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 [2] [3]. 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 [4] [5], but the efficiency proof performed with the first one to obtain 97% - 99% in the final basic solution from a ¹³⁷Cs-^137mBa acid

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-Ba^137m represents one extreme case of different half lives for radioactive parent and daughter, since t_1/2(¹³⁷Cs) = 30.07 years, while t_1/2(^137mBa) = 2.55 minutes. As a consequence, the proportion between both decay constants is as great as: λ 1 ( 137 Cs ) = 0.693 / 30.07 × 365 × 24 × 60 = 4.385 × 10 − 8 min − 1 and

λ 2 ( 137m Ba ) = 0.693 / 2.55 = 0.272 min − 1 . 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 ( A 1 = A 2 , λ 1 N 1 = λ 2 N 2 _, where λ 2 ≫ λ 1 and N 1 ≫ N 2 ), is recovered in only 3.68 minutes. In this way, if the equation proposed by G. R. Choppin [6], 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:

N 2 = λ 1 N 1 / ( λ 2 − λ 1 ) is the same that N 2 = λ 1 N 1 / λ 2 and N 1 = N 2 λ 2 / λ 1

As a matter of fact, it is possible to use for this case the simpler equation of radioactive father and daughter in equilibrium: A 1 = A 2 , N 1 λ 1 = N 2 λ 2 , N 1 = N 2 λ 2 / λ 1 , where λ 2 / λ 1 = K (constant value). It means that constant value K is equal to quotient t 1 / 2 ( 1 ) / t 1 / 2 ( 2 ) = 0.272 / 4.358 × 10 − 8 = 6.241 × 10 6 .

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 N 1 + N 2 = R , where N₂ may be replaced by its value N 2 = λ 1 N 1 / λ 2 , and in such a case N 1 + λ 1 N 1 / λ 2 = R , and N 1 ( 1 + λ 1 / λ 2 ) = R . 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 R − N 1 = N 2 , ^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: t 1 / 2 ( 137 Cs ) ≪ t 1 / 2 ( 4 0 K ) and λ 1 ( 137 Cs ) ≫ λ 2 ( 4 0 K ) . Consequently, if A 1 ( 137 Cs ) = A 2 ( 4 0 K ) , then N 1 λ 1 ( 137 Cs ) = N 2 λ 2 ( 4 0 K ) and

N 1 ( 137 Cs ) / N 2 ( 4 0 K ) = λ 2 ( 4 0 K ) / λ 1 ( 137 Cs ) = t 1 / 2 ( 137 Cs ) / t 1 / 2 ( 4 0 K ) = 30.07   years / 1.28 × 10 9 years = 2.35 × 10 − 8 = 2.35 / 10 8 .

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 (t_1/2 = 30.17 years), from the exchange resin, it is estimated the necessary time to get up the radioactive equilibrium with her daughter ^137mBa (t_1/2 = 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:

N 2 = ( N 1 − N 1 e − λ 1 t ) e − λ 2 t = N 1 e − λ 2 t − N 1 e − ( λ 1 + λ 2 ) t = N 1 ( e − λ 2 t − e − ( λ 1 + λ 2 ) t )

where the time function f ( t ) = e − λ 2 t − e − ( λ 1 + λ 2 ) t determines the daughter ^137mBe growing up by the parent ¹³⁷Cs decaying, and the first derivative f ′ ( t ) equal 0 means the time when N₂ stops growing and gets the equilibrium with parent, that is to say N 1 λ 1 = N 2 λ 2 and radioactive equilibrium A 1 = A 2 :

f ′ ( t ) = − λ 2 e − λ 2 t + ( λ 1 + λ 2 ) e − ( λ 1 + λ 2 ) t = 0

λ 2 e − λ 2 t = ( λ 1 + λ 2 ) e − ( λ 1 + λ 2 ) t

λ 2 / ( λ 1 + λ 2 ) = e − ( λ 1 + λ 2 ) t / e − λ 2 t = e − λ 1 t = 1 / e λ 1 t

e λ 1 t = ( λ 1 + λ 2 ) / λ 2 = λ 1 / λ 2 + 1

λ 1 t = ln ( λ 1 / λ 2 + 1 )

t = ln ( λ 1 / λ 2 + 1 ) / λ 1

Therefore:

λ 1 = 0.693 / 30.17 × 365 × 24 × 60 = 4.37 × 10 − 8 min − 1

λ 2 = 0.693 / 2.55 = 0.272 min − 1

t = ln ( 1 + 4.37 × 10 − 8 / 0.272 ) / 4.37 × 10 − 8 = 3.68 min

Due to great difference between both radioisotopes: contaminant (¹³⁷Cs, t_1/2 = 30.17 years) and natural (⁴⁰K, t_1/2 = 1.28 × 10⁹ years), their decay constants are much greater for the minor half life (¹³⁷Cs, λ 1 = 0.693 / 30.17 = 2.297 × 10 − 2 years − 1 ) than that of much greater half life (⁴⁰K, λ 2 = 0.693 / 1.28 × 10 9 = 5.414 × 10 − 10 years − 1 ). 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% [7]. But this light contamination also implies the continue production of ^137mBa(t_1/2 = 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 × t_1/2(¹³⁷Cs)/t_1/2(^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

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 [7], 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.

The authors declare no conflicts of interest regarding the publication of this paper.

Fernández, K., Navarrete, J.M., Zúñiga, M.A. and Hernández, E. (2020) Isobars Separation (¹³⁷Cs-^137mBa-¹³⁷Ba) from Marine Sediments, in Order to Evaluate Directly Their Radioactive Contamination by Mass Spectrometry. World Journal of Nuclear Science and Technology, 10, 32-38. https://doi.org/10.4236/wjnst.2020.101004