Geiger Müller Tube – Lab Report 4 copy PDF

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Geiger-Müller Detector

Abstract: This experiment was conducted to measure the efficiency of a GeigerMüller tube using Strontium-90 and Cobalt-60. To do this the correct operating voltage of GM tube was found to be 770V, and the background radiation of the laboratory where the experiment was conducted rb = 0.67  0.03 s-1. With this data the deadtime of the Geiger-Müller tube was found to be  = (495  27) s and then the efficiencies of the GM tube for a source of Strontium90 and for Cobalt-60 were found. These were found to be 4.3% for the Cobalt-60 source and 107% for the Strontium-90 source. As an efficiency of over 100% is not physically possible, it was concluded that the data gathered to obtain this efficiency for the Strontium-90 source was inaccurate, suggesting that either the apparatus used in the experiment was faulty or that the uncertainties in the experiment were not accounted for properly.

Theory Radiation is a naturally occurring phenomenon in the world that occurs because of the decay of unstable isotopes into more stable ones. During this decay process, an atom can emit subatomic particles1 (known as alpha or beta radiation) or energy (known as gamma radiation). As all these types or radiation have energy, and when they interact with molecules, they can cause particles to break chemical bonds in a process known as ionization. For humans on earth, exposure to radiation can lead to the breaking down of cells in the human body which can be deadly. One such example of this is skin cancer caused by prolonged exposure to the sun’s rays2 because while the earth’s atmosphere absorbs some of the radiation from space, it does not absorb all of it. The radiation that reaches earth’s surface interacts with molecules in the human body and leads to the breaking down of cells. This process is invisible to the eye, however the charged particles that the ionizing radiation creates as it passes through a gas can be measured and provide an indication of how much radiation is passing through a gas. This is the theory underpinning the operation of a Geiger Counter, invented by Hans Geiger and Walter Müller in the early 20 th century3. A Geiger Counter consists of a large metal cylinder filled with a low-pressure gas sealed in by a fragile end window at one end of the GM counter. A thin metal wire runs down the center of the tube and is connected to a high voltage power source, so that a strong electric field exists between it and the outside of the GM tube. The thin window allows radiation to enter the GM counter, and when it ionizes molecules of the gas in the tube, the charged particles are attracted to the high voltage wire in the middle of the tube. When they arrive at the wire, they cause a pulse of electricity that can be detected and measured on a meter. In this way, the number of radioactive particles or rays that have entered the GM tube can be measured. A diagram of how this works is shown below (figure 1.0)

Radiation entering the tube

Short current pulse produced by ionized particles

Fig 1.0 – Geiger Müller Counter Radiationoperation ionizing particles of the gas

While there are many types of gas-filled detectors that include ionization chambers and proportional counters, what determines their response to ionizing radiation is the strength of the applied electric field between the inner wire and outside of the GM tube. For a Geiger Müller counter, the

relationship between count rate and applied voltage contains a plateau where the obtained count rate is independent of the applied voltage. This means that a GM counter receives an output pulse of the same magnitude regardless of the energy of the incoming radiation, and for this reason the tube cannot differentiate between radiation types. The various operating regions of gas-filled detectors are shown in figure 1.1 below.

Number of Ions collected

Regions of Operation for Gas-Filled detectors

Fig 1.1 – Operating regions for gasfilled detectors4

Detector Operating Voltage (V)

As figure 1.1 shows, the Geiger-Müller region has a plateau where the number of ions collected is the same for particles of different energy. With this knowledge the operating voltage of the detector can be determined by mapping out the plateau region and reading off the voltage halfway across this region. The sources used in this experiment consist of both beta decay and gamma decay, and since the GM tube cannot differentiate between energies of incoming radiation, the counts it records for each source do not indicate what type of radiation each source emits. In addition to this, as a radioactive particle or ray enters the GM tube it may cause a discharge from a charged particle that, in the period immediately following the discharge, causes the electric field in the tube to drop below its normal operating value. This means that there is a period of time during which the GM tube is unable to measure later particles entering the tube until it has returned to a sufficiently close enough operating voltage value. The time during which the GM tube is unable to measure later particles is called the dead time of the tube. The relationship between the true count rate R, and the observed count rate, can be expressed as R=

