Radioactivity (Part I and Part II) Objectives: To measure the absorption of beta and gamma rays To understand the concept of half life and to measure the half life of Ba 137* Apparatus: Radioactive source, aluminum absorbers, lead absorbers, Geiger counter, computer interface, computer, Event Counter software, weak HCl solution ( for Part II ) Overview: In this experiment we will study the decay of a radioactive nucleus, Cesium 137 with symbol Cs 137. Cesium 137 is an artificial nucleus made in a fission reactor. It has 55 protons and 82 neutrons. It has a relatively long half life of 30 years, i.e. if you have N of these nuclei, N/2 of them will decay over the course of 30 years. Cs 137 decays by emitting a beta ray (or particle), which carries away one negative charge, converting the Cs 137 into Barium, symbol Ba 137. [When radioactivity was first discovered the nature of the various types of emitted particles was not known, so they were labeled alpha, beta, and gamma. Today we know that the alpha-ray is a He 4 nucleus, the beta-ray is an electron and the gamma-ray is a high energy photon. In beta decay the electron is emitted together with an anti-neutrino, which carries away part of the available energy.] The beta decay of Cs 137 can occur in two different ways, as shown in Fig. 1. The direct decay to the ground state of Ba 137, releasing 1.176 MeV, is rather infrequent (6.5%) and we will ignore this possible mode. The other, dominant (93.5%) decay mode of Cs 137 is to an excited state Ba 137* which is metastable (i.e. it decays still further to the ground state). The released energy in this first step is 0.514 MeV, which is carried away by an electron and an anti-neutrino. The half life of Ba 137* is only about 2.5 min. and it decays by gamma decay to Ba 137. This second step occurs by emission of a 0.662 MeV gamma ray. Figure 1: The Decay Modes of Cesium 137 Radioactivity 1
We will study two aspects of the radioactivity: 1. How does matter absorb the beta and gamma rays emitted during the decay of Cesium 137? 2. What is the half life of the Ba 137* state? The absorption of charged particles like the beta ray by matter is fundamentally different from that of neutral gamma rays. Let us consider the beta ray first. Absorption of beta rays: When a beta ray (electron) passes through a material, there is an electric force between it and the electrons of the atoms it passes. With each "collision the beta particle gives up a little of its energy, sometimes stripping an electron from an atom, ionizing it. (This ionization is the chief cause of the biological damage done by radiation.) After many such collisions the beta's kinetic energy is converted into thermal energy of the material. The distance the beta ray travels in the material before stopping is called its range. Beta particles having the same initial energy will have virtually identical ranges. But for the decay shown in Fig. 1, the beta rays are not emitted with a single energy. This is because during the decay another particle, the anti-neutrino, which has no charge and we cannot detect, is also emitted and carries away some of the 0.514 MeV released energy. The exact amount -- from zero to 0.514 MeV -- that the beta ray carries depends on the angle it makes with the neutrino. Thus, the beta rays emitted during the decay will have a spread of ranges in matter from almost zero to a maximum which depends on the energy released by the parent nucleus. Increasing thicknesses of absorber will stop beta particles with larger and larger energies, up to the maximum range or stopping distance. For the radioactive source used in this experiment, a semi-log plot of the beta ray count rate vs. absorber thickness D is approximately a straight line with a sharp kink when the absorber thickness equals the stopping distance of the beta rays. For thicknesses larger than this critical thickness all beta rays are completely absorbed and the remaining radiation consists of pure gamma rays. Thus by measuring D at which the beta radiation ceases and using Fig. 2, we can determine the energy released during the beta decay. Radioactivity 2
10 1 E (Mev) 0.1 0.01 0.01 0.1 1 10 100 D (mm) Figure 2. Energy Dependence of the Stopping Distance of Beta Rays in Aluminum Absorption of gamma rays: For photons the process of energy loss (i.e. gamma ray absorption) is entirely different. A gamma ray with energy less than 1 MeV as in this experiment transfers its energy to one or more electrons by one of two processes: (1) the photoelectric effect: the photon's energy is used in part to remove an electron from an atom. All of the remaining energy is given to the electron as kinetic energy; the initial photon disappears. (2) the Compton effect: only part of the photon's energy is given to an electron. The remaining energy goes into a new photon of (lower) energy (scattered in a different direction). Thus we see that beta particles dribble their energy away, a little bit at a time, until it is all gone, while photons give theirs away all at once resulting in electrons which, in turn, lose that energy by excitation and ionization. The mechanisms by which beta rays lose energy in matter are much more efficient than for gamma rays resulting in a much shorter range for beta rays than gammas. Radioactivity 3
