Advanced Physics Labs 9/11/08 Radioactivity Modern physics began with the study of radioactivity by Becquerel in 1895. Subsequent investigations by the Curies, Rutherford, and others quickly revealed that nuclear decays produce three distinct kinds of ionizing radiation: alpha, beta, and gamma. In this experiment you will study the operation of radiation detectors and the penetrating properties of these three forms of ionizing radiation. You will also be required to apply basic methods of data analysis. Background In about 1903 Rutherford showed that there are three types of ionizing radiation by separating them in a magnetic field. Alpha particles are helium nuclei ejected from heavy nuclei. Beta radiation consists of electrons or positrons emitted in the weak decays of unstable nuclei. Atomic electrons can also be emitted as secondary particles as a result of decays. Gamma radiation is made up of high energy photons emitted in transitions from excited states of nuclei formed by emission of a beta particle or electron capture. These three forms of radiation are absorbed very differently in materials. For alpha and beta radiations traveling through matter, the interaction of the particles charges with the atomic electrons of the material results in energy deposited by ionization of the atoms. The result is energy loss by the charged particle at a rate de/dx that depends on the particle mass and charge, its energy, and the density and nature of the material. In general, de/dx for a non-relativistic particle is proportional to z 2 m/e where m is its mass and ze its charge. Therefore α particles have much greater de/dx. The particle s range for an initial energy E 0 is related to de/dx. The range, R, is defined by the integral of de/dx: R de E 0 = dx 0 dx Alpha particles have large de/dx and a correspondingly short range R in any material a few cm in air and fractions of a millimeter in matter. For example, a piece of paper or aluminum foil can stop alpha particles. Beta particles have ranges of a few meters in air or a few millimeters in aluminum. Gamma rays are photons and therefore do not lose energy by ionization as α s and β s do. Gamma rays interact with atomic electrons and nuclei in three distinct ways: 1. The photoelectric effect results in the absorption of the photon and transfer of its energy to an electron. The photoelectric effect is an inelastic process because some energy is lost to overcome the binding energy of the electron in the material. This binding energy is the work function and is significant for visible photons, but generally negligible for gamma ray photons. 2. The Compton effect is the scattering of a photon from electrons in the material and results in energy transfer to the electron and a gamma ray photon of reduced energy propagating along a new trajectory at some angle θ relative to the initial trajectory. 3. The conversion of a photon into an electron-positron pair is possible if the photon energy exceeds 1.022 MeV = 2m e c 2.
2 In each of these processes, the incident gamma ray disappears, and the resulting energetic electron (and positron in the case of pair production) deposits energy in the material at the rate de/dx. Gamma ray interactions in matter, therefore, result in attenuation of the gamma ray flux or intensity. For a beam of gamma rays with intensity I(x) where x is the position in an absorber, there is a decrease of intensity di, due to the absorption in a very small thickness dx : di dx = λi where λ is a constant called the linear absorption coefficient in the given material. The solution to this well-known differential equation is an exponential: I(x) = I 0 e λx The length 0.693 / λ at which I = I 0 /2, is called the half thickness. The absorption of alpha and beta radiation, which is due to the interaction with electrons, depends almost entirely upon the density of electrons through which the particles pass. This density, about one electron per proton in the material, changes very little over the entire range of elements. Therefore the thickness in centimeters is usually replaced by the areal density, ρx. Thus de/dx will be in units of MeV/(gm/cm 2 ) and x in units of gm/cm 2. Reading Knoll, Radiation Detection and Measurement, Chapters 5-7 Bevington & Robinson, Data Reduction and Error Analysis, Chapters 1 and 2 on Statistics and data analysis Apparatus A Geiger tube usually consists of a fine tungsten wire placed axially along the axis of a conducting cylinder. These are sealed in a container that is filled with some gas, such as argon, at about one-tenth of an atmosphere of pressure. The central wire is at a positive potential of several hundred volts with respect to the cylinder. In the Geiger tube used in this experiment, the inside wall of the glass is covered with silver, thus eliminating a separate conducting cylinder. In order to understand the action of the Geiger counter, consider it connected as in Figure 1. Figure 1. A schematic diagram of the Geiger tube and circuit. The time constant for recovery of the high voltage after a pulse is τ=rc, where C is the capacitance of the tube.