R0 1−R 0 T

[1]

where T is the dead time of the GM tube. The dead-time of the GM counter can be determined using the two-source method. Firstly, the count rate given from one source can be measured (r1) and then, placing a second source beside the first one (without disturbing the position of the first source), the count rate of two sources together (r12) can be measured. Then, removing the first source, the count rate of just the second source can be measured (r2), and then removing all sources, the background radiation can be taken as rb. If the true count rates for all of these sources are written as R1, R2, R12 and Rb then they can be related by: R1 + R2= R12 + Rb

[2]

Combining this equation with equation [1] yields a simplified equation that relates the dead time of the GM tube to 4 different count rates: 1 1 1 1 + = − 1−r 1 T 1−r 2 T 1−r 12 T 1−r b T

[3]

Since the count rate of the GM tube is the number of counts recorded over N time, r i= i equation [3] can be written in terms of the counts Ni and a t T dimensionless variable x= t This produces the following relationship: 1 1 1 1 + = − 1−N 1 x 1−N 2 x 1−N 12 x 1−N b x

[4]

This relationship can be programmed to produce a value for x, and therefore T = xt. This was how the dead time of the GM tube in this experiment was found. In this experiment, a Geiger Müller counter was used to measure various count rates for different radioactive materials. Other features of the Geiger counter, including its efficiency and deadtime, were also investigated.

Experimental Procedure: The first step in this experiment involved determining the operating voltage of the GM tube. This value would determine where the operating voltage of the GM tube should be set to for the GM tube to obtain count rate data later in the experiment. The operating voltage of the GM tube was found by mapping out the GM plateau region given theoretically in figure [1.1]. This was done by graphing various count rates (N/T) as the

tube voltage increased. The operating voltage could then be read off as the voltage halfway across the plateau region. The GM tube was then set to this operating voltage and the background radiation of the lab was determined. This was achieved by removing all radioactive sources from the vicinity of the GM tube and the number of counts recorded over 10 minutes were recorded. From this measured count number the number of counts per second could be found. The dead time of the GM counter was then found using two different sources of Strontium90. The first source was placed in front of the GM tube and the number of counts recorded over 1 minute (60 seconds) was found. The second source was then placed alongside the first source and the number of counts recorded from both these sources measured over 60 seconds. The first source Strontium source was then removed and the number of counts measured by the GM tube over 60 seconds for just the second source was found. The dead time programme in MatLab was then used to find the dead time of the GM counter. Following this the efficiency of the detector for the two different sources was determined. As the source can be considered isotropic (emitting particles in all directions) the fraction of particles that the GM tube detects is proportional to the ratio of the area of the GM window to the surface area of a virtual sphere around the source. The activity of the source at the current date was determined using the half-life of the source, and then multiplying this activity to the ratio of particles detected by the GM tube, the number of counts that the detector was expected to read per second was found. The GM tube was then used with firstly the Cobalt60 source and then the Strontium90 source and the number of counts that the detector actually measured was recorded for each one. The efficiency of the detector for each source was then determined as the efficiency is given by the observed number of counts divided by the expected number of counts. From this the detector efficiency of the GM tube for both Cobalt60 and Strontium90 was determined.

Results & Analysis: Determining the Operating Voltage of the GM tube: Firstly the threshold voltage (where the count rate of the GM tube is constant) was found. This threshold voltage determines the point on the graph shown in figure [1.1] where N/T is equal to zero. Using the Strontium90 source, the threshold voltage was found to be just below 700V at approximately 690  10 V. The voltage of the GM tube was then altered to 850 V and the Strontium source moved to a distance so that the count rate was around 100 counts per second. Then, in steps of 10V from 700V to 850V, data for the counts recorded over 30s was gathered.

As radioactive decay is a random process, the uncertainty on the number of counts, N, recorded is given by √ N . For the percentage uncertainty on N to be 1% or less, the value of N measured must therefore be of the magnitude 104, and if the count rate is 100 per second, then the required timing interval for this uncertainty must be  100 seconds. Since a 3% uncertainty is acceptable it was decided that the timing interval over which N should be recorded would be 30s. This timing interval shortened the exposure time while still ensuring the uncertainty on N was not disproportionately large. The voltage of the GM tube was varied by 10V from 700V to 850V and the count rate was measured over 30s for each voltage measured. This allowed data to be obtained for V, N, and T. From the data the count rate, N/T could also be determined. This data is summarized in table 1.0 given below. Tube Voltage V (V)

