geiger-mueller counters
TRANSCRIPT
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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
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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
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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
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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.
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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:
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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
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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
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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.
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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