Francisco Vega Physics C1494 Partners: David Platt, Peter Sabino 02/15/09 Experiment 10: Absorption of Beta and Gamma Rays Purpose The purpose of this experiment is to study the behavior of beta (β) and gamma (γ) rays passing through matter; to measure the range of β‐particles from a given source and hence to determine the endpoint of energy decay; and to determine the absorption coefficient in lead of the gamma radiation from a given source. Procedure In all parts of the experiment, a Geiger counter circuit set up as seen in the following diagram and picture was used. • Setting up the Geiger Counter The source of Thallium‐204 was placed under the Geiger counter tube and the high voltage was set to 500 V. The high voltage was increased in 20 V steps until the tube began to count, which was when the high voltage equaled 720 V. The number of counts, N, for a time interval of ∆t=15 seconds was recorded for high voltage values that were increased in 20 V steps. This was done until we noted that the count rate rose by less than 10% for a 100 V increase. • Background Measurement No source was placed under the Geiger counter tube, and the counts in a 60 second time interval were recorded. This amount was averaged to be N= 48
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Francisco Vega Physics C1494 Partners: David Platt, Peter Sabino 02/15/09
Experiment 10: Absorption of Beta and Gamma Rays
Purpose
The purpose of this experiment is to study the behavior of beta (β) and gamma (γ) rays passing through matter; to measure the range of β‐particles from a given source and hence to determine the endpoint of energy decay; and to determine the absorption coefficient in lead of the gamma radiation from a given source.
Procedure
In all parts of the experiment, a Geiger counter circuit set up as seen in the following diagram and picture was used.
• Setting up the Geiger Counter
The source of Thallium‐204 was placed under the Geiger counter tube and the high voltage was set to 500 V. The high voltage was increased in 20 V steps until the tube began to count, which was when the high voltage equaled 720 V. The number of counts, N, for a time interval of ∆t=15 seconds was recorded for high voltage values that were increased in 20 V steps. This was done until we noted that the count rate rose by less than 10% for a 100 V increase.
• Background Measurement
No source was placed under the Geiger counter tube, and the counts in a 60 second time interval were recorded. This amount was averaged to be N= 48
counts, which means a background count rate of RB=0.80 counts/sec and
.
.
• Range of β Particles
The Thallium‐204 source was placed on the second shelf below the detector as seen in the following diagram. The counts were recorded for varying aluminum absorber thickness until the counting rate reached the background level.
• Absorption of γ Rays
The Thallium‐204 source was replaced by the Cesium‐137 source. This Cesium‐137 source was placed on the lowest shelf below the detector as seen in the following diagram. The counts were recorded for varying lead absorber thicknesses.
Data Analysis
• Setting up the Geiger Counter
The Geiger counter was calibrated as explained in the procedure and the results are summarized in the following chart and graph. The final high voltage value was 860 V and was left there for the remainder of the experiment.
HV (V) N (Counts) σN (Counts) ∆t (sec) R=N/∆t (Counts/sec)
σR (Counts/sec)
720 1324 36.39 15 88 3.8
740 1581 39.76 15 105 4.4
760 1719 41.46 15 115 4.7
780 1843 42.93 15 123 5.0
800 1826 42.73 15 122 5.0
820 1850 43.01 15 123 5.0
840 1896 43.54 15 126 5.1
860 1880 43.36 15 125 5.1
880 1978 44.47 15 132 5.3
Where , , .
0 20 40 60 80 100 120 140 160
700 720 740 760 780 800 820 840 860 880 900
counts/sec
HV (V)
Geiger Counter HV Plateau
• Range of β Particles The counts were recorded for varying aluminum absorber thickness until the counting rate reached the background level and the results are summarized below:
Absorber thickness (cm Al)
N (Counts) σN (Counts) ∆t (sec) R=N/∆t (Counts/sec)
σR (Counts/sec)
0 1204 34.7 15 80 3.5
5.08E‐03 795 28.2 15 53 2.6
1.02E‐02 541 23.3 15 36 2.0
1.52E‐02 445 21.1 15 30 1.7
2.03E‐02 278 16.7 15 19 1.3
2.54E‐02 207 14.4 15 14 1.1
3.05E‐02 146 12.1 15 10 0.87
3.56E‐02 102 10.1 15 6.8 0.71
4.06E‐02 130 11.4 30 4.3 0.39
4.57E‐02 86 9.3 30 2.9 0.31
5.08E‐02 71 8.4 30 2.4 0.28
5.59E‐02 49 7.0 30 1.6 0.23
6.10E‐02 43 6.6 30 1.4 0.22
6.60E‐02 69 8.3 60 1.2 0.14
7.11E‐02 56 7.5 60 0.93 0.12
7.62E‐02 58 7.6 60 0.97 0.13
8.13E‐02 54 7.3 60 0.90 0.12
Where , , . Also, the thickness of
1 Absorber was 0.00508 cm, so the thicknesses given are multiples of this thickness since the absorbers were added one by one.
From the line sketched on the graph by hand, we see that the approximate value of the range is:
r= 0.078 +/ 0.020 cm.
where σr was estimated using 1 σ of the background counting rate, RB.
The value of the maximum beta energy for Thallium‐204 for the range found was determined using the equation that follows:
, where
E=0.595 +/ 0.118 MeV
The result obtained for E is consistent with the value of 0.765 MeV, as it is within 2 ’s.
0
1
10
100
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
counts/sec
absorber thickness (cm Al)
Range of Beta Particles
• Absorption of γ Rays Before we began these measurements we re‐measured the background rate and obtained a value of RB=1.4 counts/sec. The counts were recorded for varying lead absorber thicknesses and the results are summarized below. Two graphs and charts are shown, one showing counts/sec from the source and the background and another showing counts/sec for just the source(background corrected).
Absorber thickness (cm Al) = x
N (Counts)
σN (Counts)
∆t (sec)
R=N/∆t (Counts/sec)
σR (Counts/sec)
σm (cm1)
1.30E‐01 176 13.3 15 12 1.0 2.57E-01
2.60E‐01 164 12.8 15 11 0.93 1.37E-01
3.90E‐01 125 11.2 15 8.3 0.80 1.15E-01
5.20E‐01 87 9.3 15 5.8 0.65 1.23E-01
6.50E‐01 82 9.1 15 5.5 0.63 1.04E-01
7.80E‐01 71 8.4 15 4.7 0.58 1.02E-01
9.10E‐01 64 8.0 15 4.3 0.55 9.80E-02
Where , , .
Since
€
lnR =14.18e−µx as seen in graph below,
€
σ µ =1
Rx lnRσR.
Also, the thickness of 1 Absorber was 1.3mm, so the thicknesses given are multiples of this thickness since the absorbers were added one by one.
ln(R)= 14.18e‐1.41x R² = 0.953
1
10
100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
counts/sec
absorber thickness (cm Pb)
Absorption of Gamma Rays (source + background)
Therefore, taking the averages of
€
σ µ and seeing that
€
µ=1.41cm‐1 from the graph below we obtain a value of the absorption coefficient of:
€
µ=1.41 +/ 0.13 cm1
Absorber thickness (cm Al) = x N (Counts) σN (Counts) ∆t (sec)
R=N/∆t (Counts/sec)
σR (Counts/sec) σm (cm1)
1.30E‐01 176 13.3 15 10 1.0 3.08E‐01
2.60E‐01 164 12.8 15 10 0.93 1.66E‐01
3.90E‐01 125 11.2 15 6.9 0.80 1.52E‐01
5.20E‐01 87 9.3 15 4.4 0.65 1.92E‐01
6.50E‐01 82 9.1 15 4.1 0.63 1.70E‐01
7.80E‐01 71 8.4 15 3.3 0.58 1.86E‐01
9.10E‐01 64 8.0 15 2.9 0.55 2.01E‐01
Where , , .
Since
€
lnR =13.36e−µx as seen in graph below,
€
σ µ =1
Rx lnRσR.
Also, the thickness of 1 Absorber was 1.3mm, so the thicknesses given are multiples of this thickness since the absorbers were added one by one.
lnR= 13.36e‐1.78x R² = 0.961
1
10
100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
counts/sec
absorber thickness (cm Pb)
Absorption of Gamma Rays (background corrected)
Therefore, taking the averages of
€
σ µ and seeing that
€
µ=1.78cm‐1 from the graph below we obtain a value of the absorption coefficient of:
€
µ=1.78 +/ 0.20 cm1
By using the following graph and plotting lines where this
€
µ and its uncertainty are located, we can estimate the energy of the gamma rays.
In doing so we obtain a value for the gamma ray energy and its uncertainty as follows:
Eγ=0.550 +/ 0.05 MeV
This value is close to consistent but may disagree with the accepted value of Eγ=0.662 as it is within 3
€
σEγ’s of the accepted value. This measurement is
limited in precision as it is based on handwritten lines drawn on the graph, which is obviously not very precise. Also, extrapolating the curve on the absorption of Gamma Rays with limited data points also limits the precision of this value.
Another way of detecting Gamma Rays would be to use a Gamma Ray spectrometer.
Conclusion
Our result in the range of Beta particles part was within 2 ’s, therefore it was consistent with the given value. Ourr result for the Gamma Ray part were within 3
€
σEγ, so it was close to consistent. This was expected as
a Geiger counter can not measure Gamma ray photons as precisely.