14.7.1 Statistical Error of Radioactivity Measurement

The activity of radioactive substances is usually measured indirectly. This means that the number of the particles or photons counted in the detector is proportional to the radioactivity, the number of decompositions in a unit of time (see Section 4.1.2). As mentioned in Section 4.1.1, radioactive decay is a statistical pro­cess, so repeated measurements give a statistical distribution around a mean value. On the basis of the statistical laws, the statistical error of the measurements can be determined accurately.

The statistical laws postulate that as the measured counts (N) increase, the abso­lute error (AN) also increases. The relative error (ДN/N), however, decreases. When N tends to be infinity, the relative error tends to be zero.

AN

lim 0 14.9)

N! N N

The real value of N is determined by the time, which can be chosen for the mea­surements. Thus, the relative error can be decreased under a certain value at most.

Let’s measure the intensity of a radioactive sample k times under the same conditions. The counts are Ni, N2,.. .,Nj,…, Nk, and their mean value is N. In principle, the distribution of the values (PN) can be given by Poisson’s discrete probability distribution:

P — <№) є-®

For sufficiently large values, the probability distribution obtained for the measured values and Poisson’s probability distribution function is the same (Figure 14.12). For smaller values, the regular process of radioactive decay was disturbed by an external factor (e. g., the instability of the measuring tool, the aging of the detector, the change in the position of the sample). On the basis of Poisson’s distribution, the standard deviation expected for N counted impulses (s. d.) is:

s. d. — VN e Xt

At Xt« 1 (i. e., when the activity of the radioactive sample remains the same during the measuring time):

s. d. — PN <14.12)

As seen in Eq. (14.8), the standard deviation can be calculated for one measure­ment when the counts are high enough.

In the case of the many counted impulses (N > 100), the Poisson distribution becomes identical to the Gauss distribution, which is simpler and accurate enough:

The value and the distribution of the differences between the individual mea­sured values and the mean value

Д = Nj — N (14.14)

usually fulfill the Gauss distribution (Figure 14.12).

The degree of accuracy is the degree of closeness of the measurements to the actual value. When 50% of the measurements are within this given value, it is called “probable deviation.” The mean error or the standard deviation is the error obtained for 68.27% of the measurements.

If the Gauss probability distribution function is integrated from N — VN to N + VN, 0.6827 is obtained. If the Gauss probability distribution is valid, 68.27% of the measurements fall into the interval N ± VN. Accordingly, the standard devi­ation is ± VN, the square root of the mean value. This value is equal to the value obtained in Poisson’s probability distribution.

When the Gauss distribution function is integrated from N — c VN to N + cVN, a certain portion of the measurement falls into the interval N ± c VN. Table 14.2 shows these probabilities.

In most cases, the standard deviation is used. This value can be calculated as follows:

As discussed previously, 68.27% of the measurements fall into the interval

n ± vN.

The standard deviation of the mean value (SD) is less than the standard deviation of the individual measurements (sd) because the mean value is obtained from k independent measurements. The time of the measurements is t, and the number of the counted impulses is N. The standard deviation of the mean value is expressed as:

The standard deviation of the mean value per time (in other words, the standard deviation of the activity or intensity) is:

SD = y/NTk t t

As seen in Eq. (14.17), the standard deviation can be decreased by increasing the measuring time and the number of the measurements.

14C emits negative beta particles with 165 keV maximal energy. Its half-life is 5,730 years. It is produced by the 14N(n, p)14C nuclear reaction. B-, Be-, or Al — nitrides are used as the target, and it is oxidized after irradiation, e. g., by hydrogen peroxide. By this method, 14CO2 can be obtained, and it then can be dissolved in NaOH and precipitated with Ba(OH)2 as Ba14CO3. This is the basic compound, which is mostly used in organic syntheses. The procedure is shown in Figure 8.10. For organic syntheses, Ba14CO3 is transformed in several different ways:

1. It can be dissolved in hydrochloric acid. In this process, 14CO2 is formed. From 14CO2, the following compounds can be produced:

• Carboxylic acids (e. g., acetic acid) can be prepared in the Grignard reaction:

14CO2 1 CH3MgBr 12H2O! CH314COOH 1 Mg(OH)2 1 HBr (8.22)

The acetic acid is specifically labeled on the carboxylic carbon atom.

• 14CO2 can be reduced with LiAlH4 to methanol.

