Birth of an Unique Parent-Daughter Michael F. L'Annunziatal
University of Arizona Tucson, 85721
Relation: Secular Equilibrium An experiment in radioisotope techniques
Secular equilibrium, a steady-state condition of equal activities between a long-lived parent radionuclide and its short-lived daughter, is commonly depicted as one of the most interesting phenomena occurring in radioactive decay. For the study of this decay process most lab manuals in radioisotope techniques propose the separation of parent-daughter nuclides by means of coprecipitation of either the parent or daughter with its stable isotope ( I S ) . The disintegration rate of the newly isolated parent is then assayed by a suitable counting technique, and the ingrowth of daughter with the parent is thus observed until an equilibrium or steady state is obtained. A recent report (4) describes the use of a solvent extraction procedure which can be used for the observation of secular equilibrium occurring in the 2a8Udecay chain. It is intended here to describe the use of an electrophoretic separation of the parent-daughter radionuclides to enable the observation of not only the ingrowth of daughter with the newly separated parent, but also to simultaneously observe the rapid decay of the separated short-lived daughter. Rarely is there opportunity to witness the birth of secular equilibrium outside of those laboratories containing a nuclear reactor in which is produced a long-lived isotope having a very short-lived daughter. The electrophoretic separation of parent-daughter nuclides in secular equilibrium permits the simultaneous observation of the ingrowth of daughter with the isolated parent and also the rapid decay of the isolated daughter. In addition to observing the birth of this parent-daughter relation, the student also becomes acquainted with the use of electrophoresis for the separation and purification of radionuclides. Principle
The procedure involves placing an isotope sample of two radionuclides in secular equilibrium onto an electrophoretic paper strip in a suitable electrolyte and under a given electric potential. After a definite time period the electrophoresis is terminated, the strip is scanned with a suitable detector, and the radioactivity of the separated nuclides is plotted on a recorder. Several scans of the electrophoretic strip are made at suitable time intervals to observe the rapid decay of the daughter peak and the increase in activity of the parent peak due
'Present address: Amohem Products, Inc., Ambler, Pennsyl~ania19002.
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to the production of new daughter until a constant peak height or secular equilibrium is attained. The important criteria upon which secular equilibrium depends are that the parent must be long-lived, that is, negligible decay of the parent occurs during the period of observation, and also that the daughter must have a relatively short half-life. The relative difference in half-life in this latter criterion is further clarified by the equation
that is where and XB are the decay constants of the parent and daughter isotopes, respectively. The importance of these two requirements can be clearly seen in the g0Sr(90Y) equilibrium taken as an example. The infamous fallout isotope =OSris the parent of the decay scheme
!Br
--
8-(0.61 M e V
IL,, = 28.8 yr
8-(2.18 MeV)
%Y
= 2.7 da
DZr(strtble)
The long half-life (ts,J of W r definitely satisfies the first requirement for secular equilibrium since over a quarter of a century of time is needed for it to lose 50y0 of its original activity. As will be seen, less than three weeks are required for secular equilibrium to be attained, and in this interim negligible decay of 9% occurs. To satisfy the second requirement, the decay constants XA and XB for "Sr and respectively, must be compared and are easily calculable from their halflives to be 6.60 X da-' and 2.57 X lo-' da-', respectively. Consequently in the comparison An/ XB = 2.57 X 10W4and is in agreement with the order of magnitude required for secular equilibrium. In discussions on radioactive equilibria it is almost invariably useful to resort to graphical representations of the activity changes occurring with the separate and combined radioisotopes. An accurate graphical description of secular equilibrium is easily constructed by applying decay equations for both the parent and daughter nuclides, The decay of the parent is described by the simple rate equation
which is integratable to the form N A = NA0e-"'
(2)
where NnO is the number of atoms or activity of the parent at time t = 0 and N A is the number of atoms or activity after a given period of time t = t ~ . The decay rate of the daughter is dependent both on its own decay rate in addition t.o the rate a t which it is formed by the parent, and is written
where XBNBis the rate of decay of daughter alone and XANAis the rate of decay of parent or rate of formation of daughter. Equat,ions (2) and (3) are transposed into the linear differentialequation
which is easily solved for t.he number of atoms or activity of daughter, N B , as a function of time t o give
Although unnecessary in this discussion, a solution to eqn. (4) is given by Friedlander and Kennedy (5). An equation for the growth of daughter atoms from the parent can be obtained from eqn. (5) by consideration of the limiting requirements for secular equilibrium. Since X A = 0 and X A pcr 'lrlp. .\ f-n~n, -1il w.t- u ~ c d- d
that the detector would observe only 6 mm of the paper a t one Volume
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time. The paper strip and recorder were set at a rate of 3.8 e m b i n . The detector, fed with counting gas consisting of 98.7% helium and 1.3y0butane, was operated in a. windowless fashion to increase detection efficiency. Prior to the scanning procedure, a rsdioactive marker should
he placed on the strip to permit proper alignment of the strip with the recording. This may be done by placing s. radioactive ink spot approximately 2 mm in diameter on a remote end of the paper. The ink can be tagged by adding any waste radioactive solution into commercial ink. After 8. scan is made, the peak on the recording due to the radioactive ink is aligned with the ink spot on the paper permitting determination of the positions of other radioisotopes on the paper strip.
Example of Results Obtained
The recordings shown in Figure 2 were obtained in one afternoon laboratory period and two subsequent sessions lasting only approximately a half hour. The center line labeled as the origin marks the relative position on the electrophoretic paper strip where the wSr(goY)was placed prior to electrophoresis. The arrows pointing toward the positive and negative side of the origin represent the possible directions of migration toward the anode or cathode sides of the electrophoretic cell, respectively. The recordings represent an activity of 300 cpm (counts per minute) full-scale. In all the recordings three peaks are observed corresponding to the separated and W r besides tagged ink which served as a marker. The T and soSrpeaks were easily identified by the fact that the "Y diminished with time due to isotopic decay, and the 9% peak increased with time as a result of the ingrowth of daughter. Six days subsequent to the electrophoresis, the peak had decayed almost below detection whereas the %r peak had grown in activity off-scale of the recorder. Quantitative measurements of this phenomena were not conducted due to the poor accuracy of the GM detector at low levels of activity (-300 cpm) and also due to the unavailable additional laboratory time needed to utilize more efficient methods of detection. If time is available, the experiment can be conducted on a semiquantitative basis by more sensitive means of detection such as liquid scintillation. The positions on the electrophoretic paper strips occupied by the separated isotopes can be cut out and eluted with dilute HC1 into liquid scintillation vials, the dilute HC1 evaporated off in an oven, followed by cooling and the addition of scintillation fluor prior to counting. With the high energy 8-emitters, very high counting efficiencies (>80(ro) are easily obtained with liquid scintillation. Once in scintillation vials, the count-rate of the separated nuclides could be determined intermi& tently over a period of approximately two to three weeks. This would permit the determination of the time required to attain secular equilibrium, which would be the time interval from the stad of the electrophoretic separation to the time in which there is no further ingrowth of wY with Wr. These results can be compared to the time interval of approximately 18 da indicated by curve b in Figure 1. Discussion
Figure 2. Remrdingr of mdiooctivity on an electmpheretic paper strip representing 300 cpm full-scale. 1.1 Immediateiy after the electrophoretic separation of P % ~ ond l b l One day subsequent to electrophoresis, (c) Four doy* s~bsequehtfo electrophorerir. The "Sr peak in .ecording lo1 is iabeled 0 % "SrP"1 in recordings lbl and lcl to indicate ingrowth of
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As a point of interest and an example of the practical utility of this phenomena, the application of secular equilibrium theory in the analysis of "Sr fallout could he discussed. One method entails the initial coprecipitation of radiostrontium with stable strontium, as SrSOa; resulting from the addition of Sr(NO& and H2S04to an aqueous extract containing radiostrontium. The SrS04is then transformed to SrCOaby fusion with Na2C03.
is milked Radioassay is not conducted until the from the gDSr tied-up as gQSrCOa. Milking of "Y involves its coprecipitation as Y(OH)a at a basic pH. The Y(0H)a is precipitated by firstly dissolving the SrCOain dilute HCl followed by the addition of Y(NO& and sufficient NH,OH to obtain a basic pH. The milked can then be assayed by suitable low-background counting techniques. Because an investigator is interested in the original "Sr activity, the 9QYis assayed by plotting its decay semi-logarithmically against time over a two-week period. The linear decay, as illustrated in Figure 1, curve a, is extrapolated to time zero, where it crosses the axis indicating the original activity of and/or "Sr at the time of milking. Although the milking and preparative procedure prior to milking are time consuming, the secular equilibrium phenomena permits a radiochemist to
repeat his analysis on the same sample as many times as desired. From eqn. (7) it is calculated that two weeks after milking, the activity of "Y grows to 97.4% of its original activity. In this case, an analyst can check his results by repeated milkings and radioassays of 9QYfrom the same sample at two-week intervals. It is a rare case indeed when a chemist is able to conduct repeated analysis on the same sample. Literature Cited (1) R ~ n n *NOBMAN . (Ed%tov).'TLzdioisotopeExperiment8 for The Chemistry Curri~ulum." U S . Dept. of Commerce, Wsahington, D. C.. 1 9 W . p. ",7.,
-. 0.
D., AND RIBINOWITS,J. L.. "Principles of Radioisotope Methodology.'' Burgeas Publishing Co.. Minneapolis. Minn.. 196'Ii p. 104-8. (3) C B A T EH. ~ . L..MACCXION~. J. B..G ~ M I L W L .. J., A N D KRAMGB. H, H.. J. Cnsla. Eouc.. 4 6 . 287 (1969). . H . . J. CXEX.EDVC..4 6 , 665 (1969). ( 4 ) H s n e ~ n ROLBE AND K m ~ e n r ,J o s s ~ xW., "Nucle~rand ( 5 ) F n r m ~ m o m .OEFG~ART. Radioahemistry," John Wiley & Sons, Ino.. New York. 1955. P. 129(2) Cn~el;.
"". 2"
( 6 ) L~zannmr,E . J., J . A p p l . Rod. ondI8olopcs. 16, 443 (1965)
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