700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850

Counts

Time

N

T (s)

Uncertaint y N = √ N

Count Rate

Uncertaint y

N/T (s-1)

N/T (N/N) (s-1)

3882 30 62 129.4 4494 30 67 149.8 4740 30 69 158.0 4821 30 69 160.7 4925 30 70 164.0 4965 30 70 165.5 4962 30 70 165.4 4893 30 69 163.1 4990 30 70 166.3 4998 30 70 166.6 4945 30 70 164.8 4980 30 70 166.0 5272 30 72 175.7 5242 30 72 174.7 5344 30 73 178.1 5550 30 74 185.0 Table 1.0 – Data for determining operating voltage

2.07 2.23 2.34 2.31 2.32 2.33 2.33 2.36 2.35 2.33 2.33 2.33 2.34 2.33 2.36 2.47 of GM tube.

With this data, the plateau region of the GM tube could be mapped out. This graph was plotted using MatLab (script given in the appendix) and is shown below

Fig 1.2 Determining Operating Voltage of GM tube From this graph it is clear that the plateau region of the GM tube occurs from about 740V to 820 V. The middle of this plateau region is at 770V, and this was what the operating voltage of the GM tube was set to for measurements taken later in the experiment. Determining the background radiation of the lab: As natural and man-made radiation is constantly present in the environment it is also found in the laboratory where measurements were taken for this experiment. Therefore it also had to be measured and considered for measurements in the experiment. The operating voltage was set to 770V and all radioactive materials were removed from the vicinity of the GM tube and the GM counter was then left counting for 10 minutes. Over ten minutes the number of counts recorded by the GM tube were N = 408  20 counts This yields the number of counts per second as rb = 0.67  0.03 s-1

Determining the dead-time of the GM counter: To determine the deadtime of the GM tube used in this experiment, two Strontium-90 sources were used. The first source used had a count rate over 60 seconds of r1 = 20479  143 per min. Then, the two strontium sources were placed alongside each other and the combined count rate found to be r12 = 37926  195 per min. The count rate of the second strontium source was then found to be r2 = 24438  156 per min. As the background radiation of the lab is given by R = 0.67  0.03 s-1 it has a count rate per min of rb = 40.2  1.8 per min.

Using the MatLab dead-time code given in part 2 of the appendix, the dead-time of the GM tube along with its uncertainty can be calculated from these measurements. The dead-time of the GM tube was found to be  = (495  27) s Determining the efficiency of the detector using both Cobalt-60 and Strontium-90: The window through which the GM tube detects counts has a finite size, AGM, and is separated from the source by a distance of lGM. As the source is considered isotropic and emits particles in all directions, the GM tube therefore only detects a fraction of the particles emitted. This fraction is proportional to the ratio of the area of the GM window, AGM to the surface area (ASP) of the virtual sphere around the source (which has a radius lGM). The diameter of the detector window was found to be D = 28.5  0.1 mm Therefore the radius of the detector window is RGM = 14.3  0.1 mm The distance from the source to the GM detector (radius of sphere lGM) lGM = 523  1 mm = (0.523  0.001)m 2 2 −3 2 (14.25 ×10 ) A GM π R GM RGM −4 = =1.8559 × 10 = = 2 −3 2 2 A SP 4 π lSP 4 lSP 4 ×(523 ×10 )

Uncertainty analysis of this ratio yields an uncertainty on the ratio r ∂r 2 2 ¿ δL ∂ lSP ( SP ) ¿ 2 ∂r 2 ¿ ( δ RGM ) +¿ ∂ RGM ¿ δr= √ ¿ so r = (1.86  0.06) x 10-4 . By multiplying the activity of each source by this ratio, the fraction of counts that should be detected by the GM tube can be found.

