Badboys/attenuation

From Physiki
(Difference between revisions)
Jump to: navigation, search
(→List of Figures)
(→Theory)
 
(30 intermediate revisions by 3 users not shown)
Line 9: Line 9:
 
== Abstract ==
 
== Abstract ==
  
−
This experiment uses an NaI(T1) to determine mass attenuation coefficients for lead and aluminum, for 662 keV gamma rays, which are then compared to published values. The error present in the measurements is less than XX%, and published values agree with experimental results within that error.
+
This experiment measured 662 keV gamma rays with a NaI(T1) detector to determine mass attenuation coefficients for lead and aluminum. The HVL values for Al and Pb were calculated at 5.04 and 3.80 (respectively).The experimental results agreed with published figures within 20% error.
  
 
== List of Figures ==
 
== List of Figures ==
Line 20: Line 20:
  
 
== Theory ==
 
== Theory ==
−
 
+
When Gamma rays travel through a material, attenuation can be caused by photoelectric and Compton interactions with the material, as well as pair production.  In this lab these interactions are between the gamma rays and the Aluminum or Lead barriers placed in between the Cesium source and electrons in the atoms of the the gamma ray spectrometer.  Lambert’s law gives the intensity of the radiation after it has passed through the barrier as[1]:
−
Gamma attenuation occurs in a variety of ways.  When Gamma rays travel through a barrier, attenuation is caused by photoelectric or Compton interactions with the material.  In this lab these interactions are between the gamma rays and the Aluminum or Lead barriers placed in between the Cesium source and the gamma ray spectrometer.  Lambert’s law gives the intensity of the radiation after it has passed through the barrier as[1]:
+
  
 
<center>
 
<center>
Line 41: Line 40:
 
This density thickness is the product of the density of the material and the thickness of the barrier.
 
This density thickness is the product of the density of the material and the thickness of the barrier.
  
−
In this particular experiment we can measure I, <math>I_0</math>, and x and must use equation (1) to calculate the attenuation coefficient.
+
In this particular experiment we measure I, <math>I_0</math>, and x.  We then use equation (1) to calculate µ.
  
  
Line 61: Line 60:
  
  
−
The gamma ray spectrometer works by photon emissions from excited electrons.  The gamma rays that make it to the spectrometer are absorbed by electrons, moving these electrons in to excited states.  As these electrons leave their excited state they emit photons which are measured by the spectrometer.  The resulting readings look like a downward spike, when using the anode on the spectrometer, with a very steep initial slope because the beginning of the measurement has a very small time difference between no photon emissions and when the electrons first begin to emit photons, and a quadratic rising decay back to zero because electrons can only emit photons once if they are only excited once and so as more electrons emit photons, there are less electrons remaining to emit more photons.  We observed this process at step 5 in our provided lab procedure.
+
The gamma ray detector works by photon emissions from the decay of excited electrons.  The gamma rays that make it to the spectrometer are absorbed by electrons, moving these electrons in to excited states.  As these electrons leave their excited state they emit photons which are measured by the spectrometer.  The resulting readings look like a downward spike when using the anode on the detector, with a very steep initial slope because the beginning of the measurement has a very small time difference between no photon emissions and when the electrons first begin to emit photons, and a quadratic rising decay back to zero because electrons can only emit photons once if they are only excited once and so as more electrons emit photons, there are less electrons remaining to emit more photons.  We observed this process at step 5 in our provided lab procedure.
 +
 
 +
<center>
 +
[[Image:untitled1.png]]
 +
 
 +
''*Fig. 1 - Oscilloscope reading from gamma ray detector anode''
 +
 
 +
</center>
  
 
We see a similar signal when using the dynode on the spectrometer but because the dynode is positively charged the spike is in the positive direction instead of the negative direction.  The dynode itself is positive because it is used to amplify the cathode signal.
 
We see a similar signal when using the dynode on the spectrometer but because the dynode is positively charged the spike is in the positive direction instead of the negative direction.  The dynode itself is positive because it is used to amplify the cathode signal.
Line 91: Line 97:
  
 
12.  Calculate the attenuation coefficient using equation (1) and the half-value layer for lead and aluminum for 662 keV photons using equation (2).
 
