Fine and hyperfine structure of optical spectra. Theoretical introduction

An analysis of the spectra of complex atoms showed that not all, but only some, electronic transitions from the highest energy level of the atom to the lowest are realized in practice.

This is because the allowed transitions must satisfy the condition ( selection rules).

For example, D = ±1, Dm = 0, ±1, where D - the difference between the values ​​of the orbital quantum number; Dm is the difference between the values ​​of the magnetic quantum number corresponding to two states of an electron, etc.

In addition, it was discovered thin and ultra-thin structure spectral lines. For example, the yellow D - sodium line splits into two lines (l 1 = 5.890×10 - 7 m and l 2 = 5.896×10 - 7 m). Such a phenomenon is possible when the energy level is split, electron transitions between which lead to the appearance of these spectral lines.

The fine structure of spectral lines is caused by the influence of the spin of electrons on their energy and the influence of other factors. . Dirac taking this into account, he obtained a relativistic wave equation, the solution of which made it possible to explain the spin-orbit interaction of electrons.

The study of the fine structure of the spectral lines and direct measurements of the splitting of the levels of the hydrogen and helium atom by radiospectroscopy confirmed the theory. In addition to splitting, there is a shift in energy levels - a quantum effect caused by recoil during radiation. Along with thin observed hyperfine structure energy level, due to the interaction of the magnetic moments of the electron with the magnetic moment of the nucleus, as well as isotopic displacement, due to the difference in the masses of the nuclei of the isotopes of one element. If there are several electrons in an atom, then their magnetic interaction leads to the fact that the magnetic moments of the electrons add up to the resulting magnetic moment. There are several types of interactions.

In the first type of interaction - normal magnetic coupling (L-, S-connections)- orbital moments are added separately in the resulting moment, separately - spin moments and already their resultant moments are added to the total angular momentum of the atom. Second type of interaction (spin-orbit coupling) the orbital and spin angular momentum of each electron add up to a common momentum, and the already total moments of individual electrons add up to the total angular momentum of the atom.

There are other types of links as well.

Thus, in the vector model of an atom in the case of L -, S - bonds, we have

,

where , s i are the corresponding orbital and

spin moments of individual electrons; L is the total orbital angular momentum; S is the total spin angular momentum; J is the total angular momentum of all electrons in the atom.

According to quantum mechanics

(10)

where L, S, J are the quantum numbers of the total moment, respectively, for the vectors .

For example, given L and S, the total angular momentum J can take on the values: L + S, L + S - 1, L + S - 2, ... , L - S + 1, L - S.

In a magnetic field, the projection

. (11)

The magnetic quantum number m J can take the following values:

J, J - 1, J - 2, ... , -J + 1, -J.

There are 2J + 1 values ​​in total.

Consequently, in a magnetic field, the level with the quantum number J is divided into 2J + 1 sublevels.

In this case, the selection rule Dm J = 0, ±1 is observed.

In classical physics, the angular momentum vector of a particle relative to the origin 0 is determined by the vector product of the vectors and , i.e.

In quantum mechanics, this does not make sense, since there is no state in which both vectors and have certain values ​​(Heisenberg's uncertainty relations).

In quantum mechanics, the vector product corresponds to vector operator

It follows from quantum mechanics that there is no state in which the angular momentum vector has a definite value, i.e., would be completely determined both in magnitude and in direction. The angular momentum operator vector depends only on the direction of the coordinate axes.

The physical quantities that characterize the angular momentum of a particle in quantum mechanics are:

1. Projection of the operator of rotational (angular) momentum of a particle

, (12)

where m z = 0, ±1, ±2, ... , is the magnetic quantum number.

2. K square of the particle's total torque(not the square of the vector , but the eigenvalues ​​of the square of the torque operator), i.e.

. (13)

Therefore, there is a state in which the square of the torque and one of its projections on the selected direction (for example, on the Z axis) simultaneously have certain values.