• Methanol can be converted to methyl iodide, formaldehyde, or methyl cyanide.

2. By heating Ba14CO3, different compounds are obtained, dependent on the conditions and reagents:

• With metallic potassium in molten NH4Cl, K14CN is produced.

• With metallic barium, it gives universally labeled acetylene:

Ba14CO3 1 Ba ! Ba14C2 1 H2O! 14C2H2 (8.23)

• Acetylene can be used in many syntheses, e. g., universally 14C-labeled benzene. By addition of water, acetaldehyde is obtained. In the reaction of labeled acetylene with formaldehyde, heterocyclic compounds with oxygen as a heteroatom can be produced.

Ba(OH)2

і__ £

Ba14CO3

Filtration, washing, drying

Figure 8.10 The separation of C-14 from Be3N2 and preparation of Ba14CO3.

• By heating Ba14CO3 in dry NH3, barium cyanamide is produced, from which urea, thiourea, and guanidine can be synthesized.

3. By the reduction of NaH14CO3 or KH14CO3 by H2, formic acid is produced, using Pd as a catalyst.

4. A special problem of organic chemistry is the preparation of labeled aromatic compounds. As seen previously, universally 14C-labeled benzene can be produced from 14C2H2.

As mentioned in Section 8.4, biological syntheses are also possible:

• Clostridium aceticum is produced from CO2 to acetic acid.

• Chlorella vulgaris is produced from CO2 to amino acid in an L-configuration.

• Canna indica is produced from CO2 to carbohydrate in a D-configuration.

• Pigeon produces from formiate to acetic acid.

• Rat produces from acetate to cholesterol.

Because of the easy detection of their radiation, radioactive isotopes provide a use­ful approach to determine the local, time, and concentration distribution of sub­stances. Consequently, the radioisotopic tracer method can be used for reaction kinetic, mechanism, and equilibrium studies. In this chapter, some radiotracer meth­ods will be shown. In these studies, the radiotracer is most often in solution, so the most important properties of highly diluted solutions (solutions of carrier-free radioactive isotopes) and the basic rules of working with them will be discussed.

When an isotope has a relatively short half-life, the number of the radioactive nuclides is very few. For example, when the half-life of an isotope is 100 years, 1 kBq activity is emitted by about 7.5 X 10-12 mol radioactive nuclides. So, the preparation of a solution in so small concentration range demands very careful pro­cedures. The stock solution is usually kept in a 10-1 or 10-2 mol/dm3 concentrated acidic solution (e. g., in nitric or perchloric acid to avoid the formation of com­plexes with the radioactive isotopes), and this acidic stock solution is diluted step by step. In each dilution process, the solution has to be left to mix for at least 12 h before the next solution, since the carrier-free isotopes are mixed via the self-diffu­sion of the solvent and stirring does not increase considerably the rate of this pro­cess. To avoid the formation of radiocolloids, the pH of the solution may be increased gradually. The radioactivity of the solution must be checked regularly. Only very pure solvents (bidistilled or tridistilled water) are applied because even these pure solutions can contain more contaminants than the total quantity of the radioindicator.

The solutions containing carriers in macroconcentrations can be handled more easily; however, carrier-free radioisotopes have to be added to the solution of the carrier according to the rules mentioned previously.

Neutron radiography and tomography are imaging procedures that are based on the different absorption properties of the substances. An object is irradiated by a neu­tron beam; the intensity of the neutrons is measured on the other side of the object

(Figure 10.9). The neutrons are detected using a LiF + ZnS detector (as discussed in Section 14.5.5). The measuring time is between a few seconds to even a day, depending on the resolution and the neutron flux. When the neutron beam is paral­lel, the size of the object and the image is the same; the resolution is 100—300 pm. If the beam is divergent, a magnified image is obtained; the resolution is about 10 pm.

Neutron radiography and tomography can be combined with PGAA (see Section 10.2.2.2). In this way, the chemical composition of the objects can also be analyzed (Figure 10.10).

10.2.2.1 Neutron Scattering/Diffraction

Scattering methods are based on the interaction of neutrons with nuclei to study the microscopic structure, kinetic processes, and magnetic field (see Section 5.5.3). Most applications, which are interesting for chemists, were made in the first two fields and commenced in the 1970s, when the first high-flux research reactors were built.