12.  Calculate the attenuation coefficient using equation (1) and the half-value layer for lead and aluminum for 662 keV photons using equation (2).
 +
 +
<center>
 +
[[Image:ExperimentalSetup1tn.jpg]]
 +
 +
''*Fig. 2 - Experimental Setup: source, detector, absorber, and computer''
 +
 +
</center>
  
 
== Analysis ==
 
== Analysis ==
Line 103: Line 116:
  
 
Where, <math>I_{avg}</math> is our average intensity, <math>I_o</math> is our base intensity reading, <math>\rho</math> is the density of the sample, and <math>x_{avg}</math> is the average thickness of the sample.
 
Where, <math>I_{avg}</math> is our average intensity, <math>I_o</math> is our base intensity reading, <math>\rho</math> is the density of the sample, and <math>x_{avg}</math> is the average thickness of the sample.
 +
 +
Using the calculated <math>\mu</math>, we can find the HVL using the HVL equation from the theory.
 
=== Data: ===
 
=== Data: ===
  
Line 136: Line 151:
 
|0.970
 
|0.970
 
|0.948
 
|0.948
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.05
  
 
|-
 
|-
Line 145: Line 160:
 
|6.335
 
|6.335
 
|6.340
 
|6.340
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.05
  
 
|-
 
|-
Line 154: Line 169:
 
|2.270
 
|2.270
 
|2.255
 
|2.255
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.05
 
|}
 
|}
 
</center>
 
</center>
Line 173: Line 188:
  
 
! <math>I_o</math> (Count Rate)
 
! <math>I_o</math> (Count Rate)
 +
 +
!Error (<math>I_o</math>)
  
 
! <math>I_1</math>
 
! <math>I_1</math>
Line 181: Line 198:
  
 
! Average <math>I</math>
 
! Average <math>I</math>
 +
 +
! Error (Average <math>I</math>)
  
 
! <math>\mu</math> (<math>cm^2/g</math>)
 
! <math>\mu</math> (<math>cm^2/g</math>)
Line 194: Line 213:
 
|11.434
 
|11.434
 
|90.59
 
|90.59
 +
|<math>\pm</math> 0.9586
 
|75.54
 
|75.54
 
|75.92
 
|75.92
 
|73.03
 
|73.03
 
|74.83
 
|74.83
 +
|<math>\pm</math> 1.179
 
|0.176  
 
|0.176  
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.00930
 
|3.93
 
|3.93
  
Line 207: Line 228:
 
|11.434
 
|11.434
 
|90.59
 
|90.59
 +
|<math>\pm</math> 0.9586
 
|38.11
 
|38.11
 
|40.23
 
|40.23
 
|37.11
 
|37.11
 
|38.48
 
|38.48
 +
|<math>\pm</math> 1.753
 
|0.118
 
|0.118
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.00931
 
|5.86
 
|5.86
  
Line 220: Line 243:
 
|11.434
 
|11.434
 
|90.59
 
|90.59
 +
|<math>\pm</math> 0.9586
 
|62.25
 
|62.25
 
|64.50
 
|64.50
 
|63.75
 
|63.75
 
|63.50
 
|63.50
 +
|<math>\pm</math> 1.700
 
|0.138
 
|0.138
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.00305
 
|5.03
 
|5.03
 
|}
 
|}
Line 261: Line 286:
 
|5.030
 
|5.030
 
|5.044
 
|5.044
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.05
  
 
|-
 
|-
Line 270: Line 295:
 
|0.411
 
|0.411
 
|0.419
 
|0.419
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.05
 
|}
 
|}
 
</center>
 
</center>
Line 289: Line 314:
  
 
! <math>I_o</math> (Count Rate)
 
! <math>I_o</math> (Count Rate)
 +
 +
! Error (<math>I_o</math>)
  
 
! <math>I_1</math>
 
! <math>I_1</math>
Line 297: Line 324:
  
 
! Average <math>I</math>
 
! Average <math>I</math>
 +
 +
! Error (Average <math>I</math>)
  
 
! <math>\mu</math> (<math>cm^2/g</math>)
 
! <math>\mu</math> (<math>cm^2/g</math>)
Line 310: Line 339:
 
|2.702
 
|2.702
 
|90.59
 
|90.59
 +
|<math>\pm</math> 0.9586
 
|72.47
 
|72.47
 
|74.04
 
|74.04
 
|73.67
 
|73.67
 
|73.39
 
|73.39
 +
|<math>\pm</math> 1.314
 
|0.154
 
|0.154
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.00149
 
|4.50
 
|4.50
  
Line 323: Line 354:
 
|2.702
 
|2.702
 
|90.59
 
|90.59
 +
|<math>\pm</math> 0.9586
 
|84.45
 
|84.45
 
|84.81
 
|84.81
 
|84.04
 
|84.04
 
|84.43
 
|84.43
 +
|<math>\pm</math> 1.075
 
|0.623
 
|0.623
−
|<math>\pm</math> 0.005
+
|<math>\pm</math> 0.0735
 
|1.11
 
|1.11
 
|}
 
|}
Line 335: Line 368:
 