Total states in which the square of the torque has certain values, 2 +1

where = 0, 1, ... , n - 1 - orbital quantum number that determines the square of the angular momentum.

Processes that determine projection of the particle torque operator L z and the square of the torque L 2 are called spatial quantization.

Rice. one

Graphically, spatial quantization is presented in a vector diagram (Fig. 1), which shows the possible values ​​of the projection L z and possible values ​​of the squared angular momentum L 2 . Possible values ​​of m z are plotted along the Z axis as projections of the length operator vector | |= .

At =1, = , if h / 2p is taken as a unit of torque. Knowing the spin, for example, for the nucleus of the sodium atom, allows us to consider in detail the hyperfine splitting of energy levels and spectral lines for this element. The spin moment of the nucleus is quantized. It has been established that the maximum value of the spin of the nucleus of the sodium atom .

If we take as the unit of the nuclear spin moment, then its projection on the chosen direction (determined by the external magnetic field) can take only discrete values: 0, ±1, ±2, ... or The fine structure of the spectral lines is explained by the spin-orbit interaction of electrons and the dependence of the electron mass on velocity.

The value of the fine splitting of energy levels for light atoms is ~10 - 5 eV.

For heavy atoms, it can reach fractions of an electron volt.

The set of sublevels into which an energy level is split is called multiplet: doublets, triplets, etc.

Simple levels that do not split into sublevels are called singlets. The fine structure of the spectral lines is characterized by the fine structure constant a » 1/137. The hyperfine structure of the spectral lines is explained by the interaction between the electron shell and the atomic nucleus. For sodium, the lines D 1 and D 2 are manifestations of the fine structure of the spectral lines. On fig. 2, in accordance with the selection rules, the possible transitions are shown (not to scale).

Below is the observed pattern of hyperfine splitting of spectral lines. The relative intensities of the components give the lengths of the vertical segments depicted under the corresponding quantum transitions. For the hydrogen atom, the hyperfine structure is also observed for the ground energy level (n = 1, = 0); the fine structure is absent in this case. This is explained by the interaction of the total angular momentum of the electron with the spin momentum of the nucleus (proton). When an electron passes between two emerging sublevels of the hyperfine splitting of the ground energy level of the hydrogen atom, radiation occurs with a wavelength l = 21 cm, which is observed for interstellar hydrogen. In the study of the fine structure of spectral lines, a certain role was played by simple and complex (anomalous) Zeeman effects, which is observed only in paramagnetic atoms, since they have a non-zero magnetic moment and can interact with a magnetic field. A simple Zeeman effect is observed when a radiation source is introduced into a magnetic field, which causes splitting of energy levels and spectral lines into several components. The quantum theory of the Zeeman effect is based on the analysis of the splitting of the energy level of a radiating electron in an atom introduced into a magnetic field. In this case, it is assumed that the electron has only an orbital magnetic moment and in a magnetic field the atom acquires additional energy DW = - m 0 p mz H, where H is the magnetic field strength; p mz is the projection of the magnetic moment onto the Z direction of the magnetic field; m 0 - magnetic constant.

In a weak magnetic field, a complex Zeeman effect is observed.

This effect was explained after the discovery of the electron spin and is used to describe the vector model of the atom. The splitting of energy levels in a magnetic field is caused by the phenomenon of magnetic resonance, which consists in the selective (selective) absorption of the energy of an alternating magnetic field and is associated with forced transitions between sublevels of the same Zeeman multiplet, which appeared as a result of the action of a constant magnetic field. Magnetic resonance due to the presence of electron magnetic moment is called electronic magnetic resonance(ferromagnetic resonance and nuclear magnetic resonance). Nuclear magnetic resonance is caused by the presence of magnetic moments in nuclear particles (protons and neutrons).

There is also electron paramagnetic resonance, which was first observed by E.K. Zavoisky in 1944

If the spin and orbital moments in an atom are nonzero, then due to the interaction of the spin and orbital moments (spin-orbital interaction), the energy levels can further split. As a result, the shape of the EPR spectrum becomes more complicated and several lines appear in the EPR spectrum instead of one spectral line. In this case, the EPR spectrum is said to have a fine structure. In the presence of a strong spin-orbit interaction, splitting of the Zeeman levels can be observed even in the absence of an external magnetic field.

