The scintillator materials are classified into two groups: inorganic and organic. The classification is done on the basis of the mechanism of the scintillation process. In the case of inorganic scintillators, the crystal lattice, including its defects, plays an important role, while in the case of organic scintillators, the physical—chemical processes within the molecules of the solid or liquid scintillator material result in light photon emission.

In inorganic scintillators, the radiation or the electrons produced as the result of interactions between the radiation and the scintillator material excite the electrons on the outer shells of the inorganic crystal. During the return of the excited elec­trons to the ground state, photons are emitted. As postulated in the theory of solids, instead of having discrete energies as in the case of free atoms, the available energy states form bands. In the ground state, the electrons are in the valence band. The criterion of the electric conduction process is whether there are electrons in the conduction band or not. In insulators, as the inorganic scintillator materials, the electrons in the valence band are separated from the conduction band by a large gap. Under the effect of radiation, the electrons can pass from the valence band to the conduction band and then return to the valence band, emitting photons whose energy is in the ultraviolet range. These photons, however, are absorbed by the scintillator material. The photons can be detected outside the scintillation material only when the crystal defects are such that they result in the formation of lumines­cence centers in the gap between the valence and the conduction bands. After exci­tation, the electrons return to the valence band through these luminescence centers, emitting blue light. This blue light then provokes the emission of electrons from the cathode of the photomultiplier. In some inorganic scintillators, the crystal defects are created by adding a small percentage of doping material.

The most important inorganic scintillation materials are as follows:

• Zinc sulfide (ZnS): for scintillation purposes, ZnS crystals are dopped with silver or sometimes with copper. ZnS has historical importance (see, for example, the discussion of Rutherford’s scattering experiments in Section 2.1.1). A relatively high portion (about 25%) of the radiation is converted into light photons. The wavelength of the emitted photons is within the sensitive range of the photomultipliers. However, the time of the
light emission is relatively long (2 X 10_7 s), resulting in a longer dead time than other scintillation materials. Another disadvantage of ZnS is that it is produced in a polycrystal­line form consisting of small particles. Both the gamma photons and the emitted light photons are diffracted on the surfaces of the crystal particles, inhibiting the measurements of the radiation energy. For this reason, the ZnS scintillator is usually applied in thin layers for the detection of radiations in a low range (such as alpha particles, protons, deu — terons, and fission products).

• Sodium iodide dopped with tallium [NaI(Tl)]: the luminescence centers formed from the tallium doping. The conversion of radiation to light photons is relatively good (about 8%), and the wavelength of the photons is within the sensitive range of the photocathodes. The main advantage of NaI(Tl) detectors is that large single crystals can be produced that will allow the linear movement of the gamma and light photons without diffraction. Thus, the energy of the radiation can be measured.

Sodium iodide is widely used for spectroscopic purposes. Each of its three main interactions with gamma radiation (the photoelectric effect, Compton scattering, and pair formation, as discussed in Section 5.4) result in the emission of electrons. These electrons are the source of the scintillation that is measured in the detector (Figure 14.4). In the case of the photoelectric effect, the number of emitted elec­trons is proportional to the energy of the gamma radiation, i. e., the intensity of the

Energy of gamma photons entering the scintillation crystal increases ►

The energy transmitted to the scintillation crystal increases; the energy of the gamma photon

simultaneously

decreases

light is also proportional to the energy of the gamma radiation, providing a way to measure gamma energy. The energy of the electrons emitted in the Compton scat­tering depends on the angle of scattering producing a continuous range in the gamma spectrum. In the case of the pair formation, besides the peak associated with the total energy of the gamma photon, other peaks may also be observed. These peaks have 511 keV and 1.02 MeV less energy than the energy of the gamma photon. The 511 keV relates the rest mass of the electron and positron pro­duced in the annihilation process. The occurrence of these peaks with lower energy depends on whether the annihilation photons (one or both) leave the detector or absorb in it.

As seen in Section 5.4, the interactions of the gamma photons with matter, including the interactions with the scintillation material, strongly depend on the energy of gamma photons. At small energies, the photoelectric effect is dominant. When gamma energy increases, so does the cross section of Compton scattering. This scattering leads to a decrease of the energy of the primary gamma photons, and the produced secondary gamma photons that have smaller energy can cause the photoelectric effect. When the energy of gamma photons exceeds 1.02 MeV, pair formation also takes place, again producing secondary gamma photons with smaller energy. As a result, the gamma photons lose their energy in several consecutive processes. Well-defined peaks with characteristic gamma photon energy are obtained by cascade interaction within a short time if there are no scattering and diffraction.

