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Geiger-Mueller Experiment February 25, 2014 Instructor: Prof. Robert Kramer Dane Mettam

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Page 1: Geiger-Mueller Counters

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Geiger-Mueller Experiment

February 25, 2014

Instructor: Prof. Robert Kramer

Dane Mettam

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1. Abstract

The primary purpose of this experiment was to consider the setup, use, and characteristics

of a Geiger-Mueller (GM) counter. Americium-241 was used to check the GM counters

operational condition by varying the supplied voltage to the counter as it detects the

decay of the source and observe the plateau region that is created as voltage increases.

This plateau region is the GM counters operational voltage range and should have a slope

less than 10% to be considered good, the counter used was computed to have a slope of

5.62±0.17%. The GM counter was then used to determine the nuclear decay of

Barium-137m. The Bariums decay count (c) was recorded every 30 seconds for 15

minutes to observe the decay activity (A). The time it took for the activity to half itself

from a specific start time with a given activity is the samples half-life (𝑇12 ). Bariums 𝑇1

2

was algebraically found to be 2.51±0.27 minutes and with a percent error of 1.44%. It

was then found again graphically to be 2.51±0.27. The actual 𝑇1 2⁄ of Ba-137m is 2

minutes and 55.1 seconds.

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2. Introduction/Background

The Geiger-Mueller tube and counter is used to

measure radioactive decay. There is a thin mica window

in the tube that gets pointed at the source. A voltage

source is connected to the tube to provide a potential

difference within it. The inner wall of the GM tube is

positively charged while an inner wire is negatively

charged. An inert gas fills the space between the charged

walls and wire which is usually either Helium or

Argon. When a radioactive source is placed in front of

the tube, it releases alpha, beta, and or gamma radiation

which enters the tube. (There is no way to differentiate

between the 3 types of radiation with a GM counter). The

radiation ionizes the gas within the tube and knocks off loose electrons from the stable

nuclei. The loose electrons go towards the positively charged walls and the positively

charged nuclei goes to the negatively charged wire. This produces a small electric

current. The current pulse created from the ionized gas is the scalar count. There is a

count every time the radiation ionizes the gas.

If there is not a high enough voltage in

the tube then the electric field within it will

be too small to create the pulses. The minimum

voltage required to begin detecting the counts

is the starting voltage. As the voltage increases,

the counts increase rapidly and will eventually

increase less rapidly. The point it does this is

the threshold and immediately after this threshold

is the GM plateau region. This plateau is not

completely flat and should have a slight angle.

A good GM counter will have less than a 10% increase in counts per 100 volts. A tube

with 3% per 100 volts or better is considered excellent. The middle of the plateau is

known as the operating voltage. This plateau region does not last if more voltage is

applied. The counts will increase exponentially if too much voltage is applied. This jump

in counts is minimally affected by an increase in detecting the radioactivity. A continuous

discharge is the result of a process called multiplication. Multiplication is when the

electrons released in the tube from ionization acquires enough energy to cause further

ionization in its next collision with the wall. The photo-electric effect is seen here. This

amplifies the charge on the electrodes. The charge builds up and can create a spark which

will damage the GM tube. To prevent this, a quenching agent is used to quench the

discharge process. Ethyl alcohol is a common quenching agent that absorbs the emitted

energy which dissociates the agent while preventing further ionization. A high enough

applied voltage will damage the tube. The tube in this experiment uses a halogen

Image 1:

Inside diagram of a GM Tube

Continuous discharge

Image 2:

Example graph of a decaying source

Page 4: Geiger-Mueller Counters

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quenching agent which prevents deterioration of the tube. Excessive use of ethyl alcohol

will damage the tube.

Different positions and distances of the source (with respect to the tube) will also

vary the decay detected by the GM counter. The metal casing on the side will absorb

radiation to prevent ionization within the tube so the source should be in front of the mica

opening and relatively close to capture a greater amount of the decay.

Once the operating voltage has been obtained, it can be used on a sample to

measure radioactivity and the half-life of a substance. For this experiment, Barium-137m

is used. The Barium used is created by disintegrated CS-137. The Barium, newly formed,

is in a very excited state. To stabilize it will emit gamma radiation. The diagram below

shows the decay of Cesium into Barium and then the isomeric transition of Barium. The

Barium decay is as follows: 𝐵𝑎56137𝑚 → 𝐵𝑎56

137 + 𝛾. The gamma radiation ionizes the GM

tube and the activity is seen on the counter. The nuclei decaying in the sample is directly

equivalent to the activity being observed from the sample. The time it takes for half the

nuclei to decay is Ba-137m’s half-life. The total activity observed by the counter will be

half in the same amount of time since one half the nuclei has decayed; half the counts

will be observed.