Spectral line width

EPR signals are characterized by a certain width of the spectral line. This is due to the fact that the Zeeman energy levels between which resonant transitions occur are not infinitely narrow lines. If, due to the interaction of unpaired electrons with other paramagnetic particles and the lattice, these levels turn out to be smeared out, then the resonance conditions can be realized not at one value of the field H 0 , but in a certain range of fields. The stronger the spin-spin and spin-lattice interactions, the wider the spectral line. In the theory of magnetic resonance, it is customary to characterize the interaction of spins with a lattice by the so-called spin-lattice relaxation time T1, and the interaction between spins by the spin-spin relaxation time T2. The width of a single EPR line is inversely proportional to these parameters:

The relaxation times T1 and T2 depend on the nature of the paramagnetic centers, their environment, molecular mobility, and temperature.

The study of the shape of the EPR spectrum depending on various physicochemical factors is an important source of information on the nature and properties of paramagnetic centers. The shape of the EPR spectra of radicals is sensitive to changes in their environment and mobility; therefore, they are often used as molecular probes to study microviscosity and structural changes in various systems: in solutions, polymers, biological membranes, and macromolecular complexes. For example, from the temperature dependences of the intensity and width of the EPR spectra of spin probes, one can obtain important information about phase transitions in a system containing paramagnetic centers.

The characteristics of the EPR spectra listed above—the g factor, the fine and hyperfine structure of the EPR spectrum, and the widths of the individual components of the spectrum—are a kind of "passport" of a paramagnetic sample, by which one can

identify the source of the EPR signal and determine its physicochemical properties. For example, by observing the EPR signals of biological objects, one can directly monitor the course of intracellular processes in plant leaves, animal tissues and cells, and in bacteria.

NUCLEAR MAGNETIC RESONANCE

Until recently, our ideas about the structure of atoms and molecules were based on studies using optical spectroscopy methods. In connection with the improvement of spectral methods, which have advanced the field of spectroscopic measurements into the range of ultrahigh (approximately 103–106 MHz; microradio waves) and high frequencies (approximately 10–2–102 MHz; radio waves), new sources of information about the structure of matter have appeared. During the absorption and emission of radiation in this frequency range, the same basic process occurs as in other ranges of the electromagnetic spectrum, namely, when moving from one energy level to another, the system absorbs or emits a quantum of energy.

The energy difference between the levels and the energy of the quanta involved in these processes are about 10-7 eV for the radio frequency region and about 10-4 eV for microwave frequencies. In two types of radio spectroscopy, namely, nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy, the difference in the energy levels is associated with different orientations, respectively, of the magnetic dipole moments of nuclei in an applied magnetic field and electric quadrupole moments of nuclei in molecular electric fields, if the latter are not spherically symmetrical.

The existence of nuclear moments was first discovered when studying the hyperfine structure of the electronic spectra of some atoms using high-resolution optical spectrometers.

Under the influence of an external magnetic field, the magnetic moments of the nuclei are oriented in a certain way, and it becomes possible to observe transitions between nuclear energy levels associated with these different orientations: transitions that occur under the action of radiation of a certain frequency. The quantization of the energy levels of the nucleus is a direct consequence of the quantum nature of the angular momentum of the nucleus, which takes 2I + 1 values. The spin quantum number (spin) I can take on any value that is a multiple of ½.

The values ​​of I for particular nuclei cannot be predicted, but it has been observed that isotopes with both mass number and atomic number even have I = 0, while isotopes with odd mass numbers have half-integer spins. Such a situation, when the numbers of protons and neutrons in the nucleus are even and equal (I = 0), can be considered as a state with "complete pairing", similar to the complete pairing of electrons in a diamagnetic molecule.

