In the fission of U-235, two cesium isotopes form with a high cross section, Cs-134 and Cs-137. Their ratio of the two isotopes as the result of fission is well deter­mined; however, the decay rate of Cs-134 is higher. Therefore, the ratio of the two fission cesium isotopes gives information on the time of the environmental pollu­tion by radioactive cesium. Cs-134 can be produced in the 133Cs(n, Y)134Cs nuclear reaction; its half-life is 2 years, and it has (3_ and gamma radiation. The half-life of Cs-137 is 30 years, and it emits (3_ and gamma radiation. Since cesium ion is strongly sorbed on soils, its migration is rather slow. For these reasons, Cs-137 can be applied to study soil formation and erosion. In these studies, the activity of Cs-137 already present in the soil from the nuclear pollutions is measured. For more information see Section 8.8.

8.6.18 Renium-186

186Re is produced by the 185Re(n, Y)186Re nuclear reaction. Its half-life is 90.6 h, and it has (3_-radiation. It has medical applications.

As mentioned in Section 8.2, the radioactive indicator applied in carrier-free or very low concentrations can coprecipitate with any macrocomponent of the system if they can form isomorphous crystals. As an example, barium chloride (macrocomponent) and radium chloride (microcomponent) have been mentioned.

In the initial step of coprecipitation, the macro — and microcomponents are mixed in solution. When mixing entropy becomes maximal, the solution will be homoge­neous. Then, there are two ways to achieve coprecipitation:

• By fast cooling of the solution. In this case, fine grains are produced. For example, (RaBa)Cl2 is precipitated by the addition of concentrated hydrochloric acid under cooling. The composition of the crystalline phase is the same in any small volume. This can be expressed by the Henderson—Kracek equation:

У = D-—У (9.118)

x a — x

where x and y are the quantities of the macro — and microcomponents in the crystalline phase, respectively; a and — are the quantities of the macro — and microcomponents in the whole system; and D is the fractionation coefficient. Fractionation by coprecipitation is possible when D ^ 1.

• The crystals are grown slowly; e. g., by the slow evaporation of the solvent. In this way, the composition of the solution continuously changes, and therefore the composition of the phases also change continuously. As a result, the composition of the crystal varies with the depth of the grains, as expressed by the Doerner—Hoskins equation:

a-

ln — = A ln — (9.119)

a— x -— y

where A is the fractionation coefficient and the other signs have the same meaning as in Eq. (9.118).

Equations (9.118) and (9.119) can be related, assuming a thermodynamical equi­librium for any infinitely short time of the crystal growing:

Separating the variables:

dx _ ^ dy

a — x b — y

Equation (9.121) can be solved for the whole period of crystal growth, assuming that the crystal growth is determined by the surface equilibria at any time:

dx _ ^ ‘ dy

a— x b— y

The solution is:

ln(a — x) _ A ln(b — y) + C (9.123)

In order to determine the integration constant (C), we assume that at the initial time of the crystal growth, (t _ 0), x _ 0 and y _ 0 (no crystal yet):

ln a _ A ln b 1 C (9.124)

From here:

C _ ln a — A ln b (9.125)

Substituting C into Eq. (9.123), the Doerner—Hoskins equation is obtained:

ln(a — x) _ A ln(b — y) 1 ln a — A ln b (9.126)

Experiments have shown that crystals that have a composition characterized by the Doerner—Hoskins equation can transform to crystals with uniform composition characterized by the Henderson—Kracek equation by isothermic transcrystallization.

Determination of the flow rate of streaming substances is one of the most important measurements in the chemical industry. In addition to direct flow rate determina­tion, movements based on mechanical principles (e. g., the rotation speed of a pro­peller built into the stream) need accurate calibration. Both can be performed by the radiotracer technique.

A great advantage of the flow rate measurements executed with the tracer tech­nique is that these measurements provide direct flow rate values in volume per time unit. This is in contrast to other methods that measure linear flow velocity, which also need to determine the flow cross section. In chemical technology, the cross section is not always well defined, e. g., there are pipes with changing cross sections where internal deposits can cause the change, or liquid flow with bubbles where the liquid volume is not defined, or open channels with changing cross sections.