Source 1: Cobalt-60 The activity of this source in August 2013 was 3.7 M Bq. Since this date, 4.833 years have passed. The half-life of Cobalt-60 is 5.2714 years5. Using this information the current activity of cobalt was found to be

( −ln 2 )×4.833=1.9 ×10 6 Bq

A=3.7 × 106 e 5.2714

As this is the activity of the source emitting particles in all directions, the theoretically calculated fraction of particles emitted in the direction of just the GM tube is equal to −4

6

C c =1.9× 10 × 1.8559 × 1 0 =353 ±13 s

−1

The counts measured experimentally over a time interval of t = 30s was then measured 5 times and an average was taken Trial # 1 N 451 T 30 N/T 15.03

2 437 30 14.57

3 476 30 15.87

4 488 30 16.27

5 471 30 15.70

From these five observed count rate values, an average observed count rate value could be found along with its uncertainty (sample standard deviation) that yielded R0 = 15.5  0.6 s-1 As the dead time of the GM tube means that there are a number of counts that the GM tube does not measure, this observed count rate is not the same as the true count rate. Correcting for the dead-time of the GM tube using equation [1] yields a true count rate value R=

R0 15.5 = =15.6 s−1 1−R 0 T 1−15.5×(495 ×1 0−6 )

The uncertainty on R ∂R 2 2 ¿ ( δT ) ∂T ¿ 2 1−R 0 T ¿ ¿ ¿2 ( δT ) 2 ¿ R 02 ¿ 1 2 2 ¿ ( δ R0 ) +¿ 1−R0 T ¿ 2 ∂R 2 ¿ ( δ R0 ) +¿ ∂ R0 ¿ δR=√ ¿ Therefore the true count rate is R = 16  1 s-1 Correcting this for the background radiation in the lab yields R = 16 - 0.67 = 15  1 s-1

Dividing this by the theoretically calculated number of counts expected to hit the GM tube (Cc) yields the efficiency of the detector: 15 1 =0.04 25 353 13 Therefore the GM tube is 4.25  0.07 % efficient for the Cobalt-60 source.

Source 2: Strontium-90 The activity of this source in November 1995 was 3.1 M Bq. Since this date, 28.8 years have passed. The half-life of Strontium-90 is 22.16 years5. Using this information in equation [1] the current activity of Strontium was found to be 6

A=3.1 ×10 e

2 ×22.16 (−ln 28.8 )

=1.8 ×10 6 Bq

Using the same analysis as for the Cobalt-60 source, the fraction of particles emitted in the direction of the GM tube window was found to be equal to −4

6

C c =1.8× 10 × 1.8559 × 1 0 =338 12 s

−1

The counts measured experimentally over a time interval of t = 30s was then measured 5 times and an average was taken Trial # 1 N 9358 T 30 N/T 311.9

2 9322 30 310.7

3 9296 30 309.9

4 9372 30 312.4

5 9212 30 307.1

From these five observed count rate values, an average observed count rate value could be found along with its uncertainty (sample standard deviation) that yielded R0 = 310.4  0.6 s-1 Correcting for the dead-time of the counter produced a true count rate: R=

R0 310.4 = =366 1 s−1 1−R 0 T 1−310.4 ×(495 ×1 0−6)

Where the uncertainty on R was found using the same analysis as for the Cobalt-60 source. The true count rate for the Strontium-90 source R = 366  1 s-1 Correcting this for the background radiation in the lab yields R = 366 0.67 = 365  1 s-1 The efficiency of the GM tube for the Strontium-90 source is given by:

365 1 =1.07 ± 0.05 338 12 This yields an efficiency value for the Strontium-90 source greater than 100%. As this is not possible, it was concluded that the data contributing to the Strontium-90 count rates was inaccurate, and could have been affected by the close proximity of the other sources that would have increased the number of counts measured over the 30 second time interval. Other factors possibly contributing to this large efficiency value could be the location of the Geiger-Müller tubes window that was facing the table where the other sources were located. These other sources may have contributed to the count on the GM counter, however, as they were surrounded by lead blocks, and the table the GM counter was on also faced lead blocks, all efforts were made to ensure this was not the case and therefore it seems unlikely that these sources affected the efficiency values obtained. Another factor that could have influenced this efficiency value is the way in which the GM counter was operated. The operating voltage may have been changed from the value of 770V which it had been set to for the rest of the experiment, and this would have caused the observed count rate to be greater than it was at a rate of 100 counts per minute. This would mean that the observed count rate was larger as it may not have been measuring at a scale of 100 counts per minute, and therefore when comparing it to the activity of the source that was expected, the efficiency value obtained would be inaccurate.

Conclusions In this experiment, a Geiger Müller counter was used to measure various count rates for different radioactive materials. Firstly the operating voltage at which the GM counter should operate at was found to be 770V. Then the background radiation of the laboratory on the 3rd floor of the Ernest Rutherford building was found to be R = 0.67  0.03 s-1. With this in...