Till now, Radioactive Contamination Factor (RCF) has been established by radioactive detection of contaminant product 137Cs-137mBa, present in marine sediments, in order to compare it with 40K natural radioactivity as a percentage  . This procedure requires to set up about half kilogram of conditioned dry sample in a Marinelli container to be detected either by a NaI(Tl) low background detector during 8 - 12 hours, or to be detected longer time by a HPGe detector. Efficiencies of these procedures have been about 5.6% for 137Cs and 2.9% for 40K in NaI(Tl) scintillation detector, and 0.47% for 137Cs and 0.25% for 40K, in HPGe detector, basic figures to obtain the RCF, in spite of some high statistical variation, even when detection times were as large as possible. So, this paper describes how one cation exchanger resin allows separating isobars from IA and IIA columns of Periodic Table, corresponding to alkaline and earthy-alkaline metals, to establish only atoms number of radioactive contaminant 137Cs-137mBa. In order to obtain this result by Inductively Coupled Plasma-Mass Spectrometry (ICP-MS), it becomes necessary the previous separation of natural isotope 137Ba (11.23% of natural Ba), to count only 137Cs-137mBa atoms with much lower statistical variation than that of radioactive detection.
As cation exchanger was used AMP-PAN cesium resin, ammonium molybdophosphate (AMP), embedded in an organic matrix of polyacrylnitrile (PAN), produced by Triskem International Laboratory in Rennes, France (Figure 1). Also possible was to elaborate either zirconium antimonate or zirconium vanadate as cation exchangers  , but the efficiency proof performed with the first one to obtain 97% - 99% in the final basic solution from a 137Cs-137mBa acid
Figure 1. Triskem International AMP-PAN (ammonium molybdo phosphate embedded in polyacrylnitrile) resin cation exchanger.
solution with known radioactivity was satisfactory enough, obtained by comparing counts per hour from the acid solution and resin after it trapped the radioactive 137Cs from the initial solution (Figure 2), with counts obtained in the final basic solution (97% of 137Cs-13mBa in solution previously filtrated twice in the resin) (Figure 3). To do it, 1 gram of resin was conditioned in 10 ml of 10−5 M HCl, and put in the filtration plastic tube as compacted as possible. Then it was filtered through it 20 ml of solution pH = 1.5 (137Cs-137mBa, 10 Becquerel). Then the final recovery was performed by 10 ml, 5M NH4Cl, pH = 9.5 solution. When this basic solution was detected, it was found 97% of counts produced by 137Cs-137mBa acid solution previously filtered. Nevertheless, it should be considered for this separation, that transient equilibrium established between 137Cs-Ba137m represents one extreme case of different half lives for radioactive parent and daughter, since t1/2(137Cs) = 30.07 years, while t1/2(137mBa) = 2.55 minutes. As a consequence, the proportion between both decay constants is as great as: and
Figure 2. AMP-PAN filtration columns to trap 137Cs from acid solution and exchange it into a basic solution.
Figure 3. Activity detection of 137Cs-137mBa standard acid solution before filtration, and after recovery of radioactive pair in basic solution.
. Therefore, the difference between the larger one λ2(137mBa) and the smaller one λ1(137Cs) is negligible: 0.272 − 4.385 × 10−8 = 0.27199, while the quotient between the larger and the smaller one is very great: 0.272/4.385 × 10−8 = 6.203 × 106. So, when this radioactive pair is separated, their radioactive equilibrium ( , , where and ), is recovered in only 3.68 minutes. In this way, if the equation proposed by G. R. Choppin , to evaluate either number of daughter or parent nucleus in radioactive equilibrium, as a function of λ1 and λ2, when half lives of both are in a relation from days to hours (not so great as years to minutes), may be simplified, since the difference λ2 − λ1 is negligible (0.272 − 4.385 × 10−8 = 0.27199), and we can consider that:
is the same that and
As a matter of fact, it is possible to use for this case the simpler equation of radioactive father and daughter in equilibrium: , , , where (constant value). It means that constant value K is equal to quotient .
So, if a number of nucleus are counted by mass number, for the isobaric pair 137Cs-137mBa, will be obtained some number R, sum of , where N2 may be replaced by its value , and in such a case , and . But if it is considered that 1 + 6.241 × 106 is equal to 6.241 × 106 for our purpose, then N1 = R/6.241 × 106, which means number of 137Cs atoms, while , 137mBa number of daughter atoms in all cases. Therefore, if it is related the atoms number of radioactive contaminant 137Cs, with atoms number of natural radioactive 40K, in order to evaluate the intensity of radioactive contamination in marine sediments, we have to consider that in the extremely remote case the activity of contaminant 137Cs could reach up that of natural 40K, the meaning of that unlikely but possible event, should be 2.35 single atoms of 137Cs related to 1 × 108 atoms of natural 40K, because: and . Consequently, if , then and
Time calculation to get the radioactive equilibrium between parent 137Cs (valence 1), and daughter 137mBa (valence 2), after their separation by using ion exchange resins.