In addition to this, in the case of several phases flowing together, the flow rate of the individual phases can be determined separately with the tracer technique. For instance, in the case of pneumatic powder transport, it is possible to label the transported air and powder separately, or in the case of suspensions transported with water, the water and the solid granules can be labeled separately. These exam­ples demonstrate the unique character of the radiotracer technique. When labeling
the phases individually and determining flow rates for the phases separately, the slip between the transporting (e. g., air and water) and the transported phases can also be determined.

Determination of the flow rates with the tracer method is based on measuring the dilution rate of the injected tracer in the pipe. The injected total activity is expressed as the volume and radioactive concentration of the radioactive tracer:

A = Va (11.5)

The dilution process of the tracer is described as integral to the radioactive con­centration by cross section and length as follows:

Introducing linear velocity of the flow: v = dL/dt (and from this, dL = v dt) Substituting dL into Eq. (11.4), we obtain:

Separating the double integral to members of cross section and time:

One member of Eq. (11.9) corresponds to the desired flow rate:

Technically, the measurement consists of a tracer injection at a given point of the pipe (Figure 11.4) and of a detector installed at another point over the mixing distance plotting the intensity function in time. Spreading the radioactive “cloud” is

Injection of radioisotope

Flow rate Q.|

V

Q. + Q2

Flow rate Q2

V

Sampling

Figure 11.5 Spreading the radioactive “cloud” in time.

demonstrated in Figure 11.5. Mixing distance is 100 X D, where D is the diameter of the pipe. For quantitative measurements, prior to the tracer injection, both the activity and volume of the radioactive tracer and its activity versus count rate are determined.

In addition to direct flow rate measurements, if the flow cross section is well — defined, linear velocity measurements with radiotracer technique are also possible. Such so-called peak-to-peak methods have practical importance in the calibration of rotameters.

In this method, the tracer is injected instantaneously and the passing of the tracer peak is sensed by two detectors installed onto the pipe at two points (Figure 11.6). The linear velocity of the flowing substance (v) can be calculated from the distance of detectors (L2—Lj) and from the time difference of intensity peaks (f2—tj):

L2 — Li

v =

t2 — tl

Injection of radioisotope

V

Recorder plotting intensity versus
time function

Practical examples for flow rate determinations with the radioisotope tracer technique (1—direct flow rate measurement; 2—linear velocity measurement):

• Testing for flow rate ventilation systems (1).

• Cooling water consumption determination in an oil refinery (1).

• Cooling water consumption determination in heat power stations (1).

• Determination of wastewater flow rates in various factories (1).

• Capacity measurement of pneumatic powder transport pipes in a cement factory (1).

• Flow rate measurement of moving solid grains in a drum furnace of a cement factory (2).

• The flow rate in natural streams, rivers, karst waters, surface waters, and irrigation sys­tems (1).

The peak-to-peak method (2) suitable for linear velocity measurement is used primarily for calibrating flow meters.

Digital image processing plays a more and more important role in the development

of gamma cameras.

• Modern gamma cameras apply real-time, position-dependent digital corrections to com­pensate for various degrading factors, such as differences in signal amplification (energy correction), geometric distortions (linearity correction), and the remaining differences in sensitivity (uniformity correction).

• So-called full digital cameras digitize the output of each PMT directly, and then all the rest of the processing, including the calculation of coordinates and corrections, is done by the computer.

Autoradiography can be used to study the local distribution of the radioactive iso­topes. The distribution of the isotopes in the different objects and organs is studied by stripping films or X-ray films. Similar to the photo emulsions used in black- and-white photography, they contain silver bromide particles in a gelatin emulsion. When irradiating, Ag(I) ions are reduced to metallic silver. This reduction takes place only in those spots where the radiation touched AgBr. The silver particles are then magnified by a chemical procedure called “development.” The formation of metallic silver causes the blackening of the film, and a negative image is obtained. The intensity of the blackening is proportional to the intensity of radiation. Similar to traditional photography, a positive image can be produced from the negative image. On the positive image, the places exposed to high radioactive intensity become white.

As mentioned previously in this section, stripping films are frequently applied to autoradiography. These films may be in close contact with the sample, improving the quality of the autoradiographs.

In Figure 8.3, a negative autoradiogram of the radiocolloid formation is illus­trated. Moreover, in Figure 14.9, an autoradiogram (left) and a microscopic picture (right) of etched tin alloy containing 10_7% 111Ag are shown. As seen, the intro­duction of the radioactive silver takes place on the boundaries of the particle in the polycrystal.

An application of autoradiography in medical science is shown in Figure 14.10.

The Rn-222 isotope can be produced using the Hahn emanation source. The solution of 226Ra(II) ions is mixed with FeCl2 solution, and then iron hydroxide is precipitated with ammonia solution that contains no carbonate. The precipitate

obviously contains radium ions, which disintegrate to radon. At the optimal Ra: Fe = 1:55 ratio, about 95% of radon gas is emanated. As the precipitate ages, the quantity of the emanated radon decreases. When that happens, the precipitate is suspended in water; iron hydroxide is separated by extraction with ether. Radium remains in the aqueous phase, from where it can be precipitated again by iron chlo­ride and ammonia. It is very important that the ammonia solution should not con­tain carbonate ions; otherwise, radium carbonate is formed, which cannot be separated from iron hydroxide.

A scheme of an emanation source is shown in Figure 8.5. Radon can be col­lected in the ampoule (P). Radon gas has been used in medical therapy to replace the toxic Ra-226.

Sealed radioactive preparations emitting gamma radiation (e. g., 192Ir — and 60Co-sealed sources) are produced by placing reactor-irradiated metal pellets or cylinders into steel capsules, followed by sealing by welding. The overall activity
of the assembled source can be controlled by using the appropriate number of the individual pellets/cylinders of known (measured) activity. The activities of such gamma-emitting sealed sources are extremely high; they are in the range of TBq (terra-Becquerel).

Beta-emitting (e. g., 137Cs) sealed sources are produced by chemical processing of Cs extracted from fission mixtures to CsCl, followed by embedding these particles into glass beads and finally by sealing glass beads into metal capsules. Alpha-emitting (e. g., 241Am) sealed sources are produced by extracting the given radionuclide from fission mixture and deposited onto foils.

Sealed radiation sources are used both for medical and for industrial applications. In medical applications, external radiation therapy and brachytherapy, while in industrial applications radiography (e. g., testing welding seams) and gamma sterili­zation are generally known.

Similar to double isotope dilution, substoichiometric analysis is applied to the quantitative analysis of a radioactive substance (m0) if it is present in such a small quantity that the specific activity before the dilution (a0) cannot be determined. The radioactivity of the standard and the unknown sample should be the same. A reagent is added to both the standard and the unknown solution in unequivalent quantities. This is why the method is called “substoichiometric analysis.” The prod­uct of the reaction (e. g., a complex compound) is separated (e. g., by extraction), and the activity of an aliquot is measured. As a result of the addition of the reagent in an unequivalent quantity, the activity of the product is inversely proportional to the concentration of the solution.

When several standard solutions with the same activity are used, a calibration curve is plotted (Figure 10.6). The concentration of the unknown sample is deter­mined using this calibration curve. This method is applied in RIA studies (as discussed in Section 12.3.1).

10.1.6.2 The Dynamic Isotope Dilution Method

The isotope dilution method can be applied in open-flowing systems (see Section 11.2.6). Let us assume a tank with volume V and flow rate w of a liquid passing through the tank. At t = 0, a radioactive indicator with a0 specific activity (or intensity) is added to the liquid. Assuming the mixing to be ideal, at t time, the specific activity (intensity), a, of the liquid leaving the tank is:

a = a0 e— (10.12)

For a series of tanks, the specific activity (intensity) of the liquid leaving the ith tank is:

(10.13)

Nuclear methods for logging geological boreholes are used in the hydrocarbon and coal industries, in ore mining, and in water resource exploitation. The well-fitting detector is introduced into the borehole by means of a widlass installed on a vehi­cle. The detected signals are transferred to the measuring instrument located on the surface of cables (Figure 11.29).

Three types of nuclear borehole measurements exist:

• Measuring the natural radiation in each layer.

• Tracking radiation excited with sealed radiation sources.

• Methods using radiotracers introduced into boreholes.