Half Life: Radioactive decay is a random process and it is impossible to predict when a particular nucleus will decay. Instead we use the probability λ that a nucleus will decay in one second. λ is a constant that is independent of time. It does not matter how long a nucleus has survived without decaying; the probability that it will decay during a time interval Δt is exactly the same. Then if we have N nuclei, N will reduce with time. The fraction that will decay in the short time interval Δt is: ΔN = λn (1) Δt where ΔN is the number of nuclei that decay. Eq. (1) can be rewritten as dn = λn. (2) dt The solution to this differential equation is the exponential function N N e λt = o, where No is the number of nuclei you start with at time t = 0. We are interested in the half life -- the length of time τ it takes for half of the nuclei to decay. Setting N = No/2 and t = τ, we find N o 2 = N o e λτ Taking the natural logarithm we find or e λτ = 2 τ = ln2 λ (3) Apparatus: The apparatus you will use is extremely simple. You only have to become familiar with the program called Event Counter (if not on the desktop, do a search), which is very similar to the Data Logger which you have previously used. Every time a beta or gamma ray passes into the Geiger tube, the tube emits a pulse which is counted by Event Counter for a length of time, the Count Interval, which you can adjust using the Collect menu. After each Count Interval, the number of counts is plotted on a graph of number of counts versus elapsed time. This process continues for the length of the Run Time which you can also set using the Collect menu. Event Counter offers you the option of plotting instead a histogram of the number of times a given count N is obtained in a count interval versus N. It also has an Analyze menu that allows you to determine the statistics for your histogram such as the average count <N> and the standard deviation. Turn on the power switches for the "counter/timer" and for ULI circuit board. Then you are ready to use the Event Counter program. Radioactivity 4
Radioactivity (prelab questions, show work) Names Section 1: "Activity" of a radioactive source is the number of radioactive decays that occur per second. The unit of activity is the Curie (Ci). [ 1 Ci = 3.7 x 10 10 disintegrations/second.] The Curie is a large unit of activity. The Cs 137 source used in this lab has an activity of 5 μci or 5x10-6 Ci at present (slowly decreasing with time). Question A. If the Geiger counter consists of a tube 1 cm in diameter and is located at 2 cm from the source, what is the count rate of a 100% efficient Geiger counter? [ When the Cs 137 decays, the beta and gamma rays are emitted randomly in every direction. Imagine a spherical surface area 4πR 2 around the source, where R = 2 cm. The circular opening of the Geiger counter will only collect the radiation from a small part of that entire surface. That small part equals an area = πr 2, where r = 0.5 cm, the opening of the counter.] Again, what is the count rate detected by this Geiger counter? Question B. If the counter is set at 4 cm from the source, what count rate will it read? How far does it have to be moved away from the source to record a count rate equal to the natural background rate (e.g. 30 counts/minute)? 2: Absorbed Dose and biological effect. The activity of a source does not yet tell you anything about its biological effect. The absorbed dose tells you how much energy is actually deposited in your body by the radiation. The unit of Radiation Absorbed Dose is the rad. One rad is said to have been delivered to a specific part of the body when an energy of 0.01 J/kg has been absorbed. Background radiation of natural origin delivers a dose of about 0.2 rad/year. Safety Concern: A whole-body short-term gamma ray dose of 300 rad will cause death in 50% of the population. If the dose is delivered more slowly, the effect is less deadly since the body repairs some of the damage induced by the radiation. Question A. Suppose you ingested 5 μci of Cs 137. Estimate the maximum absorbed dose (in rad) you would receive in one day if all gamma rays released in the decay were absorbed by your body. [This assumption is far from correct since the body is mostly transparent to gamma rays.] Question B. Estimate the change in temperature of 1 kg of water if it absorbed a dose of 300 rad. What does this imply about heating as the source of the biological damage produced by radiation? Radioactivity 5
Report -- Radioactivity (PART I) Name Partner Partner Section Activity 1: Absorption of Beta Rays A. Use Event Counter to record the natural background activity. The background is partly from cosmic rays and partly from radioactive materials which are normally present in the ground, in building materials and even our bodies. It should be about 10 to 40 counts per minute. Make sure the Cs source is not located near the Geiger tube. Use a count interval of 1 s and a run time of 3 minutes. After the data is collected, display it as a graph and use the Analyze menu to obtain the average activity (counts/s). Include the graph in your report. Mean Background Activity c/s The background is so low that you can ignore it in this part of the experiment. You will need this background measurement for a later investigation. B. The radioactive source consists of a small, safe amount of Cs 137 covered and sealed in plastic, which emits observable beta particles and gamma rays. Place the Cs source with the aluminum side down in the holder about 2 cm below the Geiger tube. Use Event Counter again to measure the activity. Repeat with the source located 4 cm from the tube. Include in one graph the activities for both distances. Include the graph in your report. Compare with your predictions in preliminary activity 1. 2 cm: Observed Activity c/s 4 cm: Observed Activity c/s Ratio of (2 cm/4 cm) Activity: Predicted Observed C. Put the source, aluminum side down, on the bottom shelf of the stand. What is the distance between source and counter? Count for one minute. Be sure not to move the source after taking this measurement. Put one of the thin aluminum absorbers (made of four-ply aluminum foil, total thickness 0.078 mm; newer absorbers are two-ply but same total thickness) on Radioactivity 6