It is hypothesized that the observed half-life of Ba-137m will be 2 minutes 55.2

seconds so long as the GM tube and counter are observed to be good. The observed

activity of the source should closely reflect the half-life. The half-life should be seen by

statistically analyzing the number of counts every 30 seconds and finding the closest time

to the half-life over multiple trials. This experiment will be a success if a consistent half-

life is observed and the GM tube is good. It will be a failed experiment if one or both is

not observed.

Image 3: 𝐶𝑠137 𝑑𝑒𝑐𝑎𝑦 𝑐ℎ𝑎𝑖𝑛

Page 5: Geiger-Mueller Counters

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3. Equipment Description and Procedure

Image 4:

Geiger-Mueller Model 3 Survey Meter

400-1500Vdc

Image 5:

Beta Gamma Detector Model 44-38

900V Operating Voltage

Image 6:

Left: High Voltage Power Supply

Right: GM Counter, Digital Scalar

Image 7:

Meter Face 202-330

Model 44-7

Image 8:

Americium-241 Image 9:

Barium-137m

Image 10:

Planchettes

Image 11: Oscilloscope, Model V-222 Image 12: Switch Box Image 13:

BNC Cables

Page 6: Geiger-Mueller Counters

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1. Connect the power supply, switch box, counter, oscilloscope, GM meter, and GM

tube together with BNC cables.

2. Set oscilloscope to 0.5ms for time/div, 2V for volt/div, on auto mode, and to

measure AC.

3. Obtain a sample of Americium-241 and place it in front of the GM tube.

4. Turn on the digital scalar to count and the high voltage to zero. 5. Increase supplied voltage until the scalar begins to count. This is the starting

voltage. Record this voltage as exactly as possible.

6. Measure the number of counts with the starting voltage for 30 seconds. 7. Increase the supplied voltage by 25 volts then record the number of counts in a 30

second interval. Do this until the start of the continuous discharge region is

observed. Record this data and plot the count rate vs. applied voltage.

8. Find the plateau region and identify its center. 9. Using the applied voltage that is in the center of the plateau region, take 10

measurements of the same source at the same distance from the tube and record

the data.

10. Repeat step 9 but without the Americium source. This is to observe the

background radiation.

11. Redraw the source counting graph to account for background radiation. The

variance will be the square root of the count number for each point.

12. Calculate the plateau slope. Using that, conclude if the GM tube is good or bad.

13. Test different geometric positions and distances of the radioactive source from the

GM tube. Record the counts and use the same operating voltage for each position.

All positions should have 10 data points. Identify how background readings

change the conclusion.

14. Put away Americium sample and prepare the sample of Barium-137m into a

planchette. Place it by the Geiger tube front.

15. Turn on the counter and supplied voltage at the same time. 16. Observe and record every 30 seconds the count number. Continue doing this for

12-15 minutes.

17. Graph the counts vs. time and determine the natural log value of each count and

re-graph. Put a trend-line into each graph.

18. Calculate the half-life of Barium-137m and compare it to the published vale.

Page 7: Geiger-Mueller Counters

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4. Data

When voltage is applied to the GM tube, pulses appear on the oscilloscope and the

pulses appear to span 3.2 volts and cover 55msec. Over a 30 second time frame, 554

counts are observed and at 716.5 volts applied.

Americium was used to determine the operational voltage for the given GM tube.

(Table 1) It was then graphed (graph 1) and the middle of the plateau was used in the next few

measurements of Americium. The operational voltage was used to get ten data points of

Americium and then calculated to find the error on the GM tube. The background

radiation was then measured by removing the Americium (Table 2). The background

radiation is reflected within graph 1. From graph 1, the plateau can be measured to

evaluate whether the GM tube is good or not.

GM Tube Operational Voltage (Table 1)

Counts 0 554 727 786 849 901 892 877 937 992 Volts 691.5 716.5 742 767 792 817 842 867 892 917 Ln(count) N/A 6.317 6.588 6.666 6.744 6.803 6.793 6.777 6.843 6.900 C-12.4 0 541.6 717.6 773.6 836.6 888.6 879.6 864.6 924.6 979.6

825 Applied Voltage (Table 2)

Source 829 877 844 883 806 807 850 843 860 842 NoSource 13 12 10 10 12 14 17 11 14 11

From table 2, the errors are then calculated. First, both rows are summed and then divided

by the number of trials to give the mean number. The mean for no source was subtracted

from the values in table 1 before graphing in graph 1.

