b are functions of energy. This relation is called Berger’s formula.

This formula is valid for

(a) Point source

(b) Infinite thickness

3. Taylor,s formula

B(μx)=Aexp(-aμx) - – (1-A)exp(-bμx)

Where A ,a,b are functions of material and Gamma energy

Methods for the measurement of attenuation Coefficient and

mass attenuation coefficient.

Good Geometry

In such an arrangement only those photons are allowed to reach the detector which suffer

no collision with the shield or the photons which suffer Compton scattering with the shield are

not counted.

Bad Geometry

It is an arrangement of source, shield and the detector in which scattered photons in the

shield are also able to reach the detector. Bad geometry counts are always greater than good

geometry counts.

Following are the figures that represent the two geometries.

Apparatus Of Experiment:

1. Gamma rays source Cs-

2. Shielding material plates like Copper ,Aluminum ,Iron.

3. Collimators

4. Pre-Amplifier

5. Amplifier

6. Single Channel analyzer

7. Power supply

8. CRO

9. Delay amplifiers

10. Multi channel analyzer

Procedure

1. Method 1 using SCA

Before starting the experiment the apparatus is set according to the fig. To find the

good geometry counts collimators are used in such a way that the source, collimator and the

detector are exactly in line. One collimator is placed in front of source and other before detector

in this way those photons will reach the detector which suffer no scattering with collimators.

Also lead shielding around the source is adjusted to reduce the dose rate below the maximum

permissible limit. Then serial numbers are marked on each plate and thickness of all the plates is

calculated. In this experiment 3 plates of each Aluminum, Copper, Iron plates were used.

Then the connections were made as in Fig.

To carry on the experiment high power supply is turned on and voltage equal to the

operating voltage of detector is applied. Timer is fixed for 10 seconds, and then counts are

recorded first without placing any plate between the source and detector and then placing the

plates one by one until all the five plates. In this way three readings are taken for each plate and

then their average is evaluated.

Now this data is plotted

The value of attenuation coefficient is 0.3404 mm-1.

a) For Copper

Tabulated Data:

Plate No X1 X2 X3 X=(X1+X2+X3)/ Count rate Count rate2 Average ln(Average) 0 0 0 0 0 162346 162330 162338 10. 8 13.1 12.45 12.4 12.65 72589 72325 72457 10. 4 12.45 13 12.45 12.6333333 33589 33579 33584 10. 1 12.375 12.3 13.075 12.5833333 15614 15602 15608 10. 6 13.05 12.42 12.45 12.64 7429 7516 7472.5 10. 5 12.42 12.37 12.4 12.3966667 3413 3521 3467 10. y = - 0.3404x + 12. 9

10

11

12

0 7.0333 13.64996667 19.9083 26.19996667 32. ln(counts rate) Thickness of iron (mm)

Graphical Representation:

The value of attenuation coefficient is 0.766 mm-

a) For Aluminum

Tabulated Data:

Plate No X1 X2 X3 X=(X1+X2+X3)/ Count rate Count rate2 Average ln(Average) 0 0 0 0 0 162346 162330 162338 11. 24 6.3 6.25 6.125 6.225 141789 141201 141495 11. 27 6.175 6.075 6.25 6.16666667 125131 124378 124754.5 11. 25 6.15 6.175 6.25 6.19166667 111015 108782 109898.5 11. 30 6.175 6.15 6.225 6.18333333 97344 98014 97679 11. 20 6.3 6.343 6.2 6.281 86740 87000 86870 11. y = - 0.7661x + 12. 0 2 4 6 8 10 12 14 0 12.65 25.28333333 37.86666667 50.50666667 62. ln(counts rate) Thickness of Copper (mm)

c) For Aluminum

Tabulated Data:

Plate No X1 X2 X3 X=(X1+X2+X3)/ Count rate Count rate2 Average 0 0 0 0 0 1101460 1102080 1101770 24 6.3 6.25 6.125 6.225 1032480 1033548 1033014 27 6.175 6.075 6.25 6.16666667 967720 966397 967058. 25 6.15 6.175 6.25 6.19166667 902247 903017 902632 30 6.175 6.15 6.225 6.18333333 839061 838876 838968. 20 6.3 6.343 6.2 6.281 775796 776260 776028

d) For Iron

Plate No X1 X2 X3 X=(X1+X2+X3)/ Count rate Count rate2 Average 0 0 0 0 0 1101460 1102080 1101770 4 6.8 7.225 7.075 7.03333333 907305 907388 907346. 2 6.375 7.075 6.4 6.61666667 725568 726078 725823 13 6.25 6.25 6.275 6.25833333 566222 566544 566383 10 6.275 6.25 6.35 6.29166667 437779 438181 437980 9 6.375 6.175 6.45 6.33333333 332560 334614 333587

Buildup Factor

The buildup factor corresponding to different value of thickness for the three materials is

tabulated and is graphically represented in the following paragraphs.

1) Buildup Factor by SCA

Iron

Graphical Representation:

No. of Plates Accumulative Thickness Good Geometry Bad Geometry Buildup Factor 0 0 162338 1101770 6. 1 7.033333 115003.5 907346.5 7. 2 13.65 81522.5 725823 8. 3 19.90833 57745.5 566383 9. 4 26.2 49774 437980 10. 5 32.53333 29916.5 333587 11. y = 0.8698x + 6. 0 2 4 6 8 10 12 0 7.033333333 13.65 19.90833333 26.2 32. buildup factor Thickness of Iron(mm) No. of Plates Accumulative Thickness Good Geometry Bad Geometry Buildup Factor 0 0 162338 1101770 6. 1 7.033333 115003.5 907346.5 7. 2 13.65 81522.5 725823 8. 3 19.90833 57745.5 566383 9. 4 26.2 49774 437980 10. 5 32.53333 29916.5 333587 11.

Graphical Representation:

a) Copper

y = 0.4302x + 6. 0 1 2 3 4 5 6 7 8 9 10 0 6.225 12.3916666718.5833333324.7666666731. buildup factor Thickness of Alluminum (mm) No. of Plates Accumulative Thickness Good Geometry Bad Geometry Buildup Factor 0 0 162338 1101770 6. 1 12.65 72457 683853.5 9. 2 25.28333 33584 374116 11. 3 37.86667 15608 195376.5 12. 4 50.50667 7472.5 100341.5 13. 5 62.90333 3467 51988.5 14.

Graphical Representation:

2) Buildup Factor by MCA

a) Iron

Plate No. Accumulative Thickness Gross Counts Photo Peak Counts Buildup Factor 0 0 13689873 4524507 3. 4 7.033333 10722789 3715680 2. 2 13.65 3893642 1326438 2. 13 19.90833 2739625 771904 3. 10 26.2 1974753 700118 2.

b) Aluminum

Plate No. Accumulative Thickness Gross Counts Photo Peak Counts Buildup Factor 0 0 813859 287179 2. 8 6.225 379861 133301 2. 4 12.39167 176542 54688 3. 1 18.58333 89346 29119 3. 6 24.76667 46004 13229 3. y = 1.5593x + 5. 0 2 4 6 8 10 12 14 16 18 0 12.65 25.28333333 37.86666667 50.50666667 62. buildup factor Thickness of copper (mm)

Conclusion

A clear linear relationship was found between ln (I/I 0 ) and the thickness of the foils. Three

different lines were generated, and in each case the slope of the line were found to be relatively

close to the accepted value for the linear attenuation coefficient of iron, copper, and aluminum

iron at the given energy of Cs-137 beam. This verifies the theory that the attenuation depends on

the thickness as well as attenuating material.

The buildup factor for iron is in range 6.786889-11.1506, copper 6.74947-14.99524, and

aluminum 6.786889-8.933211, so in all the cases it shows increase with increase of thickness.

This increase is because of more interaction of gamma ray photon with material and hence

results in more scattering. There is also contribution from background in case of bad geometry.

The buildup factor measured with MCA was not in good agreement with the one with SCA this

might be due to the large dead time of the MCA card which was find to be 98%.