The Ra-226 isotope was discovered and prepared by Marie Curie. This isotope has been applied to the study of the general properties of radioactivity and radiation. Ra-226 has been prepared by coprecipitation with very insoluble lead and barium salts. The coprecipitate has been purified by fractionated crystallization. Metallic radium has been produced by the electrolysis of molten salt in 1910.

The Ra-226 isotope has been used in cancer therapy. Radium is contained in metallic needles, and these needles are implanted next to the tumor. The disadvan­tage of the application of radium is that it is very toxic; the lethal dose is 1 pg. Any damage of the needle containing radium could cause death.

Quality control of the unsealed radioactive preparations includes the determination of the following quality parameters:

• radionuclidic purity (detection and quantity determination of the contaminating radionuclides),

• radiochemical purity (detection and quantity determination of radionuclides found in another chemical form as that of the product),

• control of radioactive concentration,

• control of the pH of the solution,

• checking microbiological purity.

The most frequently applied quality control methods of the unsealed radioactive preparations are summarized in Table 8.17. The quality parameters of the unsealed radioactive preparations are determined on samples taken from the bulk solution. Microbiological control tests are carried out as retrospective tests after decay.

If the radioactive species of the substance to be analyzed is not available, the iso­tope dilution method cannot be applied directly. In this case, the substance to be analyzed is reacted with a radioactive reagent. This radioactive product can be then subjected to the reverse isotope dilution method (described in Section 10.1.6.2). The method, therefore, combines the preparation of a radioactive compound and the reverse isotope dilution method. The steps following the preparation of the radioactive compound are the same as for reverse isotope dilution. For example, the substance to be analyzed is A, the radioactive reagent is Bx, the excess of the reagent is Bm, and the derivate isotope dilution consists of the following steps:

A + Bx! ABx + Bm (chemical reaction) (10.5)

ABx 1 Bm + AB! (ABx 1 AB) 1 Bm (dilution) (10.6)

(ABx 1 AB) 1 Bm! (ABx 1 AB) (isolation) (10.7)

Similar to the other types of isotope dilution, the specific activities have to be determined before and after dilution, and the quantity of AB has to be known.

10.1.6.1 The Double Isotope Dilution Method

Double isotope dilution gives an opportunity to determine the quantity of a radioac-
tive substance (m0) if it is present in such small quantities that the specific activity

before the dilution (a0) cannot be determined. In this case, two aliquot samples are taken from the substance to be analyzed, and they are diluted with inactive isotopes in different quantities (m1 and m2, т1ф m2). After homogenization, the pure sub­stances of the two diluted samples are isolated and the specific activities (a1, a2) are measured. For the two dilutions, the following equation applies:

a0m0 = a(m0 + m) (10.8)

and

a0m0 = a2(m0 + m2) (10.9)

Thus, m0 can be calculated from the quantities m1 and m2 as well as the specific activities after the dilutions, a1 and a2.

The double isotope dilution method is applied in nuclear chemistry, organic, and biochemistry; however, it is the least accurate of the isotope dilution methods. This is because to determine the specific activities, a relatively large quantity of diluting substance has to be added. If m0 will become negligible compared to m1 and m2, the method cannot be applied.

Radiography (discussed in Section 14.5.2) is a nondestructive material testing method using X-ray or gamma radiation to image internal parts, structural defects, or internal structures of nontransparent materials, parts, or equipment. The main application is testing defects of welding seams by means of a radiography record (radiogram).

To make a radiogram, ionizing radiation leaving the source through a collimator penetrates the workpiece placed in front of the beam and replicates the internal structure of the material on a film placed on the opposite side (Figure 11.26).

A container with a source-controlling device is called a “defectoscope,” which is a structure on wheels. Its control unit is suitable for transporting the shielding container within the pipe to the spot of the welding seam, and it has a pneumatic device to pull the source out of the container for the length of the exposition. Prior to the exposition, the welding seam is covered outside the pipe with high-resolution photo film (Figure 11.27). To test steel structures for wall thickness between 15 and 65 mm, Ir-192 is used; between 20 and 90 mm, Cs-137 is used; and between 40 and 150 mm, Co-60 is used.

By means of radiograms, gas intrusions, slag intrusions, metallic intrusions, binding defects, welding defects, cracks, and surface deficiencies can be visualized.

Figure 11.28 A visualized catalyzer bed tested with a gamma-transmission technique.

A modern variant of industrial radiography does not search for material defects; rather, its objective is to visualize volumes, arrangements, and phases of materials to monitor the operation of equipment.

Radiation absorption executed with parallel movement of the detector and a gamma radiation source requires simpler techniques (Figure 11.28). In more com­plicated cases, a high number of detectors is installed, surrounding the entire equipment.