The diffraction is quantitatively described by the well-known Bragg formula (Figure 10.11):

As = (n)A = 2d sin 0 (10.14)

where d is distance in a chemical system determined by the structure, A is the wavelength, 0 is the angle of incidence at which the intensity maximum occur,

Figure 10.9 A scheme of neutron radiographic/tomographic system. (Thanks to Dr. Zsolt Rtsvay, Department of Nuclear Research, Institute of Isotopes, Budapest, Hungary, for the spectrum.)

Energy (KeV)

Figure 10.10 Left: A neutron radiogram of objects within a lead container (wall thickness: 7 mm). A: M6 iron bolt; B: U3O8 powder, C: three copper balls. Right: Prompt gamma spectra of the object in the lead container. There is an aluminum rod in the container which cannot be seen well on the radiogram, but its spectrum is well-seen. (Thanks to Dr. Laszlo Szentmiklosi and Dr. Zsolt Rtsvay, Department of Nuclear Research, Institute of Isotopes, Budapest, Hungary, for the radiogram and the spectrum.)

Chemical structure, e. g.,
lattice or condensed matter

and n is a small integer (at the first interference, n is 1), As is the difference of the path of the interfering waves.

On the basis of the Bragg formula (Eq. (10.14)), when we know the wavelength and the intensities at different angles, it is possible to calculate the distance charac­teristic of the different chemical structures. This is true for any electromagnetic or particle radiation; e. g., X-ray diffraction and electron diffraction are used for struc­tural analysis.

In structural research, the application of the probe particle (neutron, electron, or photon) is provided by its (energy-dependent) wavelength: it should be comparable to the characteristic size of the microstructure to be investigated. The neutron velocities produced in a nuclear reactor follow the Maxwell distribution determined by the temperature of the nuclear reactor zone, passing the neutrons through a cooled moderator; thereafter a velocity selector (between rotating slits), ~5 X 10—n —10—9m wavelength, usually can be obtained, which is calculated using Eq. (4.93). Assuming a thermal neutron with 0.01 eV energy:

д. H_ = 66256 X 10-34 J/S mv 1.67 X 10227 kg X v

and about 10210 m is given for the de Broglie wavelength.

The incident neutron is represented by a transversal plane wave:

ф(к) = ^0 exp(i к ~r) (10.16)

where ф0 is a constant amplitude, k = 2n n /A, and n is the unit vector in the direction of propagation. The upper arrows mean vectors. The moving front of the wave interacts with nucleus j at point rj of the sample with probability defined by the scattering cross section (oj) and may generate around the nucleus a spherical wave bj exp[ — i k r ]/r with amplitude bj specific of the nucleus. The wavelengths

Figure 10.12 Principles of neutron diffraction (bold letters designate vectors).

of the incident and scattered waves are equal; thus, the scattering process is elastic. Because of its length dimension, bj is called “scattering length” and

aj = 4nbj2 (10.17)

At the applied neutron energies, the phase of the scattered waves is «bk for the individual nuclei.

The scattering length of some isotopes/elements is listed in Table 10.5.

Far from the jth nucleus, the front of the spherical waves can be expressed by plane waves (Figure 10.12):

фj(k0) = bj exp(- i!'[R — j

The scattered wave from a system of N nuclei (in vacuum) is equal to:

ф(к’) = exp(— i к’ Rbj exp(i к’ rj) (10.19)

and the scattering intensity is the thermodynamic average of the squared scattered waves:

(ф*{к ’)ф(к ‘2j = ^ exp(— i к 0 R )exp(— i к’R )^2jbj exp(i к ГТ])^2кьк exp(i к ГГк))

=(ZjHj exp(— i к ‘к —кк d)

(10.20)

where the complex conjugate is denoted by * and the summation is made for

jji = 1, … ,N. к к к

Considering that к0 = к + Q, the intensity will be divided into two terms:

і(кк0)=i(k)+/(Q) = exp(— i к ‘io —кк d

(10.21)

1 exp(— iQfrj —^кі)

where І(к ) is a contribution to the direct beam, and the I(Q ) is the actual scattered intensity, where Q is the scattering vector (Figure 10.12). The magnitude of the scattering vector is:

4n $

Q = T sin 2 (10.22)

where $ is the scattering angle (Figure 10.12).

Considering that the bs are independent of one another and the coordinates, we obtain:

I(Q) = N <b2> 1 (b)2^.^ exp(— i QPj —2 ])) For a condensed phase in thermal equilibrium:

where (1/VN) ФN is the N-particle spatial correlation function.

