Physics 23 Fall 1989 Lab 5 - The Interaction of Gamma Rays with Matter
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1 Physics 23 Fall 1989 Lab 5 - The Interaction of Gamma Rays with Matter Theory The nuclei of radioactive atoms spontaneously decay in three ways known as alpha, beta, and gamma decay. Alpha decay occurs when the nucleus ejects a particle (called an alpha particle) consisting of two protons and two neutrons (i.e., a 2 He 4 nucleus). During alpha decay the atomic number Z of the nucleus decreases by two and the mass number A decreases by four. Beta decay occurs when the nucleus ejects an electron (or a positron), so that Z increases (or decreases) by 1, but A is not changed. After alpha or beta decay, the nucleus of the daughter element is often left in an excited state and will subsequently relax to a lower energy state by emitting a photon; neither Z nor A is changed. This process is called gamma decay and the emitted photon is called a gamma ray. Gamma rays are identical to the photons emitted in atomic electron transitions except that their energy range is higher - typically kilovolts-to-megavolts, as compared to volts-to-kilovolts for atomic transitions (with overlap of the ranges in the x-ray region). Gamma rays interact with matter in three main ways: photoelectric absorption, Compton scattering, and pair production. Photoelectric absorption is the ejection of an inner shell electron by a gamma ray which is totally absorbed in the interaction. For this to occur, the photon must have a minimum energy equal to the binding energy of the electron. The probability of this occurring, the interaction cross section, increases as Z 5, decreases with photon energy and is largest for photons with energies close to the binding energies of inner shell electrons (tens or hundreds of kilovolts). Compton scattering is the scattering of photons by free electrons. Electrons in the outer shells of atoms are so loosely bound (a few volts) as compared to the energy of the gamma rays that they can be considered free. The cross section of this reaction varies linearly with Z and inversely with photon energy. Pair production is the creation of an electronpositron pair from a gamma ray in the field of a nucleus. The minimum photon energy required is 1.02 MeV, twice the rest mass of an electron. When a gamma ray beam penetrates matter, the number of photons in the beam decreases with the depth of penetration as photons are eliminated from the beam by absorption and by scattering out of the beam as shown in figure 2a on the top of the next page. It is relatively simple to derive the mathematical expression describing this process. Let N be the number of photons per unit area per unit time incident on a sample of matter of thickness dx and let dn be the number of photons removed per unit time by a unit area of the sample. The probability that a photon will encounter an atom, and hence be eliminated from the beam, becomes greater with increasing thickness of dx and increasing
2 (a) (b) Figure 1 photon flux N. In other words, dn is proportional to dx and to N. This can be expressed mathematically as dn = -µn x dx (1) where the proportionality constant µ is called the linear absorption (attenuation) coefficient. The value of µ depends on the material of the absorber and it is essentially the probability per unit length that a photon will be absorbed or scattered out of the beam. In the CGS system, its units are cm -1. The minus sign indicates that N decreases as x increases. Rearranging terms in equation (1), integrating x from zero thickness to a finite thickness x and integrating N from an initial incident flux N o to N, the flux emerging from an absorber of thickness x, yields N x = N o e -µx. (2) Equation (2) gives the number of photons per unit time emerging from an absorber of thickness x when the initial incident flux is N o. In some instances µ is replaced by µ m, the mass absorption coefficient. The mass absorption coefficient is defined as µ m = µ/ρ where ρ is the density of the absorber. Equation (2) would then become The CGS units for µ m are cm 2 /g. N x = N o e -µ m ρx. (3) Equation (2 ) can be used to experimentally measure µ and µ m. The experimental technique would consist of placing blocks of varying thickness, x, of the given material into a beam of gamma rays and measuring the number of gamma rays per second, N, which emerge from the other side. Thus, the raw data would consist of a series of (N,x) data pairs. If we take the natural log of both sides of equation (2), we get ln N = -µx + ln N o. (4)
3 If we let ln N = y, -µ = a and ln N o = b, we see that equation (4) is a linear equation of the form y = ax + b. A plot of ln N vs x would be a straight line with a slope equal to µ. Therefore, to obtain an experimental value for µ, we would simply have to plot ln N vs x and compute the slope of the graph. The mass absorption coefficient can be computed from µ and the density of the material. In this lab, you will use this technique to experimentally measure µ and µ m for aluminum and lead. References The sections in Tipler's Modern Physics which are pertinent to this lab are listed below. They should be read before coming to lab. 1. Chapter 3 section Chapter 11 sections 11-3, 11-6, and 11-7 Experimental Purpose The purpose of this lab is to experimentally measure the linear absorption coefficient, µ, and the mass absorption coefficient, µ m, for aluminum and lead. Procedure A schematic of the apparatus to be used is shown in figure 2 at the top of the next page. The gamma rays come from a sealed stainless steel capsule containing 55 Cs 137. (The subscript is the atomic number and the superscript is the mass number). The 55 Cs 137 decays to an isotope of barium, 56 Ba 137, by beta decay. Figure 3 shows a schematic of the transition. In 92% of the transitions, the 56 Ba 137 is in an excited state and relaxes to the ground state with a mean time of seconds by the emission of a 0.66 MeV gamma ray. The sealed steel capsule is attached to an aluminum rod which is inserted into the center of a cylinder of lead called a pig. Radiating from the center of the pig at 90 intervals are four holes called ports. The primary purpose of the pig is to shield the room from the gamma