3 The Geiger tube is connected to a high-voltage source through a resistor R of the order of 10 8 ohms to limit the current. The capacitor C represents the total capacitance of the tube, the input capacitance of the circuit to which the central wire is connected, plus any externally added capacitance. The output of the tube may be connected to an oscilloscope or an amplifier. Consider now what happens when ionizing radiation such as alpha or beta particle, or a pulse of gamma rays enters the tube. The ionization removes electrons from the atoms of the gas, producing free electrons and positive ions. The electrons move toward the positive central wire and the positive ions to the negative cylinder of the tube. If the applied voltage V is small, ~100 volts, no further ionization takes place, and the charge collected on the wire is that produced by the initial ionizing event. The tube is then behaving as an ionization chamber. The free electrons produced by the initial ionizing radiation are accelerated by the electric field in Geiger tube. If the electric field is large enough, these electrons gain sufficient energy between collisions to remove more electrons from neutral atoms in the gas. These secondary electrons are then accelerated and produce more ionization, so that an avalanche takes place. The gas amplifies the original ionization by some factor A called the gas amplification factor. In a limited region of voltage the tube behaves as a proportional counter; that is, the amplification factor A is a constant, and the output charge is proportional to the charge produces by the initial ionizing event. If the voltage is increased further, the tube eventually reaches the Geiger region where the output charge saturates and is almost independent of the charge produced in the initial ionizing event. Before the tube can successfully register a second ionizing event, it must have completely recovered from the first ionizing event. Owing to the presence of ultraviolet photons in the gas discharge, electrons can be ejected from the negative electrode. These electrons can sustain the discharge. The discharge will continue indefinitely unless there is some means of quenching it. There are a number of ways of quenching the discharge, among which are a high resistance R in the electronic circuit, or a small amount of organic vapor mixed with the gas in the tube. This organic vapor absorbs the ultraviolet photons without the production of electrons and thus quenches the discharge. The Geiger region continues for about 200 volts above the threshold voltage, and then the tube goes into continuous discharge that may damage the tube. In a radiation counter the small pulses from the Geiger tube are amplified so that they are above threshold to trigger a comparator circuit and a pulse shaper, which produces a pulse of constant width and amplitude if the pulse from the tube is above a certain threshold. These pulses are then counted in a scaler. A Geiger counter is used to measure or to count the number of ionizing events produced by a source of radiation. Excellent discussions of Geiger tubes and circuits are to be found in the books by Price and Knoll. The response of your Geiger counter depends on tube voltage. With voltage up to a few hundred volts, the amplification is small, and ionizing events do not register scaler counts. Just below the voltage at which the tube reaches the Geiger region, the efficiency increases steadily and then reaches a plateau, after which it becomes almost independent of the applied voltage. This plateau extends for a hundred or so volts. Do not go beyond the plateau because the tube continu-
4 ously discharges and can be seriously damaged. It is usual to operate the Geiger tube from 75 to 100 volts above the starting voltage in about the middle of the plateau. There will always be background even when all known radioactive sources are removed from the vicinity. Background is due to cosmic rays and local radioactive contamination, for example, 40 K in concrete. Their background rate is ~30 counts/minute and can be determined by counting with all sources removed. Things to measure Three radioactive sources are supplied: Polonium-210, Strontium-90, and Cobalt-60. (Others are also available.) The decay rate of these sources is a fraction of a microcurie (1 μci =3.7x10 4 decays/sec). They are sealed (except for the alpha source) and are safe if handled carefully. Polonium-210 ( 210 Po) decays by α-particle emission with E = 5.3 MeV and a half life of 0.39 yr; 90 Sr beta decays with E <2.27 MeV, half life 28 yr; while 60 Co gamma decays with E =1.17 MeV and half life 5.2 yr. When using the sources, make sure you put the business end toward the Geiger tube. Usually this is the unlabelled side, but it s a good idea to check by turning the source the other way and seeing which side gives the higher counting rate. A good web site for information on radionuclides is http://ie.lbl.gov/toi. Also supplied are lead, aluminum, and polyethylene (plastic) absorbers of various mass densities. Be sure to record all pertinent details as you go along. The Characteristic Curve of the Counter We use several different Geiger counters. In this write-up, we ll assume you are using one of the older ones by The Nucleus. Check with the instructor for additional information if you are using a different one. NOTE: In order to count α's the entrance window of the Geiger tube must be very thin, and is therefore very fragile. Do not touch the window or allow anything to contact it. Connect the instrument to 115-volt a.c. power. Turn the High Voltage to 0. Connect the Geiger tube in its housing to the connector on the back of the control box. Set the power switch to the ON position. Reset the counter. Set the time control for 1 minute of counting and test the builtin scaler using the test push button. Set the time control for continuous (Manual) counting and place the gamma-ray source below the tube. Use an external digital voltmeter connected to the Meter terminals on the back to monitor the high voltage. [Be careful not to touch these terminals. The current is small but you can get a significant shock!] Place a gamma source several cm. from the Geiger counter. Slowly increase the voltage and note the reading at which the first counts appear. This is the starting voltage. The operating voltage, which is in the middle of the plateau, should be about 100 volts above this starting voltage. Never increase the voltage more than about 200 volts above the starting voltage on these Geiger tubes as they may go into continuous discharge and be damaged. With the gamma source in place, raise the voltage in successive small steps of about 10 volts from below the starting voltage, and record the number of counts per minute at each setting.
