The isotopes are used as chemical indicators, so they must fulfill the same require­ments as the usual chemical indicators. This means that they have to indicate the presence and concentration of a substance in a given place at a given time, but they should not have any effect on the studied process. The radioactive isotopes usually satisfy these criteria, since they are chemically the same as the inactive isotopes of the same elements. For example, when a 12C atom of an organic substance is

replaced by a 14C isotope, the type and strength of the chemical bond and the physical and chemical properties of the compound do not change significantly. Of course, the differences between the masses of the isotopes can result in some differences—in other words, isotope effects (see Chapter 3). These isotope effects, however, can usually be observed only for light elements. For heavier elements, the effects are negligible because the experimental errors are generally higher than the influences of the isotope effects. Therefore, the isotope effects are usually negligible in radioactive indicator methods.

The requirements can be classified into two groups: (1) the usual requirements for all chemical indicators and (2) special requirements only for radioactive indica­tors. The usual requirements are as follows: the indicator should be sensitive and selective, and can be measured precisely; and the distribution of the indicator should be homogeneous in the system.

The sensitivity of a radioactive indicator depends on its decay rate, and as a con­sequence, so does the activity of the isotope. The sensitivity can be shown in the next example. Let’s take a radioactive indicator with 1000 counts/minute (cpm) radioactive intensity; this intensity can usually be measured easily. The standard deviation of the measurement of 1000 cpm is ±3.3% (see Section 14.7.1). When the measuring efficiency is 10%, this intensity can be obtained if the activity is 10,000 disintegrations/minute (dpm). Assume that the half-life of the radioactive isotope is 60 min (such as for 212Bi). These data can be substituted into Eq. (4.12) as follows:

dN л ln 2

A = -■ = Xn= N

dt t1=2

From Eq. (8.1), N = 9 X 105 nuclides are obtained. Expressing this number in mols (dividing by the Avogadro number), you get 9 X 105/6 X 1023 = 1.5 X 10_18 mol. Therefore, this very small quantity can be measured easily on the basis of its radio­activity. When the decay constant is higher, the sensitivity decreases.

The homogeneous distribution of the radioactive indicator is very important. The radioactive indicator is homogeneously mixed in a system, that is the mixing entropy is maximal (see Section 9.1) if the chemical species of the radioactive indi­cator and the studied substance is ab initio the same or a fast isotope exchange can be possible between the chemical species of the radioactive indicator and the stud­ied substance. The rate of the isotope exchange depends on the strength of the chemical bonds; therefore, it changes in a very wide timescale. For example, the binding energy of iron(II) ion in hemoglobin is high, so the rate of the isotope exchange between iron(II) ions in hemoglobin and in 55Fe ions dissolved in water is practically zero. In such cases, the indicator gives no information on the sub­stance in the other chemical species.

In radioactive tracer experiments, the concentration of the indicator is frequently very small. (As seen in the previous example, even 10_18mol can be measured.) For instance, carrier-free radioactive isotopes could be mentioned. The term
denotes a radioisotope of an element in pure form; i. e., essentially undiluted with a stable isotope. In fact, the term “no-carrier-added” is more correct than “carrier — free.” This means that no carrier is added. However, one can still be present in the system during the experiments, for example, as the result of the interaction with the environment or as the pollutants in the chemicals used.

In other applications, the inactive isotopes (carriers) of the radioactive isotope are added to the system containing the isotope at a low concentration. However, the chemical identity does not need to be the same; chemically similar substances may also behave as carriers. It is known, for example, that potassium or calcium ions are carriers of Cs-137 and Sr-90, respectively, in geological as well as biologi­cal systems. It should be mentioned, though, that in such cases, the ratios of the isotopes and the carrier may be different in each phase of the heterogeneous system.

The two cases (carrier-added or no-carrier-added) must be treated differently. In the presence of a carrier, the usual (macroscopic) chemical concentrations are pres­ent for the chemical species in question; thus, the usual chemical relations and laws apply.

The chemical properties at these very low concentration ranges (no-carrier — added), however, can be different from the usual properties seen in macroscopic concentrations. In the case of such low concentrations, no chemical system can be considered homogeneous because the number of molecules on the surfaces (the wall of the laboratory vessels, any contaminants in the solution, air bubbles, small particles, great molecules, etc.) is more than, or at least similar to, the number of radioactive nuclides in the solution. The radioactive isotopes can accumulate in bulk on these surfaces and can take part in the subsequent formation of heteroge­neous phases (adsorption, colloid formation, precipitation, etc.). Similar accumula­tion also takes place in the range of macroscopic concentration; however, its effects (the accumulation of 10_7—10_8 mol of the substances) can be neglected. In carrier-free systems, however, the total quantity of the radioactive isotope can be accumulated on the surfaces, resulting in the significant decrease in its concentra­tion and activity of the bulk. The adsorption of thorium isotopes on the walls of laboratory vessels is shown in Figure 8.2.

Besides adsorption on the macroscopic interfaces, the ions in very low concen­tration can precipitate even when the concentrations do not reach the solubility product (i. e., normally, they would stay in solution) and/or pseudocolloids (or radiocolloids) may form. Even in a solution containing an alkali metal ion, Cs-137 ion in carrier-free concentration, colloid particles are formed under conditions where it would not usually be expected based on thermodynamic parameters.

For the understanding of the formation of heterogeneous phases at extremely low concentrations, two rules called Hahn’s rules (Hahn, 1926a, b, Hahn and Imre, 1929, Wahl and Bonner, 1951) may serve as starting points:

1. The precipitation rule says that an element (isotope) in extremely low concentration coprecipitates with another element in high concentration if it fits into the crystal lattice of this other element.

Figure 8.2 (A) Adsorption of thorium from aqueous solution on the wall of a 10 ml pipette versus concentration of thorium salt. (B) Equilibrium adsorption of thorium (thorium concentration is 2 X 10-8 mol/dm3) on the wall of glass and polyethylene vessels as a function of pH. Source: Reprinted from Choppin and Rydberg (1980), with permission from Elsevier.

2. The adsorption rule says that an ion in extremely low concentration adsorbs well on the surface of a solid crystal when the surface charge of solid and ion are opposite and the adsorbed compound is very insoluble. Thus, the ions in very low concentration can be precipitated even when the concentrations do not reach the solubility product (i. e., nor­mally, they would stay in solution), and/or radiocolloids may form.

The formation of radiocolloids can be interpreted by impurities present in the solution (air bubble, dust, cellulose fiber, hydrolytic products, giant molecules, etc.) that act as active sites for heterogeneous nucleation where the radioactive iso­topes can adsorb. In the case of the formation of radiocolloids, the radioactive iso­tope is not evenly distributed in the solution (Figure 8.3), so the formation of radiocolloids must be avoided, for example, by the application of very pure sub­stances, including water, and keeping the isotopes in acidic solutions.

At very low concentrations of the carrier-free radioactive isotopes, the interfaces are not covered totally, and the coverage is smaller than monomolecular. For this reason, the usual thermodynamic requirement, namely that the activity of the sur­face is one, is not satisfied. As a result, the thermodynamic relations, such as the Nernst equation, have to be applied in their complete form:

RT flox

є = £0 — ln (8.2)

zF flred

where є is the redox potential, є0 is the standard redox potential, R is the gas constant, T is the temperature, z is the change of charges, F is the Faraday constant, and aox

Figure 8.3 (A) Formation of polonium radiocolloid in water. (B) No colloid-formation in acetone. The figure shows positive autoradiograms (discussed in Section 14.5.2), and the white spots show the distribution of the radioactive isotope. The straight lines are the tracks of the alpha particles emitted by polonium. Source: Adapted from Bouissieres et al. (1947), with permission from Elsevier.

and ored are the activities of the oxidized and reduced species, respectively. In addi­tion, the activity of the solid phase (reduced species of metals) is not known, so the value of the redox potential has to be determined experimentally in each case.

As mentioned in the Hahn’s rules, an element (radioactive isotope) in extremely low concentration (microcomponent) coprecipitates with another element in high concentration (macrocomponent) if it fits into the crystal lattice of this other ele­ment. The distribution of the micro — and macrocomponents in the coprecipitate can be expressed by different formulas, namely by the Doerner—Hoskins equation:

ln—— = A ln -— (8.3)

a — x b — y

or the Henderson—Kracek equation:

У = Db-—y (8.4)

x a— x

In Eqs. (8.3) and (8.4), D and A mean the fractionation coefficients, a and b are the quantities of the macro — and microcomponents in the whole system, and x and y are the quantities of the macro- and microcomponents in the crystal phase. When the fractionation coefficient is 1, as in Hevesy’s experiments (see Section 8.1), the macro — and microcomponents are chemically the same; they are the isotopes of the same elements. When the fractionation factor is not equal to 1, the micro — and macrocomponents are different (e. g., RaCl2 and BaCl2) even if they have similar properties (e. g., isomorphous crystal lattice).

Radioactive indicators have specific properties due to the fact that they are radioactive: (1) the properties originating from the radioactive decay and (2) the properties coming from the different mass numbers.

The radioactive indicator disintegrates, that is, the activity decreases in time. This decrease is determined by the decay constant or half-life. In the tracer studies, it is desirable if the half-life of the radioactive isotopes is comparable to the time needed for the studies. If the half-life is too short, the radioisotope can disintegrate before finishing the investigations. If the half-life is too long, the measurable activ­ity demands a greater quantity of the radioactive nuclides. In addition, as the result of the decay, radioactive wastes form, the treatment of which necessitates particular procedures, and the radiation impact of the environment is also higher. This is especially important in in vivo biological and medical applications.

Radiation, especially at high activities, can also initiate chemical and biological processes (radiolytic effects as discussed in Sections 6.4 and 13.4.2). Any operation with radioactive material demands special laboratory conditions, radiation protec­tion, and waste treatment.

As mentioned previously, the sensitivity of the radioactive indication is deter­mined by the properties of the isotope. The same is true for the selectivity. As a result of the radioactive decay, daughter nuclides that are chemically different from the parent nuclides are formed which can contaminate the studied system. A special problem arises when the daughter nuclides are also radioactive. In this case, the measurements of radioactivity can become more complex. The radiations with dis­crete energy (e. g., alpha and gamma) can be separated by spectrometry. The mea­surement and separation of the continuous radiation (e. g., beta) may be difficult. As an example, the pure beta emitter parent/daughter nuclide pair, 90Sr—90Y, is mentioned. Precise activity measurements can be done only in secular equilibrium (see Section 4.1.6). Since the half-life of the daughter nuclide, 90Y, is 64 h, estab­lishing this equilibrium demands a rather long time. However, when the beta ener­gies of the parent and daughter nuclides are different enough, the spectra can be separated by mathematical methods, or the parent—daughter elements can be sepa­rated chemically.

Another special property of the radioactive indicators is due to the difference between the mass numbers of the isotopes. This is the isotope effect (discussed in Section 3.1), which is important mainly for light elements. When an inactive carrier is added to the radiotracer, the specific activity decreases because of the isotope dilution. As will be discussed in Section 9.4.1, isotope dilution is the basis of numerous analytical methods. The inactive isotopes of the carrier and the radioac­tive isotopes participate in an isotope exchange reaction, which was mentioned pre­viously relating to homogeneity.