0

200

400

600

800

1000

650 700 750 800 850 900 950

Nu

mb

er

of

Ion

s C

olle

cte

d

Voltage (V)

Americium Source Counting Graph

Graph 1:

Page 8: Geiger-Mueller Counters

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The sum of the sourced counts at 825V divided by 10 was 845.1 counts. The same

for the background radiation observations was found to be 12.4 counts. The below

formula was used to find the error of both. The counts are abbreviated as (c), N is the

total number of trials, and σ is the error. The mean is subtracted from each individual trial

then squared. All ten of those calculations are then summed together and then divided by

to total number of trials minus one. The square root of that is the error.

𝜎 = √∑(𝑐𝑖−𝑐̅)2

𝑁−1

An example calculation is done from the background radiation measurement

below. The top row is each individual (𝑐𝑖 − 𝑐̅)2 which is followed by the sum, division

by N-1 and then finally the error itself on the second row.

0.36 0.16 5.76 5.76 0.16 5.76 21.16 1.96 5.76 1.96

48.8 5.42 ±2.329 12.4±2.3 counts Table 3

The Count error is ±28.0 which is the error of both added together. The slope of the

plateau is now calculated with the formula given below.

𝑆(% 𝑝𝑒𝑟 100 𝑉) =2(𝑁2−𝑁1)∗104

(𝑁1+𝑁2)∗(𝑉2−𝑉1)

𝑁1 is the count number at the beginning of the plateau while 𝑁2 is the last count taken at

the end of the platue. 𝑉1 and 𝑉2 are the same things but with voltages. An example

calculation of this is as follows:

% =2(901 − 877) ∗ 104

(901 + 877) ∗ (865 − 817)=

2(24) ∗ 104

(1778) ∗ (48)=

480,000

(85344)= 5.62%

The Americium-241 sample was placed in three additional locations and on each

location it was either elevated 38mm in the up columns or elevated by 21mm in the down

columns in the table on the next page. Each position created very unique counts. Both

250mm away and 35mm at the side had the same results. It showed that even though

there is a steel wall blocking the Americium from getting in the tube from when the

source was at the side, the radiation still gets inside. This is probably due to gamma rays

bouncing off of surfaces and into the GM tube. The longer distance one had a straight

shot into the tube but with more distance, that radiation had more of a chance to spread

out so the GM tube cannot detect the radiation that went around it. The most interesting

result was when the source was directly in front of the tube. When elevated, the tube

measured a sizable amount of counts but when it was lowered by just 17mm, the

radiation measured was reduced in half. This drastic reduction clearly shows the

limitations of the GM tube. If a source is not close and directly in front of it, the tube will

not take in all of the radiation and the resulting counts will be inconclusive. It is also

interesting to note that in every case, the slight elevation increased the number of counts.

Equation 1

Equation 2

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35mm up 35mm down 250mm up 250mm down 35mm up side 35mm down side

1 756 348 52 51 55 43 2 746 337 55 44 58 46 3 737 344 53 38 71 53 4 740 369 52 50 51 43 5 727 346 48 38 62 40 6 755 315 42 35 68 45 7 746 316 59 39 60 45 8 727 335 62 46 68 50 9 749 344 53 47 54 53 10 694 349 44 48 59 41 Total 7377 3403 520 436 606 459 Avg. 737.7 340.3 52.0 43.6 60.6 45.9

While a GM tube can detect alpha, beta, and gamma radiation; it cannot

differentiate between them. The counts for the different types of radiation cannot be

separated with it. Background readings influences the tube on all measurements evenly

and when measuring hundreds of counts it is almost negligible but as you get less counts

the background begins to become significantly more disruptive.

The last chart depicts the half-life of Barium-137m. It was measured every 30

seconds for 14 minutes and 30 seconds. The chart shows the algebraic formation of the

half-life with a brief example of how I determined each individual half-life. The top 𝑇1 2⁄ for each trial shows the half-life measured from the bigger number, dividing by 2

and then going down to the nearest time that matches that number. The second 𝑇1 2⁄ does

the same thing but from the bottom up and doubling the amount of counts and seeing

which time best matches its count. Doing it both ways gave similar results. There were

some counts that were right in-between two different times so the time was split between

the two times. This was done if the difference was ten counts or less. The half-life times

were then all summed up and then divided by the total number of trials (48) to give the

mean half -life.

