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**Secular Equilibrium in a Cesium/Barium Isotope Generator**

Anthony F. Behof — Department of Physics, DePaul University, Chicago,IL 60614 Abstract A Cesium/Barium isotope generator is shown to be an effective device for studying the secular equilibrium in a three-level nuclear decay. The measurement of the half-life of the 662-keV level of Barium-137 extracted from an isotope generator has long been a standard experiment in undergraduate physics laboratories. In this work, the half-life is determined by observing the return of the isotope generator to secular equilibrium. Results are obtained using a sodium iodide spectrometer and multichannel analyzer and a simple Geiger counter system. This experiment lends itself to the study of a system approaching secular equilibrium and extends the usefulness of the isotope generator in the undergraduate laboratory. Summary and Conclusions This work demonstrates that the isotope generator may be used to demonstrate secular equilibrium in a three level decay. The experiment lends itself to the use of several types of nuclear counting systems. Significant results can be achieved with inexpensive Geiger counter units. The study of secular equilibrium enhances and extends the use of the isotope generator. Two samples are produced with a single elution. The experiment lends itself to data analysis, non-linear curve fitting and goodness of fit studies. Figure 3 Sodium Iodide Spectrometer HV source Pre-Amp 3” x 3” NaI Linear Amplifier PC - PHA (multichannel scaling) PC Figure 5 Geiger Counter System source PC Geiger Counter Vernier SRM-BTD LabPro Vernier Figure 4 Elution of the source and the Geiger counter System Introduction Experiments on secular equilibrium in physical systems for the introductory modern physics laboratory have taken various forms. One of the earliest [1] has the disadvantage of requiring neutron activation techniques. Some authors [2-3] have described electronic simulation methods and others [4-5] have proposed fluid flow experiments. The present work is based on isotope generator techniques [6-8] that have been used in the undergraduate laboratory for many years. For the nuclear energy levels shown in Figure 1, lA and lB are the decay constants for A and B. It is easily shown [9] that the activity R is given by: References 1. Lawrence Ruby, “Demonstration of the buildup and decay of radioactivity,” Am. J. Phys. 34 (3), (1966). 2. Francis J. Wunderlich and Mark Peastrel, “Electronic analog of radioactive decay,” Am. J. Phys. 46 (2), (1978). 3. Donald L. Shirer, “Radioactive chain decay using an analog computer,” Am. J. Phys. 39 (11), 1408 (1971). 4. J. R. Smithson and E. R. Pinkston, Half life of a water column as a laboratory exercise in exponential decay,” Am. J. Phys. 28, 740 (1960). 5. Thomas B. Greenslade, Jr., “Simulated secular equilibrium,” The Physics Teacher, 40 (1), (2002) 6. J. M. Oottukulam and M. K. Ramaswamy, “Radioactive half-life determination with an isotope generator,” Am. J. Phys. 39 (2), 221 (1971). 7. Charles R. Rhyner, “More on laboratory isotope generators,” Am. J. Phys. 39 (10), 1274 (1971). 8. W. H. Snedegar and A. R. Exton, “Comment on ‘Radioactive half-life determination with an isotope generator’,” Am. J. Phys. 39 (10), 1282 (1971). 9. A. Arya, Fundamentals of Nuclear Physics (Allyn and Bacon, Boston, 1966) 10. Spectrum Techniques, 106 Union Valley road, Oak Ridge, TN 11. Vernier Software and Technology, SW MillikanWay, Beaverton, OR 12. SigmaPlot 8.0, SPSS Inc., 233 South Wacker Drive, Chicago, IL A B C lA lB Figure 1 Method and Apparatus A physical system that satisfies the conditions for secular equilibrium is the 137Cesium/137Barium mixture. Figure 2 is a decay scheme for this system. Figure 7 Typical results using the Geiger counter. (a) Decay of Barium following separation. (b) Growth of Barium in generator following elution. Every 5th point is shown. Errors are statistical. Figure 6 Typical results using the NaI detector. (a) Decay of Barium following separation. (b) Growth of Barium in generator following elution. Every 10th point is shown. Errors are statistical. 137Cs 662 keV b- (94.6%) b- (5.4%) g 137Ba 137mBa 1174 keV T1/2 ( 137Cs) ~ 30 years T1/2 ( 137mBa) ~ 2.55 minutes Results Five Decay and growth measurements were made for each of the counting systems shown in Figures A constant background term was added to each of Equations (1) and (2) and a weighted non-linear fit [12] was computed for each data set. Figure 6 is a typical result using the NaI detector and Figure 7 is a typical result for the Geiger counter system. Table 1 summarizes the results for the two counting systems. Each entry is a weighted average of five measurements. The uncertainty is the standard error in the fitted coefficient. The measured half-life in each case is consistent with the literature value. More importantly for this work, the goodness of fit results indicate that the isotope generator and popular counting systems may be employed to study the phenomenon of secular equilibrium in the undergraduate laboratory. Table 1. Half-life values for the four methods used in this work. Each value is the weighted average of the results of five measurements. The range of Chi-square values is given for these five measurements Figure 2 The Cesium/Barium source is readily available [10] as an isotope generator that may be eluted to record the activity of the daughter (137mBa) or of the mixture. Aside from a constant background term, the activities will be given by: For further information Please contact An online, power point version of this poster is available at a. National Nuclear Data Center, Brookhaven National laboratory, Upton, New York 11973, [http://www.nndc.bnl.gov/nndcscr/testwww/AR137BA.HTML] This recommended value is the weighted average of four published measurements. b. Range of Chi-square probability: Fourteen of the twenty Chi-square probabilities fall in the range Data were acquired with a NaI spectrometer and a popular Geiger counter system [11]. Abstract AJ10, AAPT National Meeting August 3-7, 2002

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