4 Figure 2 radiation emitted by the source. The walls of the pig are thick enough to absorb almost all of the gamma radiation emitted by the source. On either side of the hole in which the aluminum rod is inserted are two brackets. On the aluminum rod are two posts. When the posts on the aluminum rod are placed into slots on the top of the brackets, the sealed source is aligned with the ports radiating from the center and a collimated gamma ray "beam" exits each of the holes. The gamma rays exiting the ports are directed towards a Geiger tube. The absorbers are hung on an aluminum rod in front of the exit port of the pig. The gamma rays which Figure 3 emerge from the absorber are detected by the Geiger tube and counted by the counter. The oscilloscope is used to display the pulses from Geiger tube, to estimate the dead time of the Geiger
5 tube, and to estimate the time between pulses. The dead time is the time it takes to detect and count one gamma ray. During the dead time, the Geiger tube cannot respond to any other gamma rays entering it. By estimating the dead time and the time between pulses, we can get an idea of the counting efficiency of our system. CAUTION: Excessive exposure to gamma radiation can be harmful. Keep the unused ports of the pig blocked with steel rods and shielded with lead bricks. Do not remove the cesium source from the pig. Keep your hands out of the beam at all times. Wear a film badge at all times while in the laboratory preferably on the wrist of the hand you use to handle the absorbers. The aluminum rod to which the radioactive source is attached can be placed in two positions. When the posts on the aluminum rod are placed in the slots in the bracket on the top of the pig, the sealed source is aligned with the exit ports in the pig and a gamma ray beam is present at the ports. In the procedural instructions that follow, this position of the aluminum rod will be referred to as the "up" position. When the aluminum rod is turned 90 and allowed to drop further down into the pig, the source is no longer aligned with the exit ports and the beams are no longer present at the exit ports. This position of the aluminum rod will be referred to as the "down" position. Except when actually taking absorption data, the sealed source should always be kept in the down position. It is especially important to lower the source before changing absorbers. 1. Sign out a film badge giving all of the required information. If possible, attach the film badge to the wrist of the hand you will use to add and remove absorbers from the hanger on the lead pig. If this is not possible, attach it somewhere on your upper body (e.g. on a shirt pocket or collar). 2. Place the source in the down position. Place the Geiger tube approximately 50 cm from the exit port of the pig. Using the meter stick, align the exit port on the pig, the absorber hanger and the long axis of the Geiger tube. [Note: If you must move the pig to accomplish this alignment, do NOT move it using the absorber hangers. Doing so will damage the hangers.] Without moving the Geiger tube from its aligned position, tape the lead shield surrounding the Geiger tube to its wooden base and then tape the wooden base to the table. Do a thorough job of the taping. Should the alignment change during the data acquisition, any data taken after the change will be invalid (Why?) and you will have to retake all of the data. Check to see that the electronic equipment is wired as shown in figure 2. Set the GATE CONTROL knob on the counter to the RESET position, set the MODE switch to the PERIOD- EVENTS position, set the ATTEN switch to the X1 position and set the TRIGGER LEVEL to
6 midrange. Set the high voltage power supply to 900 volts positive polarity and turn it on. Set the GATE CONTROL on the counter to the SEC-EVENTS position and adjust the trigger level until background counts begin to register on the counter. [Normal background rates are ~ 6-10 counts per 10 second interval.] Alternate the source from the down to the up positions. When in the up position, the counter should rapidly register a large number of counts. When in the down position the counter should return to the background rate noted above. If the detection system behaves in this manner, it is operating correctly and you are ready to take data. If it does not, then there is a problem with your setup and you should notify your TA. 3. Place the source in the up position and observe the pulses from the Geiger tube on the oscilloscope (use the magnification feature of the oscilloscope). If during a pulse, another gamma ray goes through the Geiger tube, it will not be counted. In other words, the counter can only count one gamma ray at a time. The time it takes for the pulse to occur (the width of the pulse) is therefore called the dead time of the system. If the dead time is much much smaller than the time between pulses, the probability of missing rays is small and the efficiency of your counting system high. Sketch the pulse shape and estimate the dead time, the time between pulses and efficiency of the detection system. When done, place the source in the down position. 4. Measure the thickness of each of the aluminum absorbers using the vernier caliper provided. Measure the other two dimensions of the largest aluminum absorber and the diameter of the hole in the absorber. Compute its volume. [Don't forget about the hole when computing the volume.] Measure the mass of the absorber and compute the density of the aluminum. Before taking data, three points should be emphasized. a. The production of gamma rays by radioactive decay is a random process, and so it is necessary to take a statistical approach in which many measurements of similar events are made and the average measurement computed. The greater the number of measurements made, the closer you get to the "true" average, i.e., the better the statistics. For this experiment, this means that measuring N once for a given absorber thickness is not good enough. For a given absorber thickness, you will need to measure N many times to get good statistical data. It is the average value of N as computed from the numerous trials that is used in statistical equations such as equation (2) and in plotting graphs. b. We are not concerned with the total number of counts, but rather the counting rate, the number of counts per second. This distinction becomes increasingly significant as the increasing thicknesses of the absorbers lower the counting rate for the beam to near the background level. If, for example, we made only 10-second counts, for the thick absorbers the counts would be down to a total count of about 10 with approximately 8 of those being background. Such a small number would be statistically highly uncertain. Therefore, we must increase the counting time as the thickness of the absorber increases, thus keeping the
7 number of counts high (~200 counts or higher) and statistically significant. c. We are constantly being bombarded by radiation from space and perhaps other sources. The Geiger tube will detect not only gamma rays from the Cs-137 source, but also this background radiation, thus making your average counts higher than they should be. This background radiation can be eliminated from the absorption data by measuring the average background count and subtracting that number from the average counts taken for the beam and absorbers. This is called normalizing the data. 5. Turn on the stopwatch and reset it to zero. Set the GATE CONTROL on the counter to RESET. Place the source in the up position. Simultaneously start the stopwatch and set the GATE CONTROL on the counter to the SEC-EVENTS position. When exactly ten seconds have elapsed on the stopwatch, set the GATE CONTROL on the counter to the HOLD position. If the total number of counts is less than 200, then repeat the counting process with a longer counting time. Otherwise, record the total number of counts and the counting time. Using the same counting time, repeat this measurement as many times as you feel necessary to get good statistical data. Your series of counts should be recorded in a table which is prepared before you start taking the counts (so that you do not miss a count because you were trying to construct the table, record the results, and watch the counter all at one time). Each member of your group should record the counts. Do so silently so as not to disturb those around who are also trying to record counts. This data will be used to compute N o. Place the source in the down position. 6. Hang an aluminum absorber(s) in front of the exit port of the pig. Place the source in the up position and repeat the measurement process described in step 5. Do as many trials as you feel is necessary to get good statistical data. Repeat this process for a minimum of five different thicknesses of aluminum. Remember: Always place the source in the down position when changing absorbers. This data will be used to compute (N,x) data pairs. 7. Repeat steps 4 and 6 for the lead absorbers. 8. Place the source in the down position, rotate the pig 45 and place lead bricks in front of all exit ports. Remember: Do not try to use the absorber hangers to rotate the pig. Doing so will damage the hangers. Using the same measurement technique as in step 5, measure the background counting rate. When you have finished, return the pig to its original orientation. Before leaving, put your film badge back into its appropriate slot in the film badge box. Lab Report Follow the usual lab notebook format. Your lab report should include the answers to all of the
8 questions asked in the introduction or procedure, all raw and derived data, and an estimate of the magnitude and sources of error in any data recorded. When answering any question or when giving any comparison or explanation, always refer to specific data to support your statements. (Note: There is a computer program in the public library PHYSLIB*** called GAMMA which will help you to do a number of the calculations for this lab. To use it, type OLD PHYSLIB***:P23:GAMMA. The program will tell you what it can do and what information you need to supply. If you use the program, be sure to include in your lab report sample calculations to show that you understand how to do the calculations that the program is doing for you. There is also a True Basic version of this program called GAMMA RAY ABSORPTION which can be found on the P23 Mac disks in the lab. This version can be used on a Mac without the use of D1. Use whichever program you prefer.) For this lab, also include the following: 1. tables summarizing the average normalized N vs x data for both aluminum and lead; 2. samples of computations leading from the raw data to the normalized data; 3. a sketch of the Geiger tube output pulse with an estimation of the dead time and time between pulse and a discussion of the efficiency of your Geiger tube; 4. graphs of ln N vs x for both aluminum and lead; 5. computations of µ and µ m for both aluminum and lead with a comparison between your experimental values and the accepted values (taken from (Radiological Health Handbook) given below: and Al µ = cm -1 µ = 1.17 cm -1 µ m = cm 2 /g µ m = cm 2 /g Pb 6. a discussion of the sources of error with an estimate of their magnitude and effect on the final results.
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