=== Error Analysis ===
 
=== Error Analysis ===
  
−
For the error analysis, there is an error associated with each variable. The error associated with <math>/rho</math>  
+
For the error analysis, there is an error associated with each variable. The error associated with <math>\rho</math> is neglected since density of Lead and Aluminum have been known for centuries and have been accurately calculated. The error in intensity is dependent upon multiple factors, such as length of time we took the measurement.  We obtained the error for the intensity by taking Net Count Rate/Net area from our graphs and then applying the error given to us for Net Area.  The thickness of the absorber as the final source of error.  
−
For the error analysis, there are two variable associated with an error, <math>\theta_{d}</math> and <math>\theta_{i}</math>.
+
  
−
The partial errors for each of the variable are calculated from the formulas
+
The partial error for the thickness of the absorber is calculated from the formula
 
<center>
 
<center>
 
<math>
 
<math>
−
\frac{\delta \lambda}{\delta \theta_{d}}=\frac{d}{m}Cos(\theta_{d})Sin({\delta \theta_{d}}),
+
\frac{\delta \mu}{\delta x}=\frac{ln(\frac{I_{avg}}{I_0})}{\rho x_{avg}^2}\delta x_{avg},
 
</math>
 
</math>
 
</center>
 
</center>
  
−
and,
+
Experimental error can be further reduced using an additional detection assembly on the near side of the source, providing an accurate assessment of noise.
−
 
+
−
<center>
+
−
<math>
+
−
\frac{\delta \lambda}{\delta \theta_{i}}=\frac{d}{m}Cos(\theta_{i}) Sin({\delta \theta_{i}}).
+
−
</math>
+
−
</center>
+
−
Then the total error is the sum of the two partial derivatives added in quadrature,
+
−
<center>
+
−
<math>
+
−
\delta \lambda=\frac{d}{m} \sqrt{(\frac{\delta \lambda}{\delta \theta_{i}})^{2}+(\frac{\delta \lambda}{\delta \theta_{d}})^{2}}.
+
−
</math>
+
−
</center>
+
  
−
The values for <math>\delta \theta_{d}</math> and <math>\delta \theta_{i}</math> used are half the value of the smallest unit of measure on the device, .05 degrees.
+
The total error is calculated by the summing of independent errors.
  
 
== Conclusion ==
 
== Conclusion ==
  
−
The mass attenuation coefficients for lead was determined accurately; the error was calculated at XX% and published values agree within experimental error.  However, the attenuation factor for aluminum was not calculated with satisfactory certainty, an error of XX% was calculated.  The marginal thickness of the thinner aluminum absorbers proved to have almost negligible capacity for attenuating the source.  In a more detailed experiment, a thicker gauge aluminum absorber can be studied, and the attenuation can be more precisely measured.
+
The mass attenuation coefficients for lead was determined accurately; the error was calculated at less than 15% and published values agree within experimental error.  However, the attenuation factor for aluminum was not calculated with satisfactory certainty, an error of less than 15% was calculated.  The marginal thickness of the thinner aluminum absorbers proved to have almost negligible capacity for attenuating the source.  In a more detailed experiment, a thicker gauge aluminum absorber can be studied, and the attenuation can be more precisely measured.
  
 
== References ==
 
== References ==

Latest revision as of 18:07, 3 April 2008

Gamma Ray Attenuation

Barrett Nibling, Adolfo Gomez, Micheal Bouchey

February 6, 2008

Contents

Abstract

This experiment measured 662 keV gamma rays with a NaI(T1) detector to determine mass attenuation coefficients for lead and aluminum. The HVL values for Al and Pb were calculated at 5.04 and 3.80 (respectively).The experimental results agreed with published figures within 20% error.