5 You may wish to use larger steps in the plateau region. Do not go beyond about 250 volts above the starting voltage. Do not allow the counter to run wild, i.e., discharge continuously. To reduce statistical fluctuations, use an arrangement such that you get ~1000 counts per minute on the plateau. Plot count rate vs. HV and indicate the starting voltage and plateau on your graph. Determine the slope of the plateau region. Calculate the quality factor defined as Q (1 / N )ΔN / ΔV ) in units of %/(100 volts). Here, N is the average count rate in the middle of the plateau region and ΔN/ΔV is the slope in the plateau. For subsequent measurements, use an operating voltage 100 V above the starting voltage. The Electrical Signal from the Counter Use an oscilloscope to observe the size and shape of the pulses from the Geiger counter. For these measurements it is best to use an analog scope rather than a digital one because the pulses vary significantly in amplitude. Use a coaxial cable to connect from the Oscilloscope connector on the back of the scaler box to the Channel 1 input of the scope. [This is the signal from the Geiger tube, but with a capacitor in series to remove the high voltage. Do not plug the scope directly to the Geiger tube!] Set the scope trigger to trigger on Channel 1 with negative pulses with slope negative. In order to see the true shape of the signals from the Geiger tube you may have to put a 1 KΩ resistor across the input. With the HV set to the middle of the plateau and an α source under the detector, you should see negative pulses ~100 mv about 2 μsec wide. Sketch the pulses. The total charge in the pulse is Q = idt= (V / R)dt where R is the 1 KΩ resistor across the scope input. Estimate Q for the pulses. From this, estimate how many electrons are collected at the anode to form the pulse. Suppose the pulse is initiated by a polonium α that leaves half of its energy in the Geiger tube. It requires ~20 ev of energy to ionize an atom. How many electrons are released by the α particle? Estimate the amplification factor in the avalanche. Observe the pulses from the Geiger tube with a β/γ source. Are the pulses more or less consistent in pulse height? Explain. Make a plot of pulse height vs. operating voltage from the middle of the plateau down to an HV such that the pulses are too small to observe. Make a plot of pulse height vs. HV on a log-log scale. Does the behavior near threshold appear to be a power law? With the HV on the plateau and a high activity β/γ source close to the detector, look at the pulses with the scope sweep speed ~0.5 millisec/div. Look for second pulses following the one that triggered the scope. Is there a minimum time before which a 2 nd pulse can appear? Do the 2 nd pulses change amplitude if they come later? Explain this behavior in your lab report. Be sure to disconnect the cable to the oscilloscope for the next measurements as it will affect the counting rate significantly.
6 Counting Statistics This section requires the lowest possible count rates. Therefore, remove all known radioactive sources from the vicinity of the apparatus so that the counts are entirely due to cosmic rays and radioactivity in the materials of the room. The count rate should be about 20 counts/minute. These background counts can be readily counted and a series of successive measurements may be compared with the values predicted from Poisson and Gaussian distributions. Measure the number of counts for >100 successive time intervals of 3 seconds each. Since the count rate is low, those can be done without stopping the counter. Simply record the scaler events every 3 seconds. The difference between successive numbers gives the required number of counts. Find the number of intervals in which zero, one two, etc., counts per interval and compare to a Poisson distribution, the expected parent distribution. See the Appendix for a brief tutorial on the Poisson distribution. Place the gamma-ray source at such a distance that the scaler reads approximately 200 counts per minute. Observe and record a series of ten readings of the scaler of thirty-second duration. For the ten readings, determine the mean μ, the standard deviation σ, and the standard deviation of the mean. Make a table to compare your results with that expected for a Poisson and a Gaussian distribution. Establish that about 63% of the observed data lie within the range μ - σ and μ + σ. Remove the source and record the background counts for several intervals of at least two minutes. Compute the mean background rate and compare it to that with the source. Shielding With the radioactive sources removed, determine the background in counts per minute. Place the gamma source in one of the lower positions, away from the tube. Determine the number of counts per minute with no absorber present, then with varying thicknesses of lead placed between the source and the Geiger tube. Record the thicknesses and the source distance. Check the background reading occasionally. From the counts per minute recorded for the lead absorbers, subtract the background count rate (beginning and end) and determine the net count rate with uncertainties. Record the results in a tabular form giving the thickness of the absorber, the count rate, and the net count rate with uncertainties in units of counts/minute. Plot the log of count rate vs. absorber thickness. Determine the half thickness d 1/2 (in units of cm and mg/cm 2 and the linear absorption coefficient λ (in units of cm -1 and cm 2 /mg). Determine the range (in units of cm and mg/cm 2 ) of polonium alpha particles in air as follows: Start at a source distance of about one cm and determine the count rate. Increase the distance from the detector entrance window in small steps until the background rate is reached. Note that the count rate decreases with increasing distance, but the product of rate multiplied by distance squared should initially remain approximately constant. To take out the geometric factor, plot rate x (distance 2 ) vs. distance. When estimating distances, be aware that the anode of the Geiger tube does not extend all the way to the thin window, so that the detector is effectively about 0.6 cm away from the thin window. Take this into account in the (distance) 2 term. De-
