experiment #4: radiation counting...

Experiment #4: Radiation Counting Statistics

NUC E 450 - Radiation Detection and Measurement – Spring 2014

Report Prepared By: Christine Yeager

Lab Preformed By: Christine Yeager

Martin Gudewicz

Connor Dickey

Lab Preformed On: February 27, 2014

Report Due Date: March 20, 2014

Lab Submitted On: March 20, 2014

Radiation Counting Statistics Yeager March 20, 2014

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TABLE OF CONTENTS

Summary ……..………………………………………………………………………………….. 3

Introduction ……….……………………………………………………………………………... 3

Theory …………………………………………………………………………………………… 3

Equipment …………………..…………………………………………………………………… 3

Procedure ……………………….……………………………………………………………….. 4

Data ………….………………………..…………………………………………………………. 4

Analysis of Data ……………………………...………………………………………………….. 5

Conclusion ……………………………………...……………………………………………… 10

Suggestions for Future Work …………………...……………………………………………… 10

References ……………………………………………………………………………………… 10

Appendices ……………………………………...……………………………………………… 10


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Summary

The experiment Radiation Counting Statistics is to learn more about statistics and radioactivity is

random but predictable. The normal distribution statistics, ratio test, Chauvenet’s Criterion, Chi-

Square, and the Poisson distribution have various ways of looking at the data collected. The

radioactive material is defiantly random, but from statistics it can be predicted as to when the

radioactive will decay.

Introduction

This experiment is to determine errors and statistics of radiation counting in the experiment. The

two types of errors that could happen in an experiment is systematic and random error.

Systematic error is in the measurement of data. Random error is from the randomness of

radioactive decay. Plotting and analyzing the data collected allows seeing the probability of the

data collected.

Theory

The different tests that can be performed on data creates a way to understand the material better.

The normal distribution statistics, ratio test, Chauvenet’s Criterion, Chi-Square, and the Poisson

distribution all allow a different look at the data. The equations used in this experiment are

found in the appendices of the lab manual experiment #4.

Equipment

The experiment was performed in room 112 of the Academic Projects Building. All the

equipment and computers used to complete the lab are found there. In this experiment, the

Geiger Mueller detector system that included equipment found in Table 1 was setup. In Figure 1

the GM detector system is shown schematically how it was setup. During the experiment a

gamma source counts were measured for various times and multiple trials.

Table 1: Equipment

Equipment Model Model Number Serial Number

Oscilloscope Tektronix TDS 1002 C020574

GM Detector Ludlum 1A0-9 PR217743

Pulse Inverter Ortec - -

Single Channel Analyzer Ortec 550 1047

Amplifier Canberra 2022 07033170

Timer and Counter Ortec 974 866

NIM Bin and Power Supply Ortec 4001C 00225581

Detector High Voltage Supply Canberra 3002D 07033297

Radioactive Gamma Source - -

Low Activity Beta Source 40

KCl


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Figure 1

Procedure

The GM counting system with the oscilloscope was setup as shown in the Lab Manual in Figure

1. Then the background was counted. A beta source was then used as a reference to see if the

equipment was working properly. A gamma source was then counted for a 20 second count for

20 trials and recorded. Then a low activity beta source was counted for 5 seconds 200 times.

The data was then entered in EXCEL and showed to the professor or TA to make sure the data

was in the general area of being correct. The background is then counted again to be used in the

analysis.

Data

Table 2: 20 Trials Data for 20 Seconds Each

Trial Counts Trial Counts

1 995 11 920

2 919 12 981

3 1005 13 992

4 980 14 985

5 933 15 992

6 900 16 934

7 979 17 933

8 933 18 978

9 989 19 916

10 964 20 990


Found in Appendices

Shelf

Box

GM

Tube

Pulser

Inverter

High

Voltage

Amplifier

Oscilloscope

SCA

Timer &

Counter


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Analysis of Data

Table 3: 20 Trials Standard Deviation, Theoretical Standard Deviation, and Statistical Tests from

supplied spreadsheet

20 Trials

Data:

Theoretical

Stdev Ratio Test

Chauvenet's

Crit.