An excitation radiation source can be a sealed gamma source, sealed neutron source, or neutron generator. According to the type of the measured radiation, natu­ral gamma logging, gamma-excited gamma-density logging, neutron detection, and NAA are distinguished. Methods applying open radioisotopes belong to tracer techniques.

Figure 11.29 shows depth distribution of the natural gamma radiation in an exploration of coal mine prospecting. Coal spots located among sandstone and marl layers represent higher gamma intensities.

A great benefit of nuclear borehole techniques is that they also serve data on the chemical composition of penetrated stones and then can be executed in natural
conditions where other methods are not successful. At the same time, their draw­back is that they are more labor-intensive and require complicated measuring instruments and other equipment.

Further Reading

Foldiak, G. (1986). Industrial Application of Radioisotopes. Akademiai Kiado, Budapest. Charlton, J. S. (1986). Radioisotope Techniques for Problem-Solving in Industrial Process Plants. Leonard Hill. Glasgow and London.

Rozsa, S. (1979). Nuklearis me’re’sek az iparban. Muszaki Konyvkiado, Budapest.

Baranyai, L., and Ivicsics, F. (1990). A talajviz aramlasi sebesse’ge’nek meghatarozasa. (Determination of flowing rate of groundwater.). Viziigyi Kozlemenyek 32 (4): 399—400. Lapkiado Vallalat, Budapest.

PET studies for research purposes, especially pharmacokinetic and receptor kinetic investigations, are very important. Several hundreds of different mole­cules labeled with positron emitters have been administered to animals and humans. The greatest advantage of PET is that any organic molecule can be labeled with positron emitters (see Table 12.6). It is possible to obtain images of such a small number of molecules in a living organism (e. g., bound to recep­tors) that otherwise can only be detected in sections (by autoradiography) or in vitro.

12.6.2 Imaging Myocardial Metabolism

If a myocardial perfusion SPECT study performed after infarction (as described in Section 12.5.3) shows perfusion defects in both stress and rest images, the study of glucose metabolism is the best known method of distinguishing between two states: long-term diminished blood supply may have resulted in dead (unviable) myocar­dium, or the cells may still be viable but hibernated, meaning that although they do not presently contract because of the long-lasting oxygen deficiency, the pump function of the heart may improve after restoring the blood supply. Unfortunately, the glucose molecule cannot be labeled with gamma emitter radionuclides since the molecule is too small and its atoms do not have gamma-emitting radioisotopes. However, FDG (mentioned in Section 12.6.2) allows the imaging of glucose metab­olism. While a healthy myocardium gets energy from burning glucose after eating and from fatty acids in fasting state, a hibernated myocardium can consume only glucose, and a scar does not utilize significant amounts of either glucose or fatty acids. So, for instance, in fasting state, only a hibernated myocardium accumulates FDG. A hibernated myocardium can be revived by angioplasty or coronary artery bypass graft surgery, while scars cannot be improved by either therapeutic approach.

Further Reading

Nobelprize. org. (2012). George de Hevesy — Biography. Retrieved March 23, 2012, from http://www. nobelprize. org/nobel_prizes/chemistry/laureates/1943/hevesy-bio. html [Online].

Nobelprize. org. (2012). Rosalyn Yalow — Autobiography. Retrieved March 23, 2012, from http://www. nobelprize. org/nobel_prizes/medicine/laureates/1977/yalow. html [Online].

Wagner, Henry N. (2003). Hal Anger: Nuclear Medicine’s Quiet Genius. J Nucl Med, 44, 26N, 28N, 34N.

NuclearPathways Project. (2011). Ernest O. Lawrence. Retrieved March 23, 2012, from http://www. atomicarchive. com/Bios/Lawrence. shtml [Online].

European Association of Nuclear Medicine (2010). Status of Nuclear Medicine in Europe — 2009. EANM, Vienna.

World Health Organisation. (2004). The top 10 causes of death. Retrieved March 23, 2012, from http://www. who. int/mediacentre/factsheets/fs310/en/index. html [Online].

Magill, J. and Galy, J. (2005). Radioactivity Radionuclides Radiation. Springer, Berlin.

Powsner, R. A. and Powsner, E. R. (2006). Essential Nuclear Medicine Physics. 2nd ed. Blackwell, Malden.