After recovery with a very basic solution (pH = 9.5) the 137Cs (t1/2 = 30.17 years), from the exchange resin, it is estimated the necessary time to get up the radioactive equilibrium with her daughter 137mBa (t1/2 = 2.55 m). So, if it is named N1 the number of parent atoms and N2 the number of daughter atoms, λ1 and λ2 decay constants for parent and daughter respectively, at time zero the sample has only N1 and no N2, but the time starts and N2 begins to grow up, according the next equation:
where the time function determines the daughter 137mBe growing up by the parent 137Cs decaying, and the first derivative equal 0 means the time when N2 stops growing and gets the equilibrium with parent, that is to say and radioactive equilibrium :
Due to great difference between both radioisotopes: contaminant (137Cs, t1/2 = 30.17 years) and natural (40K, t1/2 = 1.28 × 109 years), their decay constants are much greater for the minor half life (137Cs, ) than that of much greater half life (40K, ). Therefore, for a given number of nucleus, the radioactivity of contaminant 137Cs should be much greater than that of natural 40K for a factor equal to 4.243 × 107 times. But fortunately, this has not been the case for any sample examined till now, where the RCF has not surpassed 11.4% . But this light contamination also implies the continue production of 137mBa(t1/2 = 2.55 m), γ rays emitter, which decays by isomeric transition to 237Ba, in mass not appreciable to surpass the natural percentage (11.23%) of this isotope in natural elementary Ba found in marine sediment samples, which could happens with much more appreciable contamination by radioactive 137Cs. So, to get the contamination by 137Cs in terms of mass percentage related to one gram of marine sediments, once separated natural Ba and 137mBa from contaminant 137Cs by capture the 137Cs from the cation exchanger, after 3.68 minutes radioactivity from parent 137CS and daughter 137mBa get the radioactive equilibrium in which A1(137Cs) = A2(137mBa). But N1λ1 = N2λ2 implies that N1(137Cs) = λ2N2(137mBa)/λ1, and ICP-MS gives us the counts per second obtained only from 137mBa nucleus previously separated of natural 137Ba, and so 137Cs = 137mBa × t1/2(137Cs)/t1/2(137mBa), both half lives expressed in minutes. Therefore, when number of 137Cs atoms is compared with Avogadro’s number (6.02 × 1023 atoms) for the molecular weight of it (137 g), we
Table 1. Mass of contaminant 137Cs in Cuban marine sediments, obtained by mass spectrometry.
obtain the weight of contaminant 137Cs present in determined mass of sediment sample, per gram when divided by the weight sample. Even when elementary K is separated in the exchanger resin together with 137Cs-137mBa, and also present in the basic final solution with radioisotope 40K, it is not possible to obtain the number of 40K atoms by ICP-MS, because gaseous 40Ar mass is used to form the necessary plasma where bivalent cations 137mBa are counted by second. Nevertheless, it is quite possible to count 39K atoms, which have one constant proportion in elementary K equal to 93.22%, and comparing this figure with that of 40K (0.0118%), it is obtained the number of 40K atoms present in the weight of marine sediments treated, and responsible of the natural radioactivity in the marine sediment sample. So, Table 1 shows the results obtained in four samples of Cuban marine sediments, previously detected for 137Cs radioactive contamination, in order to compare it with natural 40K radioactivity , and at present using mass spectrometry instead disintegrations by time units.
Even when cation exchanger AMP-PAN results highly efficient to separate 137Cs from the marine sediments, and it shows to separate also elementary K, since the characteristic 1.46 Mev peak of 40K appears in the final basic solution filtered by the resin, the number of 39K detected by mass spectrometry as counts per second appears to be lower than that obtained by 40K radioactive detection at known efficiency, comparing 0.0118% as isotope abundance of 40K with 93% of 39K. It seems to demonstrate that only a fraction of K much more abundant that contaminant Cs present in the sediment, appears in the final basic solution filtered in the resin. On the other hand, 137Cs-137mBa mass separation results 97% - 99% efficient, and it allows to calculate directly the mass of contaminant 137Cs in atoms number as well as 137Cs (10−12 g) (picograms) per gram of sample.