OPERATING CHARACTERISTICS OF THE GEIGER COUNTER

Transcription

1 OPERATING CHARACTERISTICS OF THE GEIGER COUNTER OBJECTIVE The objective of this laboratory is to determine the operating voltage for a Geiger tube and to calculate the effect of the dead time and recovery time of the tube on the counting rate. INTRODUCTION Background & Theory In medical and biological research, radioactive isotopes are utilized in three types of measurements: studies of the various chemical and physical interactions within a living organism or with its environment, measurements of the distribution of elements and compounds in the body and measurements of radioactive isotopes in the living organisms without taking samples. The techniques used in these measurements depend on the fact that the radioactive isotopes emit ionizing radiations, which can be detected by their effects on a photographic emulsion, or by electrical methods. Gases conduct electricity only when a number of their atoms are ionized, i.e. split up into a number of free electrons and positive ions. Alpha, beta or gamma radiation emitted by radioactive materials ionizes atoms with which they collide. Hans Geiger, an associate of Rutherford used this property to invent a sensitive detector for radiation. Mica Window Outer Cylinder ( - Voltage) Central Wire ( + Voltage) + α, β, or γ radiation _ R Voltage spike to counter V FIGURE 1: SCHEMATIC OF A TYPICAL GEIGER COUNTER Figure 1 above displays a typical setup for a Geiger counter; it usually contains a metal tube that encloses a thin metal wire along the middle. The space in between is sealed off and filled with a suitable gas; the wire is set at a very high positive electric potential relative to the tube. An electron, positive ion, or gamma radiation that penetrates the tube through a mica (an extremely low density material that minimizes attenuation of radiation as it enters detector) window, will ionize a number of the atoms in the gas, and because of the high positive voltage 1

2 of the central wire, the electrons will be attracted to it while the positive ions will be attracted to the wall. The high voltage accelerates the positive and negative charges, and hence they gain more energy and collide with more atoms to release more electrons and positive ions; the process escalates into an "avalanche" which produces an easily detectable pulse of current. With the presence a suitable filling gas, the current quickly drops to zero so that a single voltage spike occurs across a resistor; an electronic counter then registers this voltage spike. A typical composition of the gas filling a Geiger counter tube was usually a mixture of argon and ethanol; more recently, tubes filled with ethyl formate in place of the alcohol are reported to have a longer life and smaller temperature coefficients than counters filled with ethanol. A very important property of the Geiger counter is its self-suppressing mechanism. The counter is triggered by the pulse from the tube and feeds back a square pulse of µsec duration to the central wire. This pulse has an opposite polarity and high enough amplitude to extinguish the discharge. This allows for the counter to reset as fast as possible in order to register the next voltage spike induced by the penetrating radiation. The Geiger detector is usually called a "counter" because every particle passing through it produces an identical pulse, allowing particles to be counted; however, the detector cannot tell anything about the type of radiation or its energy/frequency - it can only tell that the radiation particles have sufficient energy to penetrate the counter. To improve its sensitivity to alpha and beta particles, the ST150 detector has a very thin mica window with a superficial density of only mg/cm 2. This window is therefore extremely fragile and if broken cannot be repaired. Never allow any object to touch the window! The Geiger Tube Voltage Characteristic Curve The most important information about a particular counter tube is its voltage characteristic curve. The counting rate due to a constant intensity radioactive source is graphed as a function of the voltage across the counter; A curve of the form shown in Figure 2 is obtained. Counting Rate Proportional Discharge Region Start Voltage Geiger Plateau Continuous Discharge Region Geiger Operating Geiger Threshold Voltage V 0 Breakdown Voltage Voltage FIGURE 2: GEIGER TUBE VOLTAGE CHARACTERISTIC CURVE 2 Applied Voltage

3 The counter starts counting at a point corresponding approximately to the Geiger threshold voltage; from there follows a plateau" with little change in the counting rate as the voltage increases. Finally a point is reached where the self-suppressing mechanism no longer works, and the counting rate rapidly increases until the counter breaks down into a continuous discharge. In order to ensure stable operation, the counter is operated at a voltage corresponding approximately to the mid-point of the plateau. Hence, a flat plateau is regarded as a desirable characteristic in a counter; a long plateau is also desirable, but is not as important. In practice most counters have a slightly sloping plateau, partly because of geometrical limitations of the counter design, and partly because of spurious counts due to an unsatisfactory gas filling or to undesirable properties of the cathode surface. The correct operating voltage for any particular Geiger-Mueller tube is determined experimentally using a small radioactive source such as Cs-137 or Co-60. A properly functioning tube will exhibit a "plateau" effect, where the counting rate remains nearly constant over a long range of applied voltage; the operating voltage is then calculated roughly as the voltage value corresponding to the middle of the plateau region. Dead Time, Recovery Time and Resolving Time Geiger-Mueller tubes exhibit Dead Time effects due to the recombination time of the internal gas ions after the occurrence of an ionizing event. The actual dead time depends on several factors including the active volume and shape of the detector and can range from a few microseconds for miniature tubes, to over 1000 microseconds for large volume devices. The counter discharge occurs very close to the wire, and the negative particles, usually electrons, are collected very rapidly. The positive ions move relatively slowly, so that as the discharge proceeds a positively charged sheath forms around the wire. This has the effect of reducing the field around the wire to a value below that corresponding to the threshold voltage, and the discharge ceases. The positive ion sheath then moves outwards until the critical radius r is reached, when the field at the wire is restored to the threshold value. This marks the end of the true "dead time". If another ionizing event triggers the counter at this stage, a pulse smaller than normal is obtained, as the full voltage across the counter is not operative. However, if the positive ions reach the cathode before the next particle arrives, the pulse will be of full size. This effect can be demonstrated with a triggered oscilloscope; as shown in Figure 3, the period during which only partially developed pulses are formed is termed the Recovery Time. The effective Resolving Time or insensitive time following a recorded pulse, is determined by both the dead time and the recovery time, and will depend not only on a number of parameters associated with the counter dimensions and gas filling, but in principle, also on the operating voltage of the counter, on the sensitivity of the electronic recording equipment and on the counting rate. It is necessary to apply appropriate corrections to the observed counting rates to compensate for this resolving time. 3

4 PULSE AMPLITUDE Minimum Input Sensitivity Level of Counter Initial Geiger Discharge Counted Possible Events Not Counted Second Geiger Discharge Counted Dead Time Recovery Time TIME Resolving Time FIGURE 3: A PICTORAL REPRESENTATION OF DEAD, RECOVERY & RESOLVING TIME True versus Measured Count Rate When making absolute measurements, it is important to compensate for dead time losses at higher counting rates. If the resolving time T r of the detector is known, the true counting rate R t may be calculated from the measured counting rate R m using the following expression: R t R = 1 R m m T r (Eq. 1) If the detector resolving time is unknown, it may be determined experimentally using two radioactive sources simultaneously. Maintaining constant counting geometry is important throughout the experiment; hence a special container carrying both sources would be ideal for performing the measurement however, good results may be obtained by careful positioning the two standard sources side by side. With the operating voltage set for the GM tube, denoting the measured count rate for the two sources (a+b) side by side as R(a+b), the measured count rate for source a alone as R(a) and the measured count rate for the source b alone as R(b), the resolving time is given by: R(a) + R(b) - R(a + b) T r = 2R(a).R(b) (Eq. 2) Because of the solid state electronics used in the circuitry of the ST150 Nuclear Lab Station its own resolving time is very short - one microsecond or less and so, not significant compared to that of the GM tube. Therefore, only the resolving time of the GM tube affects the true count rate. 4

5 EQUIPMENT The ST160 Nuclear Lab Station (Figure 4 below) provides a self-contained unit that includes a versatile timer/counter, GM tube and source stand; High voltage is fully variable from 0 to +800 volts. Associated software that allows for operation of ST160 and data collection. Two types of radioactive sources: 137 Cs and 60 Co. FIGURE 4: THE ST- 160 NUCLEAR LAB STATION PROCEDURE 1: Part 1A: Measuring the Geiger Plateau and Determining Operating Voltage 1. **RECORD THE MODEL NUMBER OF YOUR GEIGER COUNTER**. 2. Verify that the Geiger counter has been connected to a power source and to the lab computer. 3. On the desktop, open Launchpad and open STX; this is the software program used to operate the ST-150 lab station. Open MATLAB to prepare for data collection. 4. Switch on the GM Detector. Check that the STX program is now activated. 5. Get familiar with the software program refer to the Intro to STX & Data Extraction video for guidance. 6. Sign out one radioactive source from your TA; record the ID# (Fig. 6A). 7. Place the source on a source tray and slide it into the closest grating to the window of the GM detector. 8. Determine the threshold voltage value of the GM detector: a. Start at around 200V, and run a trial for 10 seconds. b. If there are no counts measured, increase the high voltage by 10V. c. The threshold voltage value is the voltage where you first see radiation counts. 9. Start your data collection at 10V below the threshold value (the counts will be 0) and run the trial for 30 seconds. Increase the voltage in increments of 20V until you reach 800V. Refer to the Intro to STX & Data Extraction video to learn how to do this automatically. 5

6 NOTE 1: If the counts increase dramatically ( counts) before the 800V mark, consult with your TA - you may be irreversibly damaging the tube. Part 1B: Saving Data on MATLAB 1. On MATLAB, clear your workspace. 2. Import the voltage and counts from Part 1A as two separate arrays; refer to the Intro to STX & Data Extraction video for guidance. 3. From the workspace, save these two arrays as a.mat file. As a suggestion, this workspace variable can be named lab1_part1. Refer to the Saving arrays and workspace variables video for guidance. **Part 1: For your report: ** Prelab All answers provided in full sentences (mathematical q s should be typed) Data Analysis: Q1: Provide the answer in full sentences. Q2: Paste the associated m-file code. Q3: Paste the associated m-file code. Q4: Paste the associated m-file code and the graph. Q5: Provide the answer in full sentences. DATA ANALYSIS: 1. In your Report, provide: a. The serial number of your GM counter. b. The ID# of your source. c. The source (isotope) name. Create & Save an m-file named Lab1_Q2to4_Q8to15_ firstname1_firstname2_firstname3.m ; this script must: 2. Load the lab1_part1 workspace variable. Refer to the Creating m.files and loading workspace variables video for guidance. 3. Convert the counts array from (counts/30s) to (counts/min). Refer to the Arithmetic and averages of arrays video for guidance. 6

7 4. Plot the counting rate (counts/min) versus the applied voltage (for example, see Figure 5). Specifically, your graph should have (refer to the Plotting in Matlab video for guidance): a. An appropriate title. b. Labeled x/y axes (with units, where applicable). c. Visible data points. d. A curve through the data points. 5. Determine the approximate value of your instrument s operating voltage. The recommended Geiger operating voltage may be determined as the center of the plateau region. In Figure 5, the plateau extends from approximately 350V to 600V. A reasonable operating voltage in this case would be 500V. FIGURE 5: A TYPICAL GRAPH OF VOLTAGE vs. COUNTS TO DETERMINE OPERATING VOLTAGE PROCEDURE 2: Part 2A: Acquiring the Resolving Time of the Geiger Tube 1. Set the STX to be ready to run 3 trials, each of 30s duration, at the calculated operating voltage. 2. Record 3 measurements of your current source as (a). Note down the ID# of the source. See Figure 6A below for ID# location. 3. Remove your source from the GM detector. 4. Sign out a second radioactive source, same isotope as the first, from your TA and record the ID# of the source. 5. Place the second source on a source tray and slide it into the closest grating to the window of the GM detector. 6. Record 3 measurements of your current source as (b). 7. Remove your second source from the GM detector. 7

8 8. Carefully place one source on top of the other source such that the circumference of the top source grazes the boundary of the label of the bottom source - see Figure 6B below for an example. NOTE 2: Carefully insert the stacked sources into the Geiger counter; not only does this preserve the stacked arrangement, but it ensures that the mica window is not damaged. 9. Record the 3 measurements as (a+b). NOTE 3: For a quick validation, (a+b) should be close, but less than (a)+(b). If it is more, carefully tweak the stack so that the sources are further apart; also, you can switch the order of the stack. For a thorough validation, see Note 4 for details. 10. Once Note 3 has been verified, set the voltage to 0V and switch off the GM tube. FIGURE 6: A) LOCATION OF THE ID# OF A RADIATION SOURCE CIRLCLED IN PURPLE B) PLACEMENT ARRANGMENT OF TWO SOURCES ON THE TRAY USED FOR (A+B) MEASUREMENT **When you have completed the Lab, return and sign out all sources to your TA** Part 2B: Saving Data on MATLAB 1. On MATLAB, clear your workspace. 2. Import the counts from Part 2A in three separate arrays and name these arrays based on the sources used; As a suggestion, these arrays can be named a, b and a_b. Refer to the Saving arrays and workspace variables video for guidance. 3. From the workspace, save these three arrays as a.mat file. As a suggestion, this workspace variable can be named lab1_part2. Refer to the Saving arrays and workspace variables video for guidance. 8

9 Data Analysis: ** Part 2: For your report: ** Q6: Provide the answer in full sentences. Q7: Provide the table. Q8: Paste the associated m-file code. Q9: Paste the associated m-file code. Q10: Paste the associated m-file code. Q11: Paste the associated m-file code. Q12: Paste the associated m-file code. Q13: Paste the associated m-file code. Q14: Paste the associated m-file code. Q15: Paste the associated m-file code and the graph. Q16: Provide the answer in full sentences. Q17: Provide the answer in full sentences. Q18: Provide the answer in full sentences. Q19: Provide the answer in full sentences. Q20: Provide the answer in full sentences. DATA ANALYSIS CONTINUED: 6. In your Report, provide: a. The ID# of your second source. b. The source (isotope) name. c. The orientation of the stack used for (a+b) measurement (which source was on top?). 7. In a table, provide from Part 2A: a. The 3 counts/30s values for (a), (b) and (a+b). b. The counts/min for all 9 values (done in your m-file: Q9). c. The mean counts/min for each of 3 sets of measurements - R(a), R(b) and R(a+b) (done in your m-file: Q10). d. Label the columns/rows and the entire table appropriately. Continue with m-file Lab1_Q2to4_Q8to15_ firstname1_firstname2_firstname3.m ; this script must also: 8. Load the lab1_part2 workspace variable. 9. (For Q7b) Convert the three count arrays from (counts/30s) to (counts/min). 10. (For Q7c) Find the mean of each of the three arrays. 11. Calculate the resolving time of the tube with the calculated values from Q10. 9

10 NOTE 4: If the resolving time multiplied by either source s measured count rate is greater than 1, approach your GA; you may need to redo the (a+b) measurement. See Note 3 for direction. 12. Calculate the true counting rates for your first and second source, using the resolving time (Q11) and the mean count rates R(a) and R(b) (Q10). 13. Calculate the percentage difference between the measured count rate and the true count rate for your first and second source. 14. Convert your first source count array (Q3) into true counts, using the percent difference from your first source (Q13). 15. Re-plot the graph of counts vs. voltage in Q4, and with the calculated true count rates (Q14); make sure each curve is in a different color, and the graph is labelled as per instructions in Q4. Refer to the Plotting in Matlab video for guidance. 16. Determine the value of the normal operating voltage for the true count rates; refer to Q5 for guidance. NOTE 5: You may produce negative true count rates close to the 800V region; this is because the measured count rates are quite large. Please mention this fact in your report if you get negative true count rates. If the plateau region for the true count rates is negative, consult with your TA. 17. How does the resolving time affect the value of the normal operating voltage, when compared to the one determined in Q5? 18. a. Using Equation 1, explain (mathematically) the behavior of the true counting rate if the resolving time increases and decreases with respect to your calculated resolving time. b. Explain how your Q15 plot would change if the resolving time increases and decreases with respect to your calculated resolving time. c. Explain how your Q16 normal operating voltage value would change if the resolving time increases and decreases with respect to your calculated resolving time. 19. Provide two factors that could have contributed error in the lab. 20. Describe how you could improve the impact of the two factors (Q19) to reduce error in the lab. ** Before leaving the lab, confirm with the TA that you have ed the following ** 1) Report (All Prelab and Data Analysis Qs) 2) 1 m-file: Lab1_Q2to4_Q8to15_ firstname1_firstname2_firstname3.m 3) 2.mat files: a. lab3_part1 b. lab3_part2 10