List of Figures

  • Fig. 1 - Experimental Setup

Introduction

This experiment verifies the mass attenuation coefficients for lead and aluminum (Pb/Al) individually. The coefficients are experimentally determined using an NaI(T1) photomultiplier tube, computerized data acquisition, and a gamma ray source. The 137-Cs source is placed at one end of the experimental setup, opposite the detector assembly, and a base recording of incident gamma radiation is collected. Next, an absorber is inserted midway between the source and detector, and a new measure of incident radiation is recorded then compared to the base measure. The experiment is repeated using several absorbers of varying gauges. By comparing collected data to published figures, the accuracy of experimental results can be determined.

Theory

When Gamma rays travel through a material, attenuation can be caused by photoelectric and Compton interactions with the material, as well as pair production. In this lab these interactions are between the gamma rays and the Aluminum or Lead barriers placed in between the Cesium source and electrons in the atoms of the the gamma ray spectrometer. Lambert’s law gives the intensity of the radiation after it has passed through the barrier as[1]:

I = I0e − μx,

Where:

I = intensity of the radiation after it has passed through the barrier

I0 = initial intensity of the radiation before it has passed through the barrier

µ = total mass attenuation coefficient with units of cm^2/g

x = density thickness with units of g/cm^2

This density thickness is the product of the density of the material and the thickness of the barrier.

In this particular experiment we measure I, I0, and x. We then use equation (1) to calculate µ.


The half-value layer (HVL) is defined as the density thickness of the absorbing material that will reduce the original intensity by a factor of two. Once µ is calculated HVL can be calculated with[2]:

0.5 = − μx

Where:

0.5 = the ratio of I/I0. It must be one-half to represent the reduction of the intensity by a factor of two

µ = total mass attenuation coefficient calculated from equation (1)

x = HVL


The gamma ray detector works by photon emissions from the decay of excited electrons. The gamma rays that make it to the spectrometer are absorbed by electrons, moving these electrons in to excited states. As these electrons leave their excited state they emit photons which are measured by the spectrometer. The resulting readings look like a downward spike when using the anode on the detector, with a very steep initial slope because the beginning of the measurement has a very small time difference between no photon emissions and when the electrons first begin to emit photons, and a quadratic rising decay back to zero because electrons can only emit photons once if they are only excited once and so as more electrons emit photons, there are less electrons remaining to emit more photons. We observed this process at step 5 in our provided lab procedure.

Untitled1.png

*Fig. 1 - Oscilloscope reading from gamma ray detector anode

We see a similar signal when using the dynode on the spectrometer but because the dynode is positively charged the spike is in the positive direction instead of the negative direction. The dynode itself is positive because it is used to amplify the cathode signal.

Procedure

1. Mount the NaI(TI) detector and the 137-Cs source with a distance of approximately 30 cm. The center of the source should be on the same height as the center of the detector crystal. Connect the photomultiplier base (base) to the photomultiplier (PM) connector.

2. Connect the high voltage (HV) imput of te PM base to the HV output of the HV power supply.

3. Connect the anode output of the PM base to the oscilloscope. At this point we observed a flat line signal.

4. Turn on the HV power supply. The screw or switch on the back side should be on positive. Turn up the voltage in increments of 100V to a maximum of 1000V and observe the signals on the oscilloscope. We did not notice anything observable until 1000V

5. Take specific notes of results for the signals on the oscilloscope at 1000V. We observed a spike in the negative direction. It is noteworthy to give a warning that the trigger level must be below zero or the oscilloscope will give a misleading reading.

6. Perform steps 3-5 using the dynode output of the PM instead of the anode output of the PM. We observed a spike in the positive direction this time. Again, noteworthy to give warning that this time the trigger level must be above zero or the oscilloscope will give a misleading reading.

7. Return to the anode signal and connect it to the spectroscopy amplifier input. Turn on the power of the NIM bin and check the input signal polarity.

8. Connect the oscilloscope to the amplifier output (unipolar). Making sure to again move the oscilloscope trigger level to below zero record the signal. We noted a similar signal to step 5.

9. Connect the unipolar output with the ADC input and start a measurement. Adjust the amplification so that you can clearly see the photopeak in the spectrum. Record the spectrum and the oscilloscope signal and record the voltage of the photopeak. We a spectrum with a large amount of noise in the low voltage range and our photopeak in the midvoltage range.

10. Determine the count rate (net) in the photopeak region at your given distance without the absorber foils. This is a zero measurement and will give I0.

11. Determine the count rate in the photopeak region with three absorber foils of aluminum and lead each. Take three measurements with each foil.

12. Calculate the attenuation coefficient using equation (1) and the half-value layer for lead and aluminum for 662 keV photons using equation (2).