Because the scattered intensity depends on the difference of two-particle coordi­nates, in isotropic systems, the averaging is reduced to the Fourier transform of the pair-correlation function:

g(r)exp(— i Q 7)d 7 — S(Q) — 1 (10.25)

V

From here,

I(Q) = N{(b2) — (b)2 1 (b2)S(Q)} (10.26)

In this equation, S(Q) is called the “structure factor”; it provides information on the interference caused by the spatial distribution of the scattering nuclei. (b2) — (b)2 is the incoherent part of the scattered intensity, and (b)2S(Q) is the coherent part of the scattered intensity and is determined by the nuclear spin.

The practical applications of this result are promoted by introducing the concept of scattering length density (p), defined as b/v, where b is the sum of scattering lengths in a sufficiently small volume (v). For example, the volume of a water molecule (vw) is:

Vw = Vw/Na (10.27)

where Vw and NA are the molar volume of water and Avogadro’s number, respec­tively. The scattering length of a water molecule is calculated from the scattering length of the atoms:

b — 2Ьн 1 bo

The scattering length density of water is:

Pw — bw/vw (10.29)

A dissolved molecule with a certain scattering length (bs) and volume (vs) in aque­ous solution is seen by the neutrons only if the excess scattering length

Abs — bs — vspw (10.30)

or the scattering contrast

Abs/vs = APs = Ps — Pw (1°.31)

is not equal to zero.

It can be shown that the scattered intensity from mesoscopic inhomogeneities caused by molecular systems (association colloids, macromolecules, polymers, and biological structures) in the solution is described by the same expression as before,

if the bs are replaced by the Fourier transform of the spatial distribution of the scattering contrast:

By dividing I(Q) by the sample volume (V), we obtain the macroscopic scattering cross section (dS/dO, given in cm—1 units):

N

dS/dO = V{(B X (Q)B(Q)) — (B X (Q))(B(Q)) + (B X (Q))(B(Q))S(Q)}

(10.33)

On the basis of the neutrons discussed here, neutron scattering is applied for the structural studies in condensed phases. Since the neutrons are scattered by the nuclei, substances containing light elements are also studied. As seen in Table 10.5, the scattering length can be different for the isotopes of the same elements. This is especially important for the isotopes of hydrogen, 1H and 2H. The great difference in the scattering lengths of hydrogen and deuterium provides the possibility of studying hydrogen compounds, such as biological or other organic molecules, in which the exchangeable hydrogen atoms can be investigated.

During the application of neutron scattering, the intensity of the scattered neu­trons (in other words, the macroscopic scattering cross section (dS/dO)) is plotted as a function of the scattering vector (Q). Models elaborated for B(Q) and S(Q) are fitted to the experimental scattering patterns, and the reliability of the fitting para­meters is judged by the quality of the fit. In Figure 10.13, the neutron-scattering patterns from micellar solutions of sodium alkyl sulfates are plotted, together with the best-fit curves and the squared deviations of the experiment and theory. The systematic study with different alkyl chain length results in reliable structural data and in a direct proof of the electrostatic potential acting among the ionic micelles.

One of the most important technical features of neutron scattering is contrast variation. By varying the hydrogen isotope composition (hydrogen/deuterium ratio) of water (Table 10.5), pw can have a varied range, which is wide enough to cover the scattering contrast of most components of organic molecules. Therefore, certain parts of the molecules can be excluded from the observed scattering patterns (Figure 10.14). The method is unique and is used mainly in biological systems.

In condensed phases, many important kinetic processes are random and occur over a relatively long time scale. Rotational jumps of a molecule and the diffusion of a particle in liquid are two examples of the types of motion that contribute to the quasi-elastic component of the inelastic spectrum, where the sum of the changes in the energy of the neutrons scattered in a particular direction (ДЕ) equals zero.

Figure 10.13 SANS patterns from 0.0729 mol/dm3 solutions of sodium alkyl sulfates of different chain lengths (open symbols) with best-fit curves (solid lines). Residual squares are plotted with solid symbols connected with dotted lines.

Source: Adapted from Vass et al. (2000), with permission from American Chemical Society.