At the end of 1945, two groups of American physicists led by F. Bloch (Stanford University) and E.M. Purcell (Harvard University) were the first to receive nuclear magnetic resonance signals. Bloch observed resonant absorption by protons in water, and Purcell was successful in discovering nuclear resonance by protons in paraffin. For this discovery, they were awarded the Nobel Prize in 1952.

HIGH RESOLUTION NMR SPECTROSCOPY

The essence of the NMR phenomenon can be illustrated as follows. If a nucleus with a magnetic moment is placed in a uniform field H 0 directed along the z axis, then its energy (with respect to the energy in the absence of a field) is equal to – m z H 0 , where m z is the projection of the nuclear magnetic moment onto the direction of the field.

As already noted, the nucleus can be in 2I + 1 states. In the absence of an external field H 0, all these states have the same energy.

A nucleus with spin I has discrete energy levels. The splitting of energy levels in a magnetic field can be called nuclear Zeeman splitting, since it is similar to the splitting of electronic levels in a magnetic field (the Zeeman effect).

The NMR phenomenon consists in the resonant absorption of electromagnetic energy due to the magnetism of the nuclei. This implies the obvious name of the phenomenon: nuclear - we are talking about a system of nuclei, magnetic - we mean only their magnetic properties, resonance - the phenomenon itself is resonant in nature.

NMR spectroscopy is characterized by a number of features that distinguish it from other analytical methods. About half (~150) of the nuclei of known isotopes have magnetic moments, but only a minority of them are used systematically.

Prior to the advent of pulsed spectrometers, most studies were carried out using the phenomenon of NMR on hydrogen nuclei (protons) 1H (proton magnetic resonance - PMR) and fluorine 19F. These nuclei have ideal properties for NMR spectroscopy:

* high natural content of the "magnetic" isotope (1H 99.98%, 19F 100%); for comparison, it can be mentioned that the natural content of the "magnetic" carbon isotope 13C is 1.1%;

* large magnetic moment;

* spin I = 1/2.

This is primarily responsible for the high sensitivity of the method in detecting signals from the nuclei mentioned above. In addition, there is a strictly theoretically justified rule according to which only nuclei with a spin equal to or greater than unity have an electric quadrupole moment. Consequently, 1H and 19F NMR experiments are not complicated by the interaction of the nuclear quadrupole moment of the nucleus with the electrical environment. A large number of works have been devoted to resonance on other (besides 1H and 19F) nuclei, such as 13C, 31P, 11B, 17O in the liquid phase (as well as on 1H and 19F nuclei).

High-resolution NMR spectra usually consist of narrow, well-resolved lines (signals) corresponding to magnetic nuclei in various chemical environments. The intensities (areas) of the signals during the recording of the spectra are proportional to the number of magnetic nuclei in each group, which makes it possible to carry out a quantitative analysis using NMR spectra without preliminary calibration.

Another feature of NMR is the influence of exchange processes, in which resonating nuclei participate, on the position and width of resonant signals. Thus, NMR spectra can be used to study the nature of such processes. NMR lines in liquid spectra typically have a width of 0.1 - 1 Hz (high-resolution NMR), while the same nuclei examined in the solid phase will give rise to lines with a width of the order of 1 - 104 Hz (hence the concept of NMR wide lines ).

In high-resolution NMR spectroscopy, there are two main sources of information about the structure and dynamics of molecules:

chemical shift

Under real conditions, resonating nuclei whose NMR signals are detected are a constituent of atoms or molecules. When the substances under study are placed in a magnetic field (H 0), a diamagnetic moment of atoms (molecules) arises due to the orbital motion of electrons. This movement of electrons forms effective currents and, therefore, creates a secondary magnetic field proportional to the field H 0 in accordance with Lenz's law and oppositely directed. This secondary field acts on the nucleus. Thus, the local field in the place where the resonating nucleus is located,

where σ is a dimensionless constant, called the screening constant, which does not depend on H 0 but strongly depends on the chemical (electronic) environment; it characterizes the decrease in Hloc compared to H 0 . The value of σ varies from a value of the order of 10 -5 for a proton to values ​​of the order of 10 - 2 for heavy nuclei.

