Secular Equilibrium in a Cesium/Barium Isotope Generator

1
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 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), 246-248 (1966). 2. Francis J.
Wunderlich and Mark Peastrel, Electronic analog
of radioactive decay, Am. J. Phys. 46 (2),
189-190 (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), 21-23 (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 37830. 11. Vernier Software
and Technology, 13979 SW MillikanWay, Beaverton,
OR 97005-2886. 12. SigmaPlot 8.0, SPSS Inc., 233
South Wacker Drive, Chicago, IL 60606-6307
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.
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 3 - 5. 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
abehof_at_depaul.edu An online, power point version
of this poster is available at http//www.depaul.e
du/abehof/se.ppt

a. National Nuclear Data Center, Brookhaven
National laboratory, Upton, New York 11973,
http//www.nndc.bnl.gov/nndcscr/testwww/AR137BA.H
TML This recommended value is the weighted
average of four published measurements. b. Range
of Chi-square probability .10 - .97. Fourteen of
the twenty Chi-square probabilities fall in the
range .30 - .70.
Data were acquired with a NaI spectrometer and a
popular Geiger counter system 11.
Abstract AJ10, AAPT National Meeting August 3-7,
2002