In Figure 14.5, the scintillation gamma spectrum is shown. The peak associated with the gamma energy, as well as the continuous Compton edge, can be observed. A peak associated with the scattering of gamma photons appears at a lower energy.

This peak is produced by the gamma photons scattered from substances around the radioactive nuclide and the detector.

Frequently, the gamma spectra contain other peaks with low energies, such as the X-ray lines resulting from the photoelectric effects of the surrounding material, e. g., the X-ray line of the iodine of the NaI(Tl) scintillation crystal or the lead of the shield­ing. In addition, the X-ray emission of the daughter nuclide may also be present. For example, in the spectrum of the Ba-137 m isotope (the daughter nuclide of Cs-137), the X-ray emission of the stable daughter nuclide, Ba-137, can be seen. This emission is produced when the gamma photons transfer their energy to an electron on the K orbital of the daughter nuclide, 137Ba, and this K electron is emitted. This results in the excited state of the electrons of 137Ba. This excited state returns to the ground state through an electron transfer from an outer (L) orbital to the K orbital emitting the excess energy between the orbitals as a characteristic X-ray photon (see Section 5.4.4).

The energy resolution of spectroscopic scintillators is about 7—10%.

For the measurement of charged particles, NaI scintillators are not used because they are hygroscopic, so they have to be kept sealed and the charged particles with short ranges cannot transfer through the wall of the container.

Besides sodium iodide, other alkali halogenide crystals are applied in scintilla­tion spectroscopy. The most important is cesium iodide, which is not hygroscopic so it can be applied without packaging.

Nowadays, cerium-doped lanthanum bromide [LaBr3(Ce)] scintillation detectors are used. These detectors have some advantages compared to NaI(Tl) scintillation detectors. For example, the energy resolution of [LaBr3(Ce)] scintillation detectors is about 3% for the gamma line of 137mBa (662 keV). Furthermore, they have a higher photoelectron yield; the photon emission is nearly flat.

Other types of the inorganic scintillators are the Li-glass scintillators. Their application in neutron detection will be shown in Section 14.5.5.

The most important organic scintillators are aromatic compounds containing more than one aromatic ring in different combinations. The scintillations are resulted in the easy excitation of the conjugated double bond systems. The mecha­nism of scintillation is associated with the individual scintillator molecules and consists of two steps: (1) the particle transfers its energy to the scintillator mole­cules exciting the electrons and (2) the scintillator molecules go back to the ground state, emitting light photons. The intensity of the light photons is proportional to the excitation energy, i. e., to the energy of the radiation particles. The wavelength of the light depends on the identity of the scintillator.

The organic scintillators are divided into three groups: (1) crystals, (2) liquid solutions, and (3) solid solutions (plastics). From the solid organic scintillators, antracene and stilbene are used. In principle, they can measure all types of radiation (alpha, beta, and gamma); however, they are used only in some cases because other scintillators are more suitable for the measurement of each radiation.

The liquid scintillators are mainly used in the so-called liquid scintillation tech­nique for the effective measurement of beta radiation with low energy. In this technique, both the sample (beta emitter) and the scintillator are dissolved in an organic solvent. In this way, the sample and the scintillator are in direct connection within the molecular dimensions; thus, the absorption can be ignored. This is espe­cially important when measuring weak beta emitters used in medical and biological studies (3H, 14C, 35S, and 45Ca).

The liquid scintillation cocktails is composed of the following substances:

1. Solvent: alkyl-benzenes, aromatic ethers (toluene, xylene, anizole, dioxane).

2. Primary scintillator: diphenyl-oxazols, p-terphenyl, PPO (2,5-diphenyl-oxazol).

3. Secondary scintillator: POPOP (1,4-di-(2,5-phenyl-enyl-oxazolyl)-benzene) and dimethyl — POPOP (1,4-bis-2-(4-methyl-5-phenyloxazolyl)benzene) are the most important.

If the sample is water soluble, alcohol is added to the cocktail or dioxane is applied as a solvent. A suspension, an emulsion, or a gel of the sample can also be prepared and used for measurement. Liquid scintillation cocktails are commercially available.