995 31.54 1.23 1.1

919 30.32 1.35

1005 31.7 1.42

980 31.3 0.62

933 30.55 0.9

900 30 1.96

979 31.29 0.58

933 30.55 0.9

989 31.45 0.91

964 31.05 0.1

920 30.33 1.32

981 31.32 0.65

992 31.5 1

985 31.38 0.78

992 31.5 1

934 30.56 0.87

933 30.55 0.9

978 31.27 0.55

916 30.27 1.45

990 31.46 0.94

Sample Mean:

Standard

Deviation: Chi-Square

960.9 33.14 21.72

Table 4: 200Trials Sample Mean and Standard Deviation from supplied spreadsheet

First 100 200 Second 100

Sample Mean 3.47 3.485 3.5

Sample Standard Deviation 1.909334 1.878141 1.85592145

Table 5: Theoretical Standard Deviation for each trial given in Table 3

Found in Appendices


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Table 6: Histogram Development for the 200 Trial Sample

Bin Actual Poisson

0 5 6.13

1 22 21.37

2 36 37.23

3 49 43.25

4 37 37.68

5 23 26.26

6 12 15.25

7 10 7.59

8 3 3.31

9 3 1.28

10 0 0.45

11 0 0.14

12 0 0.04

13 0 0.01

14 0 0

15 0 0

Figure 2: 200 Trial Histogram Developments

A. 20-Sample

1. Compute Xe and S for this sample, compare these results with those obtained using the

computer. Also convert these values into units of counts per minute (cpm). From the

experimental mean compute the best estimate of the true standard deviation, both in counts and

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Occ

ure

nce

s

Counts per 5 Seconds

200 Trial Hisogram Development

Actual

Poisson


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cpm. Compare the experimental standard deviation with the expected

standard deviation computed from√ Xe .

∑

∑

√

∑

√

∑

The results calculated by the computer and by hand are about the same, the rounding makes the

results slightly different.

2. Compute σi for the first five of the 20 trials, assuming a Poisson distribution. Use

Equation (7) in Appendix A. Compare these results with those obtained using the

computer. Should they differ significantly from S or σ values computed in A-1

above? Explain any differences.

√ √ σ2=30.32 σ3=31.70 σ4=31.30 σ5=30.55

They should not differ significantly from S or σ.

3. Apply the Ratio Test to the first two data points in the sample to test for

statistically improbable behavior. How does this value compare with the

corresponding computer value?

| |

√ √

| |

√ √

The value calculated by hand is the same as the value calculated by the computer.

4. Apply the Chauvenet's Criterion to the first five trial results and to any trials that

were identified by the Excel spreadsheet as not meeting the criteria. How well do

your manually calculated values compare to the results obtained using the

computer spreadsheet? What do these results tell you?

| |

√

| |

√ τ2=1.35 τ3=1.42 τ4 =0.613 τ5=0.903

The results calculated by hand and by the computer are about the same. These results say the

equations in EXCEL are correct, and they all meet the Chauvenet’s Criterion.

5. Compute the Chi-square for the 20 trial sample used by the Excel spreadsheet

for this calculation. How well does your manually calculated value compare with

that obtained by the Excel spreadsheet? What does your value say about the

quality of your sample?

∑

cp20sec

The calculated values from the Excel spreadsheet and by hand are about the same. The value of

the quality of your sample is 10% probability the calculated value of Chi-square will be equal to

or greater than.


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6. If you had to reject a trial point from your sample as a result of applying Chauvenet's

Criterion, recalculate a new experimental mean and experimental standard deviation and reapply

the Chi-square test for the resulting set of the now reduced number of trials. Do these results

agree any better with your estimate of the value of the true standard deviation? Has your Chi-

square value improved over that obtained from the complete (20 point) data set? Explain any

changes observed.

If I had to reject a trial point from the sample, because it was the furthest from the average any

value. The results are not that much different from one another, but it does agree slightly better

with the estimated value of the true standard deviation, and the Chi-square value improved. This

happens because since there are fewer values further away from the average the Chi-square value

improves.

7. Sum the three backgrounds and sum all of the 20 sample counts, obtaining in this way an

equivalent 10-minute background count and an equivalent 400 second source + background

count. Assuming Poisson statistics, computers ± (σsr) for the net count rate, and express it in

units of cpm. How do these results compare with those obtained in A-1 of this section? Explain

any differences.

These results are about the same as in A-1 section. The slight change could be from the counts

that only had background and no source. The results from this a lower than A-1 section because

of the background/ no source counts.

8. Use your 20 data points set to create a control chart. Evaluate the data set using

the 4 different criteria given to you in the lectures and determine whether or not

your counting system is operating correctly.

Figure 3: Control Chart for 20 Trial Data

4400

4500

4600

4700

4800

4900

5000

5100

0 5 10 15 20 25

Co

un

ts p

er

Min

ute

Trials

Control Chart for 20 Trial Data


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The counting system is operating correctly because the LCL is 4300 cpm, the LWL is 4400cpm,

UWL at 5100cpm, and UCL is 5200cpm.

9. As a result of these tests, state your conclusion as to whether or not your sample

belongs to the same random distribution. Provide the basis upon which your

conclusion is made.

The sample used in this experiment belongs in the random distribution, because the number of

cpm varies by 500cpm in some areas. Five hundred cpm is a large number in the statistics of this

lab report.

B. 200-SAMPLE

1. Compute the experimental mean for this data set (note: you can simplify this

calculation by determining and making use of the frequency distribution of all

recorded trial values). How well does your frequency distribution and

experimental mean compare with that generated by the Excel spreadsheet?

The experimental mean for this data set is 3.49cp5sec. The frequency distribution and

experimental mean very close. The values are almost the same in the experimental mean and the

Excel spreadsheet.

2. Compare the frequency distribution of your data to the Poisson distribution calculated from

the experimental mean. Plot both distributions together on the same plot and comment on

similarities and differences.

The plot is in the Data section in Figure 2. The plots are not equal but they are

close to each other. Often the Poisson is higher than the actual, and this could be from random

errors.

3 Compute the theoretical standard deviation (σ) for your sample. How does this value compare

with that obtained experimentally?

The computed theoretical standard deviation and the experimentally computed value are similar.

The standard deviations are similar enough to be considered the same.

4. Based on your background data, what is the lower limit of detection of your

system?

The lower limit of the detection system is 0.37

Problems

1. A rule of thumb used many times in counting is that the standard deviation should


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not exceed 1% of X. Show that X = 104 counts satisfies this rule of thumb.

Stdv = 0.864% for X=104

2. If 30 minutes of total counting time are available, calculate the t+ and tb which will

minimize (σsr) for rb = 30 cpm and r+ = 100 cpm.

3. Based on your background data, what is the lower limit of detection of your detector

system?

The lower limit of the detection system is 0.37

Conclusion

Radioactive materials will not decompose a definite way, but they can be predicted. Statistics

show how probable it is for something to happen. The many ways to do statistics and to preform

tests on collected data creates a way to understand the material. The radioactive material tested

is random because of its radioactivity, but it is similar to previous tests and experiments. Since it

is similar the results can be compared and a more accurate prediction can be calculated.

Suggestions for Future Work

For this experiment there are no suggestions for future work. This experiment accomplishes the

goal of expanding our knowledge of statistics.

References

Nuclear Engineering 450 Radiation Detection and Measurement Laboratory Manual, by Dr. J. S

Brenzier, Dr. I. Jovanovic, Dr. R. M. Edwards, Dr. W. A. Jester, Dr. M. H. Vonth, and Dr. K.

Unlu.

Radiation Detection and Measurement 4th

edition, by Glenn F. Knoll

Appendices


Run Value Run Value Run Value Run Value

1 4 51 5 101 3 151 2

2 5 52 1 102 2 152 4

3 1 53 4 103 7 153 2

4 3 54 5 104 1 154 3

5 6 55 3 105 2 155 3


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6 6 56 3 106 3 156 4

7 1 57 4 107 4 157 2

8 5 58 2 108 0 158 4

9 1 59 3 109 4 159 1

10 1 60 3 110 4 160 2

11 3 61 5 111 5 161 4

12 3 62 8 112 2 162 2

13 4 63 1 113 4 163 4

14 1 64 1 114 4 164 4

15 6 65 5 115 3 165 5

16 2 66 2 116 1 166 3

17 2 67 2 117 4 167 4

18 3 68 3 118 1 168 5

19 1 69 5 119 8 169 7

20 2 70 9 120 6 170 3

21 2 71 3 121 3 171 5

22 2 72 2 122 3 172 2

23 6 73 2 123 6 173 3

24 3 74 5 124 3 174 5

25 3 75 2 125 2 175 2

26 4 76 2 126 0 176 3

27 4 77 4 127 3 177 5

28 4 78 1 128 6 178 4

29 5 79 4 129 5 179 9

30 9 80 5 130 4 180 3

31 2 81 2 131 3 181 3

32 3 82 2 132 4 182 2

33 1 83 3 133 3 183 3

34 3 84 7 134 2 184 4

35 5 85 3 135 3 185 2

36 5 86 3 136 4 186 1

37 7 87 2 137 4 187 7

38 7 88 3 138 4 188 5

39 5 89 5 139 5 189 4

40 1 90 4 140 4 190 3

41 7 91 1 141 3 191 3

42 0 92 3 142 7 192 1

43 3 93 3 143 2 193 7

44 3 94 4 144 4 194 0


12

45 3 95 3 145 2 195 0

46 6 96 3 146 4 196 1

47 6 97 2 147 6 197 2

48 2 98 3 148 8 198 7

49 6 99 1 149 4 199 4

50 3 100 6 150 2 200 1

Table 5: Theoretical Standard Deviation for each trial given in Table 3

Run Value Run Value Run Value Run Value

1 2 51 2.24 101 1.73 151 1.41

2 2.24 52 1 102 1.41 152 2

3 1 53 2 103 2.65 153 1.41

4 1.73 54 2.24 104 1 154 1.73

5 2.45 55 1.73 105 1.41 155 1.73

6 2.45 56 1.73 106 1.73 156 2

7 1 57 2 107 2 157 1.41

8 2.24 58 1.41 108 0 158 2

9 1 59 1.73 109 2 159 1

10 1 60 1.73 110 2 160 1.41

11 1.73 61 2.24 111 2.24 161 2

12 1.73 62 2.83 112 1.41 162 1.41

13 2 63 1 113 2 163 2

14 1 64 1 114 2 164 2

15 2.45 65 2.24 115 1.73 165 2.24

16 1.41 66 1.41 116 1 166 1.73

17 1.41 67 1.41 117 2 167 2

18 1.73 68 1.73 118 1 168 2.24

19 1 69 2.24 119 2.83 169 2.65

20 1.41 70 3 120 2.45 170 1.73

21 1.41 71 1.73 121 1.73 171 2.24

22 1.41 72 1.41 122 1.73 172 1.41

23 2.45 73 1.41 123 2.45 173 1.73

24 1.73 74 2.24 124 1.73 174 2.24

25 1.73 75 1.41 125 1.41 175 1.41

26 2 76 1.41 126 0 176 1.73

27 2 77 2 127 1.73 177 2.24

28 2 78 1 128 2.45 178 2

29 2.24 79 2 129 2.24 179 3


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30 3 80 2.24 130 2 180 1.73

31 1.41 81 1.41 131 1.73 181 1.73

32 1.73 82 1.41 132 2 182 1.41

33 1 83 1.73 133 1.73 183 1.73

34 1.73 84 2.65 134 1.41 184 2

35 2.24 85 1.73 135 1.73 185 1.41

36 2.24 86 1.73 136 2 186 1

37 2.65 87 1.41 137 2 187 2.65

38 2.65 88 1.73 138 2 188 2.24

39 2.24 89 2.24 139 2.24 189 2

40 1 90 2 140 2 190 1.73

41 2.65 91 1 141 1.73 191 1.73

42 0 92 1.73 142 2.65 192 1

43 1.73 93 1.73 143 1.41 193 2.65

44 1.73 94 2 144 2 194 0

45 1.73 95 1.73 145 1.41 195 0

46 2.45 96 1.73 146 2 196 1

47 2.45 97 1.41 147 2.45 197 1.41

48 1.41 98 1.73 148 2.83 198 2.65

49 2.45 99 1 149 2 199 2

50 1.73 100 2.45 150 1.41 200 1

experiment #4: radiation counting...

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