Secular Equilibrium in a Cesium/Barium Isotope Generator
Anthony F. Behof — Department of Physics, DePaul University, Chicago,IL 60614
PC
PC - PHA
(multichannel scaling)
Linear Amplifier
A
B
2
 A R A0
 B t
RB 
1

e


B
source
R A0 is the initial activity of A and
Figure 1
T1 (A) and T1 (B) are the half-lives of A and B
2
2
R B A
For t  T1 (B),
=
and B is in "secular equilibrium" with A.
2
R A0  B
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 5 Geiger Counter System
Figure 4 Elution of the source and the Geiger counter System
10000
2500
8000
2000
137m
Ba
Counts/10 seconds
Decay of
Fit
6000
4000
Decay of
Fit
0
0
600
800
1000
1200
1400
1600
0
1800
200
400
600
800
1000
1200
Time (seconds)
Time (seconds)
(b)
(b)
8000
900
7000
800
6000
5000
Growth of
Fit
4000
137m
Ba
3000
Ba
1000
500
400
137m
1500
2000
200
1400
1600
1800
1600
1800
700
600
500
Growth of
Fit
400
137m
Ba
300
2000
200
0
200
400
600
800
b
137Cs
T1/2 ( 137mBa) ~ 2.55 minutes
b 5.4%
94.6%
137mB
ga
662 keV
0
137Ba
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:
(1) For the
137m
Ba after elution
R=R   (R   R i )e t (2) For the isotope generator after elution
In both cases  is the decay constant for
137m
Ba
R i accounts for the fact that the elution is not 100% efficient
Data were acquired with a NaI spectrometer and a popular Geiger
counter system [11].
• The experiment lends itself to data analysis, non-linear
curve fitting and goodness of fit studies.
(a)
(a)
1000
1200
1400
1600
1800
0
200
400
Time (seconds)
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.
600
800
1000
1200
1400
Time (seconds)
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.
1174 keV
T1/2 ( 137Cs) ~ 30 years
R=R 0 e t
source
Figure 3 Sodium Iodide Spectrometer
B
C
• The study of secular equilibrium enhances and extends the
use of the isotope generator. Two samples are produced
with a single elution.
Pre-Amp
HV
Counts/4 seconds
2
Geiger Counter
Vernier SRM-BTD
A
and for  B   A or T1 (B)  T1 (A)
• The experiment lends itself to the use of several types of
nuclear counting systems. Significant results can be
achieved with inexpensive Geiger counter units.
LabPro
Vernier
3” x 3” NaI
0
 A R A0 A t B t
RB 
e
e 

B  A
• This work demonstrates that the isotope generator may be
used to demonstrate secular equilibrium in a three level
decay.
PC
Counts/10 seconds
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, A and B are
the decay constants for A and B. It is easily shown [9] that the
activity R is given by:
Summary and Conclusions
Counts/4 seconds
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.
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
Half-Life
Detector
Method
(minutes)
Range of Chi-squareb
Geiger Counter
Decay 2.577 +/- 0.009
0.97 - 1.14
Growth 2.568 +/- 0.042
0.85 - 1.10
NaI Spectrometer Decay 2.576 +/- 0.006
0.95 - 1.03
Growth 2.550 +/- 0.009
0.98 - 1.05
Literature valuea
2.552 +/- 0.001
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: .10 - .97. Fourteen of the twenty Chi-square probabilities fall in
the range .30 - .70.
Abstract AJ10, AAPT National Meeting August 3-7, 2002
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 halflife 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
For further information
Please contact abehof@depaul.edu
An online, power point version of this poster is available
at http://www.depaul.edu/~abehof/se.ppt