The screening effect is to reduce the distance between the levels of nuclear magnetic energy, or, in other words, leads to the convergence of the Zeeman levels. In this case, the energy quanta that cause transitions between levels become smaller and, therefore, resonance occurs at lower frequencies. If the experiment is carried out by varying the field H0 until resonance sets in, then the strength of the applied field should be greater than in the case when the core is not screened.

In the vast majority of NMR spectrometers, spectra are recorded when the field changes from left to right, so the signals (peaks) of the most shielded nuclei should be in the right part of the spectrum. The shift of the signal depending on the chemical environment, due to the difference in screening constants, is called the chemical shift.

For the first time, messages about the discovery of a chemical shift appeared in several publications in 1950-1951. Among them, it is necessary to single out the work of Arnold et al. (1951), who obtained the first spectrum with separate lines corresponding to chemically different positions of identical 1H nuclei in one molecule. This is ethyl alcohol CH3CH2OH, whose typical low-resolution 1H NMR spectrum is shown in Fig. 3.

There are three types of protons in this molecule: three protons of the methyl group CH3-, two protons of the methylene group -CH2- and one proton of the hydroxyl group -OH. It can be seen that three separate signals correspond to three types of protons. Since the intensity of the signals is in the ratio 3: 2: 1, the decoding of the spectrum (assignment of signals) is not difficult. Since chemical shifts cannot be measured on an absolute scale, that is, relative to a nucleus devoid of all its electrons, the signal of a reference compound is used as a conditional zero. Usually, the chemical shift values ​​for any nuclei are given as a dimensionless parameter δ.

The unit of chemical shift is one millionth of the field strength or resonant frequency (ppm). In foreign literature, this reduction corresponds to ppm (parts per million). For most of the nuclei that make up diamagnetic compounds, the range of chemical shifts of their signals is hundreds and thousands of ppm, reaching 20,000 ppm. in the case of NMR 59Co (cobalt). In the 1H spectra, the proton signals of the vast majority of compounds lie in the range 0 – 10 ppm.

Spin-spin interaction

In 1951-1953, when recording the NMR spectra of a number of liquids, it was found that the spectra of some substances contain more lines than follows from a simple estimate of the number of nonequivalent nuclei. One of the first examples is the resonance on fluorine in the POCl2F molecule. The 19F spectrum consists of two lines of equal intensity, although there is only one fluorine atom in the molecule. Molecules of other compounds gave symmetrical multiplet signals (triplets, quartets, etc.).

Another important factor found in such spectra was that the distance between the lines, measured in the frequency scale, does not depend on the applied field H0, instead of being proportional to it, as it should be if the multiplicity arises due to the difference in screening constants.

Ramsey and Purcell in 1952 were the first to explain this interaction by showing that it is due to an indirect communication mechanism through the electronic environment. The nuclear spin tends to orient the spins of the electrons surrounding the given nucleus. Those, in turn, orient the spins of other electrons and through them - the spins of other nuclei. The energy of the spin-spin interaction is usually expressed in hertz (that is, the Planck constant is taken as a unit of energy, based on the fact that E = hn). It is clear that there is no need (unlike the chemical shift) to express it in relative units, since the discussed interaction, as noted above, does not depend on the strength of the external field. The magnitude of the interaction can be determined by measuring the distance between the components of the corresponding multiplet.

The simplest example of splitting due to spin-spin coupling that can be encountered is the resonance spectrum of a molecule containing two kinds of magnetic nuclei A and X. The nuclei A and X can be either different nuclei or nuclei of the same isotope (for example, 1H ) when the chemical shifts between their resonant signals are large.

The distance between the components in each doublet is called the spin-spin coupling constant and is usually denoted as J (Hz); in this case it is the JAX constant.