The measuring technique based on transmitting the entire volume of equipment was used, e. g., for testing the cross-sectional density distribution of distillation

Figure 11.29 Natural gamma borehole logging.

columns where, in addition to the substance distribution on trays, the disposition of the steam and liquid phase and their relative volume rate were determined. In another case, a transmission study of a catalyzer bed was performed (Figure 11.28).

At present, most PET studies apply 2-(18F)-FDG (Fluoro-2-Deoxy-D-Glucose). F-18 is preferred for clinical studies because of its favorable half-life (see Table 12.6). Since many kinds of tumor cells have increased glucose metabolism, the most com­mon indication is searching for tumors, especially to explore whether lymph node and distant metastases are present and to identify remnants or recurrent tumors after therapy. After surgery or radiation therapy, the environment of a former tumor will be distorted anyway, so it is hard to distinguish harmless scars from tumor lesions using structural imaging methods like CT and MRI.

Figure 12.12 The detectors of PET, packed in rings around the patient, detect annihilation radiation in coincidence mode.

Most recently produced PET devices are combined with a CT. In this way, stud­ies with both modalities can be completed sequentially, keeping the same position of the patient on the table. Attenuation correction of the PET images is much faster and less noisy when using CT rather than a separate set of transmission images obtained with an external radioisotope source. Moreover, the more detailed CT image helps determine a better localization of the abnormalities, thus reducing the fraction of false positive reports compared to PET alone. On the other hand, hybrid PET/CT has a much higher sensitivity for the detection of tumors than CT alone (Figure 12.13).

See at the production of S-35.

8.6.4 Potassium Isotopes

K-38: produced in 35Cl(a, n)38K nuclear reaction, t1/2 = 7.6 min, emits (3+ particles. K-42: see at the production of S-35.

8.6.5 Calcium-45

45Ca can be produced in the 44Ca(n,^)45Ca reaction. Its half-life is 163 days, and it emits (3_ particles, similar to C-14 and S-35. 45Ca is mostly applied in biological research.

8.6.6 Chromium-51 (Cr-51)

Cr-51 can be produced in the 50Cr(n, Y)51Cr nuclear reaction, half-life is 27.7 days, and it emits (3_ and gamma radiation. 51Cr isotope is applied in biological and med­ical research in the so-called chromium release assay studies. This method is based on the adsorption of Cr-51 on the cell walls. For additional information, see Section 8.7.1.1.

Each substance in the environment, including radioactive isotopes, interacts with groundwater and geological formations (soils and rocks). Transport in the pores of rocks and soils occurs via the migration of water-soluble materials. The migration in porous solid media is influenced both by hydrological processes and by the inter­action between the soluble substances and the geological formations. The migration of a substance in a porous solid medium is influenced by the flowing medium (typ­ically groundwater in geological formations), the chemical species of the migration substance, and its sorption properties. Thus, the migration is affected by the follow­ing factors:

• Advection: the migration of soluble components with flowing medium.

• The mixing of solutions in macropores of the solid medium, which is due to the different flowing rates of solutions in the pores with different sizes.

• Diffusion of dissolved components in the liquid phase.

In addition, the interactions of solid matrices and dissolved substances are the following:

• Adsorption and ion exchange

• Precipitation

• Structural modification and destruction of materials.

In the case of the migration of nonsorbing substances, the transport of the dis­solved substances is determined by the first three processes, namely advection, mixing, and diffusion. This means that the dissolved components move with water (e. g., chloride ions in geological formations). The flux of flow is described by dif­ferent migration equations. A frequently used migration equation is:

Sc Sc

J0 = -[0Dh + 0Deff ] 7е + v0c = —0D 7е 1 qc (9.36)

ox ox

where J0 is the flowing rate of water (flux), 0 is the humidity of medium, Dh is the hydrodynamic dispersion coefficient, Deff is the effective diffusion coefficient, c is the concentration of flowing material at place x, v0 = q is the volume flowing in a unit time, and v is the linear flowing rate.

If the solid medium reacts with the dissolved components (e. g., by adsorption or ion exchange), their flowing rate decreases:

where p is the density of the matrix and a is the sorbed amount.

When the dissolved components are adsorbed on the solid matrix or they take place in ion exchange reactions, or precipitate, their migration rates can decrease significantly. The degree of decrease is determined by the chemical spe­cies of the given substance under chemical conditions characteristic of the solutions in geological formations (groundwater).