In multicomponent scintillator systems (solvent, primary, and secondary scintil­lators), the energy flow is not known exactly. In these cocktails, the concentration of the scintillator molecules is as low as l0 3 g/dm3. According to the most accepted theory, the radiation (whose energy is hv) excites the molecules of the solvent (S):

hv 1 S——— ! S* (14.1)

The star means the excited state of the molecule. Then these excited molecules (S*) return to the ground state by exciting the molecules of the primary scintillator (Ps), initiating the scintillation process:

S* 1 Ps—— ! Ps* 1 S (14.2)

The secondary scintillators (Ss), the concentration of which is about 10_4 g/dm3, shift the spectrum of the emitted light toward the higher wavelength:

Ps* 1 Ss——— ! Ss* 1 Ps (14.3)

The excited secondary scintillator emits light photons:

Ss*——- ! Ss 1 light photon (14.4)

The photons with higher wavelength coincide with the sensitive range of the photo­cathode of the photomultipliers. As a result, the quantity of the electrons emitted by the photocathode (discussed in Section 14.2.2) increases. By the application of the secondary scintillator, the efficiency of the beta measurement can be improved. When the sensitivity of the photocathode coincides with the energy of the light photon emitted by the primary scintillator, no secondary scintillator is required.

The liquid scintillators are very sensitive to the chemical impurities present in the sample because of the quenching effects. The intensity of the emitted light dramatically decreases if the sample contains substances with a high quenching
effect (organic substances, sulfur, and halogen compounds). Even the compound containing the beta emitter radioactive isotope itself can have a significant quench­ing effect. If so, the quenching effects have to be corrected by suitable measuring techniques (such as standardization).

Plastic scintillators contain POPOP or terphenyl dissolved in polystyrene. They can measure alpha, beta, and gamma radiations, as well as fast neutrons. They can be applied in any desired geometry, including samples with large sizes.

As mentioned in the previous chapter, the half-life of the radioindicator and the duration of the studies have to be comparable. Both too short and too long half­lives have disadvantages. 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 and the impact of the radiation on the environment is higher than needed. So, the most suitable isotope has to be chosen within these options. The available radioactive isotopes depend on the elements in question. Most light elements have no radioac­tive isotopes, which could be useful in practical applications; the half-lives are too short. For example, the half-lives of the 6He, 8Li, and 8B isotopes are less than a second. Tracer studies with these elements can be performed by altering the natural isotope ratio and subsequent activation. Hydrogen is an exception because the half­life of 3H, tritium, is fairly long (12.28 years). Tritium emits weak beta radiation.

As the atomic numbers become higher, the choice of radioactive isotopes increases, which can be used well for radioactive indication. If more than one radioactive isotope is available, we can choose the most suitable one for the given study. For example, carbon has two radioactive isotopes: 11C with a half-life of 20.48 min and 14C with a half-life of 5730 years. 11C can be applied for medical applications, while 14C is suitable for the synthesis of organic substances or radio­carbon dating (as discussed in Section 4.3.6).

The shortest half-life for tracer studies is about 2—3 min. For example, adsorp­tion studies have been done with the 208Tl isotope, whose half-life is 3.1 min. As another example, the application of 15O (half-life is 122 s) in medical research is mentioned. Of course, these studies with such short-lived isotopes need careful pre­liminary training. In addition, the radioactive isotopes have to be produced in very high activities, which require radiation protection and automation. The studies can only be performed in a location where isotope production can take place.

If a radioactive isotope with a short half-life has a parent nuclide with a longer half-life, the daughter element can be separated repeatedly from the parent element. Such a system is called an isotope generator or “cow”; the separation operation is called “milking.” Generators can be produced from the parent—daughter nuclides of decay series, such as:

About 50 parent—daughter pairs can potentially be applied in isotope generators. The most important is the 99Mo—99mTc generator, which is widely used in medical applications (see Sections 8.7.1.4 and 12.2.6):

99 66 hours 99m 6 hours 99

99Mo 99mTc 99Tc

The suitable compound of 99Mo is adsorbed on a chromatographic column (e. g., aluminum oxide). Since the half-life of 99Mo is 66 h, the generator can be

Parent and daughter nuclides on absorbent

transported and used for several weeks. The short half-life of 99mTc is desirable for medical applications; this isotope can be eluted (milked) by using physiological sodium chloride solution from the chromatographic column, and after some chemi­cal preparations, it can be used in many ways in medical diagnostics. The scheme of the isotope generators is shown in Figure 8.4.