the tray between the counter and the source. Count for one minute. Record the activity. Add more of the thin aluminum absorbers one at a time, and determine the counting rate each time, until it becomes approximately constant (once the rate is constant, only gamma radiation remains). In one graph show activity (and mean) for 0, 1, 2, 3, 4, 6 absorbers. Continue with more absorbers to establish this constant counting rate accurately. In a second graph show activity (and mean) for 8, 10, 12, 14, 16, 20 absorbers. Record your data in the table below. Aluminum Absorbers counting rate (c/s) Aluminum absorbers counting rate (c/s) 0 8 16 Aluminum absorbers counting rate (c/s) 1 2 10 20 3 4 12 6 14 Make a semilog plot (on the graph paper attached at the end of this report) of Activity (Counting Rate) vs. # Absorbers. Find the beta ray's maximum Range (the distance D that the most energetic beta rays can travel before being stopped) in aluminum. From the graph in Fig. 2 determine the maximum energy of the beta particles. Number of Absorbers before counting rate becomes constant: Total thickness of Al = Range of beta rays from this source = D: Maximum Beta Ray Energy (using Fig. 2 of this manual) Radioactivity 7
Expected Maximum Beta Ray Energy (Fig. 1 of this manual) The initial counting rate (0 absorbers) includes both types of rays (beta and gamma) while the constant counting rate is due only to the gamma rays. What part of the 0-absorber count is due to beta rays and what part is due to gamma rays? Activity 2. Absorption of Gamma Rays. The purpose of this investigation is to qualitatively observe the difference in absorption between beta and gamma rays. Careful quantitative measurements are not required. A. Turn the source over so that the aluminum holder is between the counter and the source. Insert the source in the second slot. What is the distance between source and counter? The aluminum holder will absorb most of the beta rays and pass most of the gamma rays. Count the activity for three minutes. Again include the activities (and means) for 0, 1, 2, 3, 4 lead absorbers for this part A and next part B in one single graph. B. Add lead absorbers, one at a time, (plate thickness 2.78 mm), until the activity is reduced by about one half (you may need up to 4 lead absorbers). Total thickness of lead required to reduce gamma count rate by 1/2 = mm Which part of this count rate is due to the natural back ground? Do you need to make a correction for the natural back ground and how would you do that? Radioactivity 8
Report -- Radioactivity (PART II) Name Partner Partner Section Activity 3. Half Life of Ba 137* In this investigation you will measure the approximately 2.5 minute half life of the metastable Ba 137* state. It is necessary to chemically separate the Ba 137* from the Cs 137 source so as to eliminate the beta rays that the Cs is emitting. These rays would confuse the half life measurement because your Geiger counter cannot distinguish between beta and gamma rays. Your instructor will separate the barium from the cesium by using a weak HCl solution which dissolves barium chloride. This must be done immediately before you take your Ba 137* data, as the Ba 137* half life is short and the Ba 137* activity is weak. Once your instructor gives you your sample, start taking the Ba 137* data immediately. Do not move the source or counter once you have started. Take your data using Event Counter with a count interval of 10 s and a run time of 10 minutes. To analyze the data for the half life, you will use the fact that the activity drops by 1/2 when you wait one half life. Because the activity is low, especially after several half lives have elapsed, you will need to subtract the background activity as follows: You measured the background activity per second before in section A of activity 1. Total activity at t = 0 s = c/ 10 s Background activity from before x 10 s = c/ 10 s Activity = Total - Background = c/ 10 s Use your result for the half life to calculate the probability that a given Ba 137* nucleus will decay in the next 5 s. Radioactivity 9
Optional analysis: Export your data for A vs. t data to Graphical Analysis. Use the Simple Math menu to subtract the background activity (for a 10 s interval). Then use the Transform menu to take the natural logarithm of the corrected activity (A-B). Plot ln (A-B) versus elapsed time t. This should give you a straight line. Make a simple fit to the data. The slope of the fit will be λ from which you can calculate τ using Eq. (3): λ = ln 2 / τ =0.693 / τ Radioactivity 10
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