As discussed in Section 9.3.2.1.1, the migration equations (including Eqs. (9.36) and (9.37)) cannot be solved generally; only partial solutions can be obtained in certain initial and boundary conditions. In addition, the sorption has to be included, e. g., by a sorption isotherm equation that describes the relation between the con­centration of the dissolved components in the solid and solution phases. As an example, the Langmuir adsorption isotherm is mentioned:

where m is the mass of the adsorbent (g), w is the pore volume saturated with water (dm3), y is the ratio of the substance dissolved in the pore water, x is the ratio of the substance sorbed on the solid phase, k is the distribution coefficient (k = x/y), Ce is the equilibrium concentration of the solution, a is the adsorbed quantity, z is the number of the active sites of sorption, and K is the parameter that is characteris­tic of the sorption energy.

Neglecting the advection, Eq. (9.37) is simplified as follows:

By substituting the adsorbed quantity (a) from Eq. (9.38), we obtain:

8C w 8C @2C

1 k = D 8t m 8t 8×2

and from here,

The quantity of the value in brackets can be interpreted as migration coefficient (Dm):

Equation (9.42) is equivalent to Fick’s second law (Eq. (9.32)), but the interpreta­tion of Dm is slightly different. A similar mathematical procedure can be applied for ion exchange too.

Figure 9.7 Migration cell for the study of radionuclide transport. Source: Reprinted from Nagy and Konya (2005), with permission from Elsevier.

The denominator of Eq. (9.41) is called the “retardation factor,” which is the ratio of the migration coefficients of a nonsorbing substance (e. g., chloride or the migrating medium, water, itself) and a sorbing substance.

As discussed in Section 7.3, geological repositories play an important role in the safe storage of nuclear waste. The migration rate of the radioactive isotopes, both in the engineering barrier system and in the surrounding geological formation, is a sig­nificant factor that must be considered. The migration rate of the radionuclides stud­ied in laboratory model experiments using a migration cell is shown in Figure 9.7.

In the migration cell, the sample (a bentonite clay layer in Figure 9.7) is located in the middle of the donor and receptor half-cells. The solution of the studied radio­active isotopes is filled into the donor half-cell and is permitted to migrate through the sample in the middle. As discussed in Section 9.3.2.1.1, there are two possibili­ties to determine the diffusion coefficient: the first is that solution samples are taken at different times from the receptor cell and the concentration of the migrat­ing substances is determined as a function of time (in this case, x = constant). The other possibility is that the rock sample is cut into thin layers after a given time (t = constant), and the concentration of the migrating substances is determined as a function of distance.

The solution of Fick’s second law for this migration cell is as follows, assuming the boundary condition (C = C0, x = 0, t > 0) and the initial condition (C = 0, x > 0, t = 0):

where erfc (z) = 1 — erf(z), where z is the fraction behind the erfc function in Eq. (9.43).

The two possibilities to determine the diffusion coefficient are shown in Figures 9.8 and 9.9.

These figures show the migration studies of chloride ions labeled by the 36Cl isotope and carrier-free 137Cs+ ions in bentonite clay. The diffusion coefficient of a chloride ion provides the maximum migration rate in the bentonite clay because the chloride ion is not sorbed in the clay. However, cesium ions are fairly easily sorbed by cation exchange in bentonite clay. As a result, the diffusion coefficient in this case is about two orders of magnitude lower than in the case of chloride ion. This illustrates that the sorption process in clay plays an important role in the isola­tion of radioactive ions from the environment.

8000 -|

7000

6000

5000 О

4000

II

3000 2000 1000 0

0.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 2.5E+06 3.0E+06
t (s)

Figure 9.8 Migration of 36Cl_ ions bentonite clay: intensity proportional to the concentration versus time. Diffusion coefficient calculated by Eq. (9.43) is 7.76 X 10_12m2/s.

As mentioned in Section 4.4.2, electrons are emitted from the nuclei as a result of radioactive decay and from the electron orbitals. The electrons emitted from nuclei are called “beta particles.” Electrons emitted from the extranuclear shell are called electrons and are designated by e_. The two terms “beta particle” and “electron” differentiate the location of the emission. The main important difference is that

2 theta (degrees) distance of the crystal planes in Angstroms

beta particles have continuous spectra, while the electrons originating from the orbitals have discrete energy. Independent of their origin, the electrons and beta particles interact with the electrons and nuclear field of other atoms. The character­istic interactions are ionization, scattering (elastic and inelastic), and absorption.

The analytical applications of beta particles were described in Sections 5.3.4 and 5.3.6. Furthermore, the industrial applications using the scattering/reflection and absorption of beta radiation will be discussed in Section 11.3. In this section, the application of electron beams with discrete energy will be illustrated. The dis­crete energy means that these electrons are ejected from the electron orbitals. The energy of these electrons can be increased in accelerators.

The most important application of the electron radiation is the electron micro­scope. There are two types of electron microscope: transmission electron micro­scope (TEM) and scanning electron microscope (SEM). The image taken by each type of microscope originates from the electrons that were elastic scattered. Besides, electrons can transfer energy to the orbital electrons of the matter (inelas­tic scattering) and eject electrons from the K and L shells. The processes following electron ejection are the same as in the case of the photoelectric effect: Auger elec­trons can be emitted, or the vacancy can be filled with an electron from the outer shell. As a result, similar to XRF, characteristic X-ray photons are formed, which
can be used for qualitative and quantitative analysis. This process is used in electron microprobes.

When a positron leaves the atomic nucleus, after traveling along a short path (a few millimeters at most, along which it can ionize or excite other molecules or atoms), it will inevitably collide with an electron, resulting in the annihilation of both. Their combined energy will be transferred to two gamma photons (each having approxi­mately 511 keV of energy) that will fly in almost opposite directions (as described in Section 5.3.3). In this way, positron decay results in gamma radiation that can be detected easily; moreover, we can utilize the coincidence detection of the pair of photons traveling in opposite directions to identify the line of their source and thus to enable the imaging of the tracer’s distribution.

The most significant characteristic of the biological effect of radiation is that a small amount of absorbed energy may have an extremely great effect. A case of

acute radiation (e. g., a 1000 sievert dose, meaning 1000 J/kg = 1 kJ/kg absorbed energy) causes death immediately. For a man who weighs 70 kg, the total absorbed energy is 70 kJ. This energy is much smaller than the energy produced when a 1 mol substance (e. g., fuel) is oxidized (a few hundred kilojoules). The question arises: why does this small amount of energy have such a dramatic effect? This can be explained by the fact that the small amount of energy is absorbed as great impulses: the energy of each particle is about six orders of magnitude higher than the energy of the chemical bonds (see Section 2.1.2). Another important character­istic is that beacuase of the high energy of each particle, the radioactive radiation ionizes the substances independent of their chemical species. Since any electron of the substances can be ejected, the cross section of the ionization is determined by the number of electrons. This means that the cross section of the ionization of the heavier elements and substances in large quantities is dominant.

The biological effect of the radiation occurs through consecutive physical, chemical, and biological steps. Since the water content of biological systems is the largest (the human body consists of about 70% water), the basic process of the bio­logical effects of radiation is the radiolysis of water. The first step of the radiolysis of water is the ionization of water, a physical process, producing a positively charged water molecule ion. Since this molecule ion contains an unpaired electron, it is a radical:

H2O radiation > H2O+ + e2 (13.4)

The products of the ionization (Eq. (13.4)), the water molecule ion/radical and the free electron, initiate different reactions, such as:

H2O+ ! H++ • OH (13.5)

e2 + H2O! OH2 + H — (13.6)

The products of the reactions in Eqs. (13.5) and (13.6), the hydrogen and hydroxide ions, can neutralize each other:

H+ + OH2 ! H2O (13.7)

The net process is the formation of atomic hydrogen and hydroxide radicals. These radicals can combine to water again or can produce other highly reactive species as described in Eq. (13.8):

H2O! H — + OH! H2O2, O2, H2, H2O (13.8)

In the presence of oxygen, which is essential in living organisms, additional radicals can be produced. Some examples are listed in Eqs. (13.9)—(13.12):

O2 + H — ! HO2-

HO2 • + H2O2 ! H2O + • OH + O2

HO2 • + HO2!H2O2 + O2 (13.11)

HO2• + H! H2O2 (13.12)

The radicals in Eqs. (13.5)—(13.12) and the free electrons can react with each other and any molecules of the biological systems, producing additional radicals. As seen in the reactions in Eqs. (13.6)—(13.12), both oxidizing and reducing com­pounds form, causing redox reactions of the biological molecules. All these chemi­cal reactions (including the reactions with radicals, electrons, and the redox agents) change the structure of biological molecules; thus, they cannot fulfill their biologi­cal functions (biological reactions). The damage to DNA under the effect of radia­tion has to be emphasized. The chains of DNA can break, leading to somatic effects of radiation, e. g., cancer and inheritable DNA defects.

The living organisms have different ways of protecting against the radiation effect. They contain natural radical scavengers. If they are present in excess of the radiolysis product, they can protect the biological molecules, including DNA. The preventing capacity depends on the age and physical conditions of the given organ­ism. In addition, the cells have various repair mechanisms for restoring the damages of the biological molecules. This mechanism is called “immune activity.” If, how­ever, this repair mechanism fails, the undesirable effects of radiation will appear.

The protection against radiation can be assisted by chemicals, namely by com­pounds that can scavenge the radicals, e. g., by compounds containing conjugated double bonds (Vitamins A and E) or compounds that are oxidized easily (Vitamin C). Sulfur compounds can also scavenge radicals. Because of the triple bond, a cyanide ion should scavenge the radicals well; however, it cannot be used for radiation protection of living organisms because of its strong toxicity.