The radioactive indicators can be used in the most effective way when their specific activity (activity per mass) is fairly high. The specific activity of the carrier — free isotopes is the highest because the radioactive isotope is not diluted with the inactive isotope of the same element (no-carrier-added). Production of the carrier — free isotopes, however, is not always simple, and it is usually more expensive than the production of carrier-added isotopes. As seen in Section 6.2.1, the simplest and cheapest nuclear reactions, namely (n, Y) reactions, do not give carrier-free isotopes because only the number of neutrons changes in the nuclear reaction. The high spe­cific activity is also important in these reactions; however, the production of the iso­topes with long half-lives would require a long irradiation time, which is too expensive or even impossible to do. For example, the half-life of 36Cl is about 301,000 years; the irradiation time is obviously much shorter, so most of the target chlorine isotope remains inactive and is present as a carrier. If the presence of the car­rier is not allowed (because the specific activity is too low), carrier-free isotopes can be produced through nuclear reactions with charged particles in accelerators. These isotopes are usually more expensive. Nevertheless, the price can differ depending on

the half-lives of the isotopes produced. For example, the [2]Na isotope (whose half­life is 24 h) produced in nuclear reactors is much cheaper than the 22Na isotope (whose half-life is 2.6 years). The 24Na isotope can be used for several days, while 22Na can be applied for years. In conclusion, the overall quantities needed for a given period should be considered when deciding which isotope should be purchased.

As usual in chemistry, the radioindicators have to be sufficiently pure. In the case of radioactive isotopes, purity includes different terms: chemical, radioactive, and radiochemical purities can be defined.

Chemical purity is the same as in chemistry: the ratio of the chemical quantities in the number of particles, moles, or masses expressed in the usual concentration units (percent, ppm, etc.). Radioactive purity is measured by the amount of radia­tion. It represents the fraction of the radioactivity that comes from a given radionu­clide. Since the radioactivity depends on the number of radionuclides and the decay constants (Eq. (3.1)), the chemical and radioactive purities are usually differ­ent because of the different values of the decay constants. The radioactive purity can be different even for a given isotope mixture if the isotopes emit different parti­cles or electromagnetic radiation. In addition, the probability of the transitions can also be different, which has to be taken into account. This is illustrated by the example of a Pu— Am isotope mixture shown in Table 8.1.

Radiochemical purity shows what fraction of the radioactive isotope is in the compound defined by a certain chemical formula. For instance, sodium carbonate labeled with the 24Na isotope (24Na2CO3) can contain sodium hydroxide (24NaOH) as an impurity. The radiochemical purity is determined by the ratio of the two com­pounds. The term of the radiochemical purity is especially important in organic chemistry and in radiopharmacons, where impurities can be formed in the synthesis and by the radiolysis of the product. So, the radiochemical purity is determined mostly by thin-layer chromatography.

The potential use of radioactive indicators is strongly affected by the range of the radiation. Because of their short range, alpha emitters are applicable only for some special cases. An example is the use of the dominantly alpha particles emit­ting transuranium elements as radioactive indicators. The measurement of alpha activity needs special preparation of the samples, so only static investigations are possible. In addition, alpha emitters are also used for therapy in nuclear medicine.

Table 8.1 Chemical and Radioactive Purities of the Pu— Am Isotope Mixture. The
bold fonts show the purity values

239Pu 241Am

Chemical purity (m/m%)

Half-life (years)

Alpha particle/100 g

Radioactive purity for alpha particles (%)

Probability of gamma radiation with ca. 60 keV Radioactive purity for gamma radiation with ^60 keV (%)

In this case, the short range is desirable; the isotope loses its high radiation energy within a short distance (e. g., within a tumor) and does not damage the healthy tissues significantly.

The so-called weak beta emitters (namely, isotopes with low beta energy (e. g., 3H, 14C, 35S, 45Ca isotopes)) are essential in the biological and medical applica­tions. Because of the self-absorption of the weak beta radiation (see Section 5.3.5), special techniques are needed for the measurements (e. g., liquid scintillation spec­trometry, discussed in Section 14.2.1). Similar to alpha radiation, only static inves­tigations can be done in biological systems. In chemical systems, however, dynamic or in situ investigations are also possible under special conditions (see Section 9.3.6).

As radioactive indicators, the hard beta emitters (isotopes with high beta energy) and gamma radiators can be used easily. The application of the gamma radiation is especially advantageous because of the discrete energy of the gamma photons. The long range of these isotopes is also required for dynamic and in situ studies.

Dual or multiple radioactive indicator methods describe the use of two types of isotopes or isotopes with differing half-lives and/or differing energies of the radia­tion. When two radioactive isotopes of the same element is used, the isotopes with shorter half-lives results in higher activity, allowing the study of the fast process. The isotope with the longer half-life gives information on the same process on a longer timescale. An additional advantage of the application of the two isotopes of the same element is that less of it is needed; thus, the radiation dose is smaller, which is an important factor in some instances, such as in medical applications.

Exploiting the differences in the energy of the radiation is mostly feasible in the case of the gamma emitters, where the spectra are composed of characteristic peaks with discrete energy, which can be separated. The separation of the beta energies is problematic because of the continuous spectra (see Figure 4.10); thus, the activity measurements frequently have to be complemented by chemical separation.

Isotope preparations that are produced through the (n, p) nuclear reaction generated by epithermal or fast neutrons belong to this group. These nuclear reactions change the atomic number of the target element; for this reason, the product must be sepa­rated from the target by radiochemical methods. Such products do not contain non­radioactive nucleus (carrier atoms), so their specific activity is high, which is very beneficial for tracer reactions.

Phosphorus is a basic element of some fertilizers, so the 32P radionuclide (see in Table 8.9) plays an important role in agrochemical and related studies. At the same time, it is also frequently used in industrial tracer investigations for studying corro­sion inhibitors.

Typical production batch activity for 32P is around 740 GBq. Due to its rela­tively long half-life, this radionuclide can be dispensed for applications for weeks.

The details of the production of sulfur-35 isotope are given in Table 8.10. The typical production batch is 370 GBq. Due to its relatively long half-life, the product can be dispensed for utilization during periods of months.

Production of the P-33 radionuclide (for medical use) also belongs to this group. It is made from the S-33 target through the (n, p) nuclear reaction (see Section 8.6).

Radiometric titration is a two-phase titration method when the equivalence point (i. e., end point) is indicated by the disappearance of a radioactive isotope from one phase. It can be used if the unknown substance and the titrant form very insoluble precipitates or an easily extractable compound, and if one of the reagents has a suitable radioactive isotope. During the titration process, different volumes of the titrant are added to the unknown compound, the phases formed are separated by fil­tration and extraction, and the activity/intensity of any phases is measured. The main advantage of the radiometric titration is that the titration curve usually con­sists of linear portions; thus, few points are enough for drawing the titration curve. In addition, the linear character provides opportunities for automation.

Both the unknown compound and the titrant can be labeled. When precipitate is produced during the titration, the titration curves will be as follows:

• The titrant is labeled by a radioactive isotope; the activity of the solution shows the back­ground activity until the equivalence point. After the equivalence point, the activity of the solution containing the excess of the titrant increases (Figure 10.2, plot A).

• The unknown compound is labeled: the activity of the solution decreases until the equiva­lence point, and then it shows the activity determined by the solubility of the precipitate (Figure 10.2, plot B).

• Both the unknown compound and the titrant are labeled: the activity has a minimum at the equivalence point (Figure 10.3).

Two or more unknown compounds can be analyzed simultaneously by precipita­tion radiometric titration if the solubility of the precipitates is fairly different. For example, copper and zinc ions can be determined by titration with Fe(CN)64_. Zinc ions are labeled with a radioactive 65Zn isotope. The solubility of Cu2[Fe(CN)6] is much less than that of Zn2[Fe(CN)6]. By adding the solution of Fe(CN)64_ to the solution of copper and zinc ions, at first, Cu2[Fe(CN)6] precipitates, and then the activity of the solution remains constant. After the equivalence point of the precipi­tation of the copper ion, Zn2[Fe(CN)6] starts to precipitate and the activity of the solution decreases. After the precipitation of the total quantity of the zinc ions, the activity of the solution becomes constant again, determined by the solubility of Zn2[Fe(CN)6] (Figure 10.4).

Dual labeling gives additional analytical opportunities. For example, the quan­tity of sulfate and iodide ions in the same solution can be measured. Both sulfate and iodide ions are labeled by radioactive sulfur (35S) and iodine (131I) isotopes, respectively. The solution is titrated with barium chloride and barium sulfate preci­pitates. Then the activity of the solution decreases until the equivalence point of sulfate is reached. When barium chloride is added in excess, the activity becomes constant. Then, titration is continued using silver nitrate and precipitating silver iodide. Silver iodide is separated, and the activity of the solution decreases again until the equivalence point of iodide ions is reached, and then it becomes constant again (Figure 10.5).

Radiometric titration can also be made by extraction. For example, the unknown metal ion is titrated with a complex forming agent. The complex compound is extracted with an organic solvent. The concentration of zinc ions can be determined by titrating dithizone dissolved in chloroform. The zinc dithizone complex dis­solves in the chloroform. When zinc ions are labeled (e. g., by the 65Zn isotope), the activity of the aqueous phase decreases until the equivalence point is reached, and then it remains constant.

The radioisotopes that are used most frequently for radiation absorption and scatter­ing type measurements are listed in Table 11.2.

11.3.2 Level Indication of Materials in Tanks

For detecting the level of materials in industrial equipment, nuclear level indicators and level measuring instruments can be used (Figure 11.20). Level indicators are suitable for detecting and transmitting given level limits (min, max), while level measuring instruments are used for continuous detection, recording, and transmit­ting the material level.

The level of materials in industrial equipment can be continuously determined either by absorption measurement of the radiation or by installing a level indicator on the servo-motor driven mechanism following the material level. Figure 11.21 shows the principle of absorption type measurement. Measurement based on radia­tion absorption utilizes the change in the relative absorption caused by the material level. Similar equipment can utilize reflection of the radiation. Radiation sources

Table 11.2 Radioisotopes Used for Radiation Absorption and Scattering Type Measurement

Radioisotope Half-Life Type of Radiation Application Field

Buzzer

Output connecting to filling unit

Figure 11.20 The principle of level indication with the radioisotope technique.

used for such measurements (depending on the wall thickness of the equipment) are 37 MBq to 3.7 GBq Co-60, and Cs-137 sealed sources. Applied detectors are the Geiger—Muller counter and the scintillation detector.

Examples of industrial level indication and level measuring solutions include:

• Maintaining the level of the mixture between limit values in a blast furnace.

• Automation of a miner’s tram filling.

• Piece counting on tile production lines.

It is a common misunderstanding that nuclear medicine is mainly about tumor imaging. In fact, we search for tumors in about half of all investigations. Unfortunately, we do not have a single optimal method for tumor imaging; how­ever, the methods of nuclear medicine are particularly powerful for many tumor types and able to answer many questions. Today, the PET/CT study of glucose

metabolism is considered the most effective for a wide range of tumors (see Section 12.6).

For many decades, the most common imaging method in the field of nuclear medicine worldwide has been bone scintigraphy. Radiolabeled diphosphonates accumulate in the bones proportionally to bone formation (osteoblast activity). As a consequence, bone metastases of various tumors show an increased uptake of Tc-99m-labeled diphosphonates (see Figure 12.10). Detecting bone metastases is very important since many of the most common tumors (e. g., lung, breast, and prostate) often have their metastases in the bones, and their early detection may influence the method and prognosis of the therapy applied substantially. Bone scintigraphy may visualize metastases in an earlier phase, months before X-ray images, as the latter detect only an abnormality that has already caused significant changes in the structure and calcification of the bones.

Note that gamma camera images from the anterior and posterior views are different (see Figure 12.10), resulting from the attenuation of radiation inside the body. (For example, the half-value layer of the 141 keV gamma radiation of Tc-99m is 4.6 cm in body tissue.) In bone scintigrams, the bones closer to the back surface of the body (e. g., the spine and back ribs) are better seen (brighter) from the posterior, while those closer to the frontal surface (e. g., the sternum and the frontal edge of the hip bone) are more prominent from the anterior view.

If the results of the intensity measurements with errors are used in subsequent calculations, including even the correction with the background, the spread-error rules must be used. In the case of addition (A + B) or subtraction (A — B) of two quantities, the standard deviation is:

sd « JsdA + sdB (14.18)

For other addition and subtraction, additional members have to be included in Eq. (14.18).For multiplication: C = A X B:

Further Reading

Choppin, G. R. and Rydberg, J. (1980). Nuclear Chemistry, Theory and Applications. Pergamon Press, Oxford.

Friedlander, G., Kennedy, J. W., Macias, E. S. and Miller, J. M. (1981). Nuclear and Radiochemistry. Wiley, New York.

Hendee, W. R. (1973). Radioactive Isotopes in Biological Research. Wiley, New York.

Lieser, K. H. (1997). Nuclear and Radiochemistry. Wiley-VCH, Berlin.

Mann, W. B., Ayres, R. L. and Garfinkel, S. B. (1980). Radioactivity and its Measurement. 2nd edition. Pergamon Press, Oxford.

McKay, H. A.C. (1971). Principles of Radiochemistry. Butterworths, London.

Millner, T., Bartha and Prohaszka, J. (1963). Untersuchunger Uber die Wanderung kleiner Silbermengen in reinem Zinn bei Verwendung von radioaktiven Silber. Z. Metallkunde 54:17—19.

21Mg ——! 21Na ———! 20Ne (4.113)

7Li(p, n)7Be

[1] In 1867, Niepce de Saint-Victor showed that uranium salts emit radiations in the dark, but Becquerel rejected this saying that “Niepce could not have observed the radiation from uranium because the author used plates that were not sensitive enough.”

Radioactive purity is shown for the alpha particles and the gamma radiation with ^ 60 keV energy.

These radioactive isotopes (preparation reactions, half-lives) are summarized in Table 8.4. They are produced in cyclotrons.

8.6.2 Sodium Isotopes

Na-24 can be prepared by the 23Na(n, Y)24Na reaction in nuclear reactors. The prod­uct is not carrier-free. Its half-life is 24 h, and it emits (3_ and hard gamma

radiation. Carrier-free 24Na isotopes can be produced in the 26Mg(d, a)24Na nuclear reaction, but this procedure is more expensive.

Na-22 can be prepared by the 23Na(n,2n)22Na nuclear reaction. The isotope con­tains an inactive carrier (Na-23). Since the (n,2n) nuclear reaction is endoergic, fast neutrons are needed. Its half-life is about 2 years, and it emits p and gamma radiation. Carrier-free Na isotopes can be produced in the Mg(d, a) Na nuclear reaction.

The solubility of very insoluble salts was first determined by Hevesy (as discussed in Section 8.1). The method was based on the specific activity of the salt, which was identical in both the solid and solution phases, a/m = constant. At first, a pre­cipitate of known specific activity (e. g., lead sulfide) was produced:

Pb(NO3)2 1 210Pb2+ 1 S2- ! PbS (9.31)

The specific activity of the precipitate is measured. Then the precipitate is dis­solved, and the activity of the solution is measured. From the activity of the solu­tion and the specific activity, the concentration of the solution can be calculated. The solubility product of lead sulfide, for example, is LPbS = 10-33 mol2 dm-6. At this small value of solubility product, the solubility determination needs a very sen­sitive analytical method.

As discussed in Section 5.4, electromagnetic radiation with high energy (X-ray and gamma radiation) interacts with the orbital electron, the nuclear field, and the nuclei. The interactions with the orbital electrons and the nuclei are used for analyt­ical purposes.

During interactions with the orbital electrons, the intensity of X-ray or gamma radiation decreases due to the photoelectric effect and elastic and inelastic

scattering (see Figure 5.25) as determined by the general formula of radiation absorption (see Eqs. (5.3) and (5.93)).

As discussed in Section 5.4.4, the photoelectric effect produces electrons, including photoelectrons and Auger electrons, and characteristic X-ray photons. The ratio of the Auger electron emission to the characteristic X-ray photon emis­sion depends on the atomic number. For light elements, Auger electron emission has a high probability, while for heavier elements, X-ray photons are produced (see Figure 4.12).

The measurements of the energy and intensity of electron and X-ray radiation are used in different analytical techniques. The measurement of the photoelectrons gives analytical information on the chemical environment of the atoms in a substance [high-resolution beta spectroscopy and XPS]. AES (see Figure 5.24) can be used for the analysis of surface layers (Table 10.2). The characteristic X-ray photons provide information on the quality and quantity of the elements of a substance (X-ray fluorescence spectroscopy, as discussed in Section 10.2.3.1).

The elastic scattering process or X-ray diffraction (discussed in Section 10.2.3.2) is used to determine chemical structures.

The excitation of the nuclei is applied for species analysis of the compounds of the elements with isotopes that have recoil-less nuclear resonance absorption (Mossbauer spectroscopy, described in Section 10.2.2.3).