7 termine the distance in air (in cm) required to stop the alpha particles, and convert this distance to mg/cm 2 of air. The range of beta particles is difficult to measure with a radioactive source because the beta energy is continuous up to some maximum energy, called the endpoint energy. The beta energy spectrum shows that the highest energy, longest range betas are relatively unlikely. Explore shielding of beta radiation with this caveat in mind. Try using aluminum absorbers and look for a sharp drop in rate when the highest energy β s start ranging out. Dead Time The dead time or resolving time of a Geiger counter is the time after a count is registered during which the system cannot detect a subsequent count even if ionization occurs within the counter. Dead time arises due to the time it takes the ionized gas to recover after an event and due to the electronics. It is the minimum time between two events in the Geiger tube that can be distinctly resolved. The dead time for a particular system depends on several factors including: the design of the counter itself, the gas used in the Geiger tube, the voltage applied, and even the count rate. If the dead time is τ in seconds, and the observed count rate is N' counts per second (cps), then the counter is insensitive for a fraction of real time equal to N 'τ seconds per second. Since the emission of particles from a radioactive source is of a random nature, there is as much a chance for pulses to occur during this time interval as during any other equal time interval. In general, the resolution time for the counting system is of the order of a few hundred microseconds. The counting losses due to the dead time are, therefore, expected to be on the order of a few percent for 100 cps. A special pair of sources shaped like quarter moons is available. Arrange them facing the Geiger tube so that the count rate from either is several hundred cps. Measure N ' I and N ' 2, the rate from each of the sources when placed separately in their positions. Then place both sources at the same time in the original positions and measure N 12, the rate with both. Because of counting losses, the number of counts per second from the two sources together, N 12, is less than the sum of the two separately,(n ' 1 + N ' 2 ). You can show that the approximate value of the resolution time is: τ N ' 1 + N ' 2 N ' 12 2(N ' 1 N ' 2 ) Compare this with the minimum time before which a 2 nd pulse can appear that was measured previously. Source Activity Determine the activity of a 90 Sr source. Carefully measure the diameter of the Geiger tube face and the distance to the source so you can estimate the solid angle subtended by the detector. Estimate both statistical and systematic uncertainties. (See the handout on Statistics and Analysis
8 on our web site.) Compare your result to that stamped on the source holder corrected for the decay of activity since the source was purchased. Repeat for 137 Cs. Appendix: The Poisson and Gaussian Distributions The Poisson distribution is appropriate for random processes that have a small probability of happening. A good example is the radioactive decay of a nucleus in this experiment. If the lifetime is ~years and your measurement takes ~1 minute, then the probability that the nucleus will decay during your measurement is very small and the Poisson distribution "works". The Poisson distribution is given by P(x) = μ x e μ / x! where μ is the mean number of counts in the measurement interval, x is the observed number of counts, and P is the probability of observing that number. For example, suppose we measure the background rate 100 times for 3-second intervals. As a shortcut, we can get the mean rate by measuring the rate for a long time. Suppose we get 100 counts in a 300 s interval, so that we expect a mean μ of 1.0 counts in a 3 s interval. Then the probability of getting 0 counts in one measurement is 1.00 0! e 1 = e 1 = 0.368. Thus if we took 100 runs, we would expect to get 0 counts about 37 times. The Gaussian or normal distribution is valid when μ is large(>>>1) and we make a large number of measurements. (We'll settle for ~10!) The probability for a Gaussian distribution is 2 1 x μ 1 P(x) = σ 2π e 2 σ where σ is the standard deviation. For radioactive decay, σ μ where μ is the mean number of counts in our measurement interval. Thus if we had an average of 100.0 counts per measurement, μ =100.0 and σ =10.0. The probability distribution will be a bell-shaped curve centered at μ =100.0 counts with a width determined by σ. Excel has built-in functions, Poisson and NormDist that you can use to make the tables. A good source for more information on data reduction and error analysis is the book of Bevington and Robinson.