Table 5 on the next page also has the natural log of each individual counts. The

graph of the natural log also gives the half-life. The slope of the line is the decay constant

(k) and is directly related to the half-life with the following equation.

𝑇1/2 =0.693

𝑘

As seen on graph 2 on the next page, the slope of the line as measured by excel is 0.2442.

When plugged into equation 3 the half-life of Barium becomes 2.838. To put the second’s

portion into a more recognizable form it is treated with equation 5 which is described on

the next page, to make it a half-life of 2 minutes and 51 seconds plus or minus 0.27

seconds or 2.51±0.27minutes.

Table 4:

Equation 3

Page 10: Geiger-Mueller Counters

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y = -0.2442x + 7.1107

0

1

2

3

4

5

6

7

8

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

ln (

acti

vity

)

Time (30 sec)

Ln(activity) vs. Time

Graph 2:

Time 0.30 1.00 1.30 2.00 2.30 3.00 3.30 4.00 4.30 5.00 5.30 6.00

C 1220 2190 3040 3800 4450 5015 5530 5985 6390 6750 7100 7376

c/30s 1220 970 850 760 650 565 515 455 405 360 350 276

𝑇1 2⁄ 2.15 2.45 2.45 3.00 3.00 3.00 2.45 3.00 3.00 3.00 2.30 2.30

𝑇1 2⁄ N/A N/A N/A N/A 2.00 2.30 2.30 2.45 2.45 3.00 3.15 3.00

ln(c) 7.11 6.88 6.75 6.63 6.48 6.34 6.24 6.12 6.00 5.89 5.86 5.62

Time 6.30 7.00 7.30 8.00 8.30 9.00 9.30 10.0 10.3 11.0 11.3 12.0

C 7620 7846 8060 8237 8386 8504 8599 8709 8810 8900 8967 9044

c/30s 244 226 214 177 149 118 95 110 101 90 67 77

𝑇1 2⁄ 2.30 3.00 2.45 3.00 3.30 2.45 3.30 3.30 3.00 2.45 2.50 2.00

𝑇1 2⁄ 2.45 3.00 3.15 2.45 2.30 2.15 1.30 2.45 3.00 3.00 2.45 3.30

ln(c) 5.50 5.42 5.37 5.18 5.00 4.77 4.55 4.70 4.62 4.50 4.20 4.34

Time 12.3 13.0 13.3 14.0 14.3 C=total counts

C 9110 9185 9235 9279 9335 c/30s=counts per 30sec

c/30s 66 25 50 40 56

𝑇1 2⁄ N/A N/A N/A N/A N/A ∑ 𝑇1 2⁄ =68.25 ∑ 𝑡𝑜𝑡 = 136.75 𝑇1/2100=2.849

𝑇1 2⁄ 3.45 N/A 3.00 3.00 4.00 ∑ 𝑇1 2⁄ =68.50 N=48 𝑇1/2=2.509

ln(c) 4.19 3.22 3.91 3.69 4.03

Barium-137m’s half-life was observed to be 2.51±0.27 minutes. The error calculation for

Barium-137m was done with equation 1 on page 7 and in the same matter as the example

given immediately after. To calculate the mean time and error the times had to first be

translated into an easier format. Since seconds are measured in 60 second intervals rather

than 100 with everything else, the seconds on the times had to be converted to the other

format. The minutes were kept the same. The seconds were divided by 60 and multiplied

by 100 to put them into a more easily calculable format. After the mean and error was

found the times were converted back by dividing the second’s part by 100 and

multiplying by 60.

𝑇1/2 =100∗𝑇100

60

𝑇100 =60 ∗ 𝑇1/2

100

Table 5:

Equation 4

Equation 5

Page 11: Geiger-Mueller Counters

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The total amount of alpha decay for the time period is seen in graph 3 below.

Clearly it can be seen that the total counts are increasing and a decreasing rate and is

approaching a limit. Unfortunately, because of the background radiation, it was not

possible for this observe that limit. This limit is fast approaching. The error bars attached

to each point is the square root of that value at that point.

If the counts for each 30 second interval is graphed the reverse picture is seen. In

this format it is also easier to see the limit which is zero. The background radiation will

prevent it from reaching that point but it is still easily seen.

0

2000

4000

6000

8000

10000

12000

-2.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00

Alp

ha

De

cay

Time (minutes)

Total Alpha Decay w/ Time

Graph 3:

0

200

400

600

800

1000

1200

1400

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

Act

ivit

y (A

lph

a D

eca

y)

Time (minutes)

Activity vs. Time

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5. Analysis

This experiment was conducted to familiarize myself to a Geiger-Mueller counter

and its applicable equipment. In the experiment the GM tube was tested to see if it was

good or not. A good GM tube’s plateau region should have less than a 10% increase in

counts per 100 volts, the tube tested had a 5.62% which shows that it is in fact good. It

was also observed that the background radiation was on average reading 12.4±2.3 counts

every 30 seconds. This background radiation affected every part of the experiment and it

is impossible to tell if the counts were from background radiation or from the source. It

didn’t affect the experiment too much but to compensate for this, the mean count from

the background was subtracted from each trial. However, this was not done on the second

part of the experiment when measuring the decay of Barium-127m. The subtraction was

only done on any count with Americium.

The second part of the experiment tested the half-life of Barium and it was

observed to be 2.51±0.27. The same half-life was found in two different methods. On

method simply took the slope of the curve from the natural log of each 30 second count.

The other method took each individual count and found the time that most closely

matched it within table 5. It then took the lowest numbers and doubled them and found

the time on the table that most closely matched its double. All of those times were

summed up then divided by the total number of times. The actual half-life is

2.551minutes or 2 minutes and 55.1 seconds. The percent error of the observed half-life

is 1.44%. The measured half-life is not only within the margin of error but it is also

accurate.

Background radiation was not the primary source of error. The two primary

sources was in the actual measuring. When taking 30 second interval counts, the counter

was switched on and off by physically flipping a switch. There is no way of telling if

every trial had exactly 30 seconds and it is generally assumed that every 30 second

interval had an error of plus or minus 1 to 2 seconds. While measuring the half-life of

Barium, the error wasn’t in flipping the switch but in reading the number of counts. The

counter was kept on for the duration of the measurement and the count number was read

every 30 second but not stopped. It would change so rapidly that the error was within 25-

10 counts per 30 second sequence. As the Barium deteriorated, the counts slowed down

and the count number error reduced eventually to plus or minus 1 to 5 counts.

Throughout the entire procedure, the count number was read at approximately 30 seconds

and not exactly 30 seconds but evened out since the timer was left to run the whole time

as well. To alleviate the counting and timing errors, the GM tube should in the future be

connected to a counter with a timer attached that can electronically record the counts per

pre-designated time interval. This would significantly reduce the error. The best way to

deal with the background radiation is to have another GM tube measure it while the

primary tube is measuring the source and to subtract the background from the counts. All

error calculations were done with statistical analysis.

No odd trends in the data that was not expected were noticed. There was however

a minor error in one count with the measurement of Barium when the count got to 25. It

can be seen on graph 2.

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6. Conclusion

The setup, use, and characteristics of the Geiger-Mueller counter was tested and

used to observe the half-life of Barium-137m. The was shown that the GM counter works

best when the source material is directly in front of its mica window so its radiation can

enter the tube. The closer the source is, the better. It was also found that when the source

is placed at the side of the tube, it does not measure much of the radiation due to the

metal shell shielding the tube. The plateau region of a GM tube was found to be between

817 and 816 volts. The half-life of Barium-137m was found to be 2.51±0.27 minutes. The

actual half-life of the source is 2.55 minutes which shows that the GM tube is accurate.

The whole experiment was a complete success.

Page 14: Geiger-Mueller Counters

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7. References

(n.d.). Retrieved from https://www.csupomona.edu/~pbsiegel/phy432/labman/geiger.pdf

BNC [Web Photo]. Retrieved from http://www.cdint.com/catalog/category/Cables

Lab handout: PHYS 34300 Modern Physics; Robert Kramer, spring 2014 34300 lab.

Ludlum measurments. (n.d.). Retrieved from http://www.ludlums.com/products/survey-

meters/gm-survey-meters

Mettam, Dane. 2013. Photograph. n.p. Web. 25 Feb 2014.

Nuffield foundation. (2007, August). Retrieved from

http://www.nuffieldfoundation.org/practical-physics/geiger-müller-tube

Physics 252 experiment no. 9 the geiger counter. (1998, August 14). Retrieved from

http://skipper.physics.sunysb.edu/~joanna/Lectures/PHY-251-

252/PHY252/HTML_Version/251-09 The Geiger Counter.htm

Zable, T. (n.d.). Experiment: Measurement of ba-137 decay & half-life. Retrieved from

http://spot.pcc.edu/~azable/ph203/labs/203-Lab09X_NuclearDecay-short.pdf