The intensity I(Q, AE) scattered in the angle defined by Q, stemming from diffus­ing molecules in a liquid, is described as follows:

h

-DQ2

KQ, AE) = A— ^ h 2 (10-34)

n [(AE)2] 1 2Ldq2

where A is the amplitude defined by the scattering amplitude b and apparative con­stants, h is the Planck constant, AE is the energy change of the neutron (inelastic component), and D is the self-diffusion coefficient of the molecule. Quasi-elastic neutron scattering provides a precise tool for determining the self-diffusion coeffi­cient in the bulk phase of liquids. Figure 10.15 shows the decomposition of a quasi-elastic neutron-scattering spectrum of a micellar solution. The solvent mole­cules were found in two kinetic states: along with the major (~94%) component moving with the bulk-phase self-diffusion coefficient, a slower water component (~6%) could also be observed. The slow component was assumed to form the hydrate sphere of the micelles.

A crucial point of imaging methods is the amount of the contrast material or tracer necessary for obtaining a reasonable image quality (see Table 12.4). For example, if a contrast agent is used to enhance X-ray imaging, the amount needed may have physiological effects, and it may activate defense mechanisms (induce an immune reaction) or saturate a secretion channel. In contrast, we need such a small number of molecules of a radiotracer that it will not change or influence the studied function.

The radiotracers used for the in vivo diagnostic and therapeutic procedures of nuclear medicine are called radiopharmaceuticals (i. e., medicines that emit radi­ation). In fact, these are not medicines in the traditional sense since they do not have any effect on the patient as chemicals due to their extremely low concentra­tions. However, similar to normal pharmaceuticals, strict rules apply for tests to be carried out before they are allowed to be administered to humans. Moreover, their radiation may have biological effects—that is what we use for radioisotope therapy.

In general, we use molecules that either are present in the body anyway in their unlabeled form or behave similarly to those present. In this way, we can image and/or study the undisturbed function.

In the atmosphere, the radioactive isotopes, including natural and artificial ones, are present as gases or bounded to aerosols. As mentioned previously, the artificial radioactivity originating from nuclear explosions is decreasing, while that from nuclear energy production is increasing. The net effect of these tendencies is the decrease of radioactivity in the atmosphere because the change of natural radioac­tivity can be disregarded.

Of the natural radioactive isotopes, radon, 3H, and 14C are important. The differ­ent isotopes of radon are the members of the natural decay series. 3H, and 14C con­tinuously form from nitrogen under the effects of cosmic radiation. Both elements form many volatile and gaseous compounds, which are present in the atmosphere.

The cloud chamber photograph (see Section 14.5.1) of radon gas (222Rn) is shown in Figure 13.3. The tracks of the alpha particles can be seen well. A solid — state detector picture (see Section 14.5.3) of radon gas is shown in Figure 13.4. The tracks of alpha particles are shown.

Among the artificial radioactive isotopes, the gaseous fission products (iodine and noble gases) and the compounds of 3H and 14C are the important radioactive isotopes of the air.

All other radioactive isotopes in the air are bounded to aerosols. Practically, all natural and artificial radioisotopes can be bounded to aerosols. The long-life fission products and natural radioactive isotopes, thus, can have an impact on the environment.

The radioactive isotopes of the atmosphere are falling onto the surface of the Earth. Depending on the amount of water that accompanies this fallout, the processes are called “dry out,” “rain out,” and “wash out.” The half-life of the fallout of radio­active isotopes from the stratosphere after a nuclear explosion is 7 years.

Figure 13.3 A cloud chamber photograph of radon gas (222Rn). (Thanks to Dr. Peter Raics, Department of Experimental Physics, University of Debrecen, Hungary, for the photograph.)

Figure 13.4 A solid-state detector picture of radon gas. (Thanks to Dr. Istvan Csige, Department of Environmental Physics, Institute of Nuclear Research, University of Debrecen, Hungary, for the photograph.)

The radioactivity of the atmosphere has seasonal changes because of the changes in the weather. The mean atmospheric radioactivity in the Northern Hemisphere in January and in June is about 10 and 2 Bq/m3, respectively.

Kr-85 is a fission product, which is emitted into the air during the operation of nuclear reactors or reprocessing plants. By measuring the krypton activity in the air, the volume of reprocessing and nuclear weapon production can be estimated. The half-life is 10.7 years.

8.6.12 Rubidium-86

86Rb is produced in the 85Rb(n,^)86Rb nuclear reaction. Its half-life is 18.7 days, and it emits (3_ and gamma radiation. It is used in nuclear medicine for metabolism studies.