ExperimentalSetup1tn.jpg

*Fig. 2 - Experimental Setup: source, detector, absorber, and computer

Analysis

After acquiring the data and the thickness of each sample, simple averages were taken with the thickness and the intensities. Then, these values were plugged into our working equation to find μ, the attenuation coefficient,

\mu = \frac{-ln(\frac{I_{avg}}{I_0})}{\rho x_{avg}}.

Where, Iavg is our average intensity, Io is our base intensity reading, ρ is the density of the sample, and xavg is the average thickness of the sample.

Using the calculated μ, we can find the HVL using the HVL equation from the theory.

Data:

Lead Data:
Thickness Data- Lead
Sample # Measurement 1 (mm) Measurement 2 (mm) Measurement 3 (mm) Measurement 4 (mm) Average (mm) Error (mm)
Sample A 0.960 0.920 0.942 0.970 0.948 \pm 0.05
Sample E 6.335 6.335 6.355 6.335 6.340 \pm 0.05
Sample C 2.260 2.250 2.240 2.270 2.255 \pm 0.05


Attenuation Data
Sample # Average Thickness (mm) Density (g / cm3) Io (Count Rate) Error (Io) I1 I2 I3 Average I Error (Average I) μ (cm2 / g) Error (cm2 / g) HVL
Sample A 0.948 11.434 90.59 \pm 0.9586 75.54 75.92 73.03 74.83 \pm 1.179 0.176 \pm 0.00930 3.93
Sample E 6.340 11.434 90.59 \pm 0.9586 38.11 40.23 37.11 38.48 \pm 1.753 0.118 \pm 0.00931 5.86
Sample C 2.255 11.434 90.59 \pm 0.9586 62.25 64.50 63.75 63.50 \pm 1.700 0.138 \pm 0.00305 5.03
Aluminum Data:
Thickness Data- Aluminum
Sample # Measurement 1 (mm) Measurement 2 (mm) Measurement 3 (mm) Measurement 4 (mm) Average (mm) Error (mm)
Size 24 5.115 5.020 5.010 5.030 5.044 \pm 0.05
Size 8 0.421 0.420 0.422 0.411 0.419 \pm 0.05


Attenuation Data
Sample # Average Thickness (mm) Density (g / cm3) Io (Count Rate) Error (Io) I1 I2 I3 Average I Error (Average I) μ (cm2 / g) Error (cm2 / g) HVL
Size 24 5.044 2.702 90.59 \pm 0.9586 72.47 74.04 73.67 73.39 \pm 1.314 0.154 \pm 0.00149 4.50
Size 8 0.419 2.702 90.59 \pm 0.9586 84.45 84.81 84.04 84.43 \pm 1.075 0.623 \pm 0.0735 1.11

Error Analysis

For the error analysis, there is an error associated with each variable. The error associated with ρ is neglected since density of Lead and Aluminum have been known for centuries and have been accurately calculated. The error in intensity is dependent upon multiple factors, such as length of time we took the measurement. We obtained the error for the intensity by taking Net Count Rate/Net area from our graphs and then applying the error given to us for Net Area. The thickness of the absorber as the final source of error.

The partial error for the thickness of the absorber is calculated from the formula

\frac{\delta \mu}{\delta x}=\frac{ln(\frac{I_{avg}}{I_0})}{\rho x_{avg}^2}\delta x_{avg},

Experimental error can be further reduced using an additional detection assembly on the near side of the source, providing an accurate assessment of noise.

The total error is calculated by the summing of independent errors.

Conclusion

The mass attenuation coefficients for lead was determined accurately; the error was calculated at less than 15% and published values agree within experimental error. However, the attenuation factor for aluminum was not calculated with satisfactory certainty, an error of less than 15% was calculated. The marginal thickness of the thinner aluminum absorbers proved to have almost negligible capacity for attenuating the source. In a more detailed experiment, a thicker gauge aluminum absorber can be studied, and the attenuation can be more precisely measured.

References

[1]Wolfram Science World - Lambert's Law (Online at http://scienceworld.wolfram.com/physics/LambertsLaw.html)

[2]Iowa State University - Half Value Layer (Online at http://www.ndt-ed.org/EducationResources/CommunityCollege/Radiography/Physics/HalfValueLayer.htm)

Retrieved from "http://inksurvey.org/csm/wiki/index.php?title=Badboys/attenuation&oldid=7274"
Personal tools
Namespaces
Variants
Actions
Navigation
Toolbox