The occurrence of doublets is due to the fact that each nucleus splits the resonant lines of the neighboring nucleus into 2I + 1 components. The energy differences between different spin states are so small that, at thermal equilibrium, the probabilities of these states, in accordance with the Boltzmann distribution, turn out to be almost equal. Consequently, the intensities of all lines of the multiplet resulting from interaction with one nucleus will be equal. In the case when there are n equivalent nuclei (that is, they are equally shielded, so their signals have the same chemical shift), the resonant signal of the neighboring nucleus is split into 2nI + 1 lines.

Soon after the discovery of the phenomenon of NMR in condensed matter, it became clear that NMR would be the basis of a powerful method for studying the structure of matter and its properties. Indeed, when studying NMR spectra, we use as a resonant system of nuclei that are extremely sensitive to the magnetic environment. Local magnetic fields near the resonating nucleus depend on intra- and intermolecular effects, which determines the value of this type of spectroscopy for studying the structure and behavior of many-electron (molecular) systems.

At present, it is difficult to point to a field of natural sciences where NMR is not used to some extent. NMR spectroscopy methods are widely used in chemistry, molecular physics, biology, agronomy, medicine, in the study of natural formations (mica, amber, semi-precious stones, combustible minerals and other mineral raw materials), that is, in such scientific areas in which the structure of matter is studied, its molecular structure, the nature of chemical bonds, intermolecular interactions and various forms of internal movement.

NMR methods are increasingly being used to study technological processes in factory laboratories, as well as to control and regulate the course of these processes in various technological communications directly in production. Research over the past fifty years has shown that magnetic resonance methods can detect disturbances in the course of biological processes at the earliest stage. Installations for the study of the entire human body by magnetic resonance methods (NMR tomography methods) have been developed and are being produced.

Until now, we have been talking about the features of the structure of the spectra, which are explained by the properties of the electron cloud of the atom.

However, details in the structure of the spectra that cannot be explained from this point of view have long been noted. This includes the complex structure of individual lines of mercury and the double structure of each of the two yellow lines of sodium discovered in 1928 by L. N. Dobretsov and A. N. Terenin. In the latter case, the distance between the components was only 0.02 A, which is 25 times less than the radius of the hydrogen atom. These details of the structure of the spectrum are called hyperfine structure (Fig. 266).

Rice. 266. Hyperfine structure of the sodium line.

For its study, the Fabry-Perot standard and other devices with high resolution are usually used. The slightest expansion of spectral lines, caused by the interaction of atoms with each other or by their thermal motion, leads to the merging of the components of the hyperfine structure. Therefore, the method of molecular beams, first proposed by L. N. Dobretsov and A. N. Terenin, is widely used at present. With this method, the glow or absorption of a beam of atoms flying in a vacuum is observed.

In 1924, the Japanese physicist Nagaoka made the first attempt to relate hyperfine structure to the role of the atomic nucleus in spectra. This attempt was made in a very unconvincing form and caused completely mocking criticism from the well-known

spectroscopist I. Runge. He assigned to each letter of the Nagaoka surname its ordinal number in the alphabet and showed that an arbitrary combination of these numbers among themselves gives the same good agreement with the experimental data as Nagaoka's theory.

However, Pauli soon established that there was a grain of truth in Nagaoka's ideas and that the hyperfine structure was indeed directly related to the properties of the atomic nucleus.

Two types of hyperfine structure should be distinguished. The first type corresponds to a hyperfine structure, the same number of components for all lines of the spectrum of a given element. The appearance of this hyperfine structure is associated with the presence of isotopes. When studying the spectrum of one isolated isotope, only one component of the hyperfine structure of this type remains. For light elements, the appearance of such a hyperfine structure is explained by simple mechanical considerations. In § 58, considering the hydrogen atom, we considered the nucleus to be motionless. In fact, the nucleus and electron revolve around a common center of mass (Fig. 267). The distance from the nucleus to the center of mass is very small, it is approximately equal to where the distance to the electron, the mass of the electron, the mass of the nucleus.

Rice. 267. Rