Geiger Counter Experiments andThe Statistics of Nuclear DecayUsing a Geiger Mueller tube, there are a number of experiments we can do. In theclassroom there are two different types of Geiger Counters: commercial and ”homemade” detectors. We describe first how to operate each detector. One of the maingoals of the experiment is to understand the statistics o f nuclear decay, and bothtypes of detectors can be used for thi s purpose. Using either detector, we can mea-sure the efficiency of the Geiger counter, and take successive measurements to see ifthe standard deviation of the total counts are consistent with Poisson statistics. TheHome-Made detector has the additional ability to see the pulse on an oscilloscope andto measure the time between successive pulses. We can check if the fr eq u en c y plotof the successive times are consist ent with the decay being probabilistic. In class wewill decide which experiments we will perform and write up.1. Operating Instructions and Voltage for the Commercial Geiger CounterIn order to determine the proper operating voltage for our Gei ger Counter tubes,we will measure the counts recorded as a function of the tube voltage. Warni n g : Donot put too much voltage across the tube, or the tube will break. For the smalltubes, do not exceed 500 volts, and for the larger t u bes do not exceed 900 volts. Note:Before turning the power on be sure the voltage is set to zero!a) Place a source under the Geiger counter tube. It really doesn’t matter which sourceyou use as long as it is fairly active (greater than 1 µCi). Use a Cs137source if wehave enough to go around, or use one of the more active sources available in the lab(i.e. Co60) t h a t the instructor gives you.b) Set the timer to count for ten minutes.c) Before turning the power on, be sure the voltage is set to zero. Slowlyturn up the voltage until the counter st ar t s to record counts. This is the ”startingvoltage”. Record this voltage.d) Take 1 minut e readings, increasing the voltage by about 10 or 20 volts each time.Make a table of your data.1Note: to prevent damaging the tube, do not increase the voltage morethan 150 volts beyond the sta rt ing voltage, and certainly not more than1000 volts.e) Graph your results on linear paper, and determine the proper operating voltage.Also, on your graph, label the starting voltage and the plateau region.In or d er to assist you (and to prevent damaging the tube), your graph shou l d looksomething like the one shown in the intr oduction on Geiger Counters.2. Operating Inst ructi ons and discharg e puls e for the Home-M ade Ge ige rCountersThere are two control knobs for the home-made Geiger counter: 1) a variabl eresistor (potentiometer) that controls the voltage acros s the tube. a n d 2) a variableresistor that control s the voltage across a pin on the microcontroller. Be sure youknow which potentiometer controls the voltage across the tube, and whichone controls the voltage to the microcontroller. First we will observe the dis-charge on an osilloscope as the voltage acr oss the tube is increased. Then, once wehave a nice discharge pulse, we will slowly increase the voltage that the microcon-troller receives till counts are registered.a) Place a source under the Geiger counter tube. It really doesn’t matter which sourceyou use as long as it is fairly active (greater than 1 µCi). Use a137Cs so u r ce if wehave enough to go around, or use one of the more active sources available in the lab(i.e.60Co) that the i n st r u c to r gives you.b) Connect the oscilloscope across the potentiometer that is on the breadboard. Yourinstructor will draw the circuit diagram on the board.c) Connect the 9V battery. Slowly increase the voltage across the tube until youget a signal on the oscilloscope. Adjust the volt ag e ti ll there is a nice pulse on theoscilloscope.d) Sketch the pulse. Be sure to mark the peak voltage on the sketch, and the timeduration of the pulse.2e) B e sure there are 3 vol t s across the mi cr ocontroller.f) Slowly vary t h e potentiometer and increase the signal to the microcontroller tillcounts are recorded. The counts a r e recorded with LEDs in the binary number sys-tem. You can write down the number of counts in base 2, then convert to base 10.3. Efficiency of the Geiger Counter (Either Geiger Counter)In this part, you will estimate the efficiency of the Geiger-Mueller tube for aparticular source. The efficienc y of the Gei g er counter will depend on the sample, sobe sure to record the dat e of ca l ibration and activity of the sample you used. We willdefine the efficiency, ε, as follows:ε =Nu mb er of Counts Detecte dNu mb er of particles emitted(1)For the Geiger Counter, our value for the efficiency will not be very accurate. This isbecause we cannot tell whi ch type of particle we ar e detecting. We will do a much bet-ter job measuring the efficiency of our gamma detectors in Experiment 3. However,this exercise will give us an estimate of th e Geiger Counter ’ s efficiency. Throughoutthe experime nts use the ope ra t ing voltage that you determined in Part 1.a) Place your sou r ce as close to the tube as you can, and record counts for 2 minutes.b) From the activity written on the source, use the half-life formula to determine theactivity in decays/sec of your source today.c) D et er m i n e the efficiency of the Geiger-Mueller tube for your source-detector set-up.For this calculation, we will assume that the number of particles emitted is equal tothe numb e r of decays. That is, we will assume that one particle is emitted per decay.This is not a good assumption, but it is the best we can do in thi s case.d) Write yo u r value for the efficiency, ε, on the board for comparison with the rest ofthe class.4. Statistics of Nuclear Counting (Either Geiger counter)In this par t of the experiment, we will examine the statistical properties of ra-diation detection. You will take 40 one minute reco r d i n gs with the Geiger counter.3Each group will take their own data with different counting rat es. We will post ourvalues on the board, and check each o t h er s results to inves ti g at e how the standarddeviation of the counts depends on the average number of counts. Throughout theexperiment, use the operating voltage you determined in Part 1.a) Take 40 one minute recordings with your sample at an appropr i a te dist ance fromthe detector. Keep the d i st an ce the same for each recording. We will label each valueas x1, x2, .