As usual for heterogenous reactions, the heterogeneous isotope exchange processes consist of several consecutive steps. The most important steps are the transport of the substances from the bulk to the interface, the exchange reaction, and then the reaction products leave the location of the exchange process and transfer into any phase. This latter process can imply dissolution, intraparticular, interparticular, sur­face diffusion, recrystallization, and so on. The overall kinetics of the isotope exchange process is determined by the slowest step(s); under steady-state condition, this is the rate-determining process.

Lajos Baranyai

Isotope Institute Co. Ltd., KonkoLy Thege Miklos Ut 29-33, Budapest, Hungary

11.1 Introduction

Industrial equipment is typically large, and for this reason, processes taking place in them need testing methods with high sensitivity. This requirement is well satis­fied by radioactive isotopes (radionuclides) because of their extremely high detec­tion sensitivity.

Another feature of industrial processes is that they often take place in closed systems, so taking the direct approach to materials is difficult or impossible. For this reason, testing methods that allow investigation of the processes without open­ing the equipment, disrupting the technological systems, disturbing the processes, and providing qualitative and quantitative information on processes taking place in the “black box” are required.

An important requirement for testing methods applied in industry is rapidity because industrial processes cannot be stopped for long periods. This is partly because it is not allowed technologically and partly because it would cause consid­erable economic loss. At continuous technologies, for instance, a startup needs con­siderable preparations (e. g., heating up the systems). Additional startup can be avoided if the system is tested without stopping the process. However, the removal of the materials for measuring its mass or volume is also impossible due to the large quantities or other hindering effects (e. g., dangerous or toxic materials). The radiotracer technique provides the opportunity to measure large quantities. Besides this, testing methods applying radionuclides often offer noninvasive testing oppor­tunities on the production line itself (“online” testing).

We have to face two contradicting requirements: we should administer short-lived radionuclides to patients (as discussed in Section 12.2.4), while radioisotopes are generally produced either in a nuclear reactor or by an accelerator, in most cases far from the location of the application. The best solution is the use of radioisotope generators, in which case its longer-lived radioactive parent element is transported. For example, to produce Tc-99m, its parent element, molybdenum-99, is used. A key point of a generator is a suitable solvent that selectively dissolves the daugh­ter element from a porous column, but not the parent element. Fortunately in the Mo-99!Tc-99m generators, physiological saline (NaCl) can be used as a solvent, so that the eluate is suitable for intravenous injection. (In other cases, we are not so lucky. For instance, before gamma cameras came into general use, indium-113m generators applied hydrochloric acid as an eluent that had to be neutralized before being administered to a human.)

12.2.6.1 Other Radionuclides

• Besides Tc-99m, Tl-201 as thallium chloride and Ga-67 in the form of gallium citrate are commonly used for gamma camera imaging.

• From among the radioisotopes of iodine, I-131 was first applied for imaging (see Table 12.3), but it has serious drawbacks: its gamma energy (with the highest peak at 364 keV) is too high, and its half-life (8 days) is longer than is generally desirable for imaging. Moreover, it is a beta emitter as well, increasing its radiation dose; that is why it is mainly used today for therapeutic purposes (and to measure iodine uptake before the therapy of hyperthyreosis). Iodide injected into the circulation primarily accumulates in the thyroid, which explains its application in measuring and imaging thyroid function already from the first half of the twentieth century (see more in Section 12.5.1). Sodium iodide labeled with I-131 was the first and is still the most common radioactive substance used for therapy, utilizing its beta radiation. Hyperthyreosis and thyroid cancer are the main indications.

• Another common radioisotope of iodine is I-123, as its 159 keV gamma energy and 13-h half-life make it a close runner-up after Tc-99m for use in gamma imaging. However, it is a cyclotron product, like Tl-201 and Ga-67, which makes it rather expensive.

• Radioisotopes of iodine, built into tyrosine, are suitable for labeling various protein molecules. For in vitro concentration measurements, I-125 is most commonly used. Its characteristic X-rays around 27 keV and gamma peak at 35 keV lead to a relatively low personnel dose, while its 60-day half-life allows a longer time for usage. In practice, it can only be used for about 6 weeks after labeling since radiolysis (chemical decomposi­tion caused by radiation) degrades the radiochemical purity of the preparation (the percentage of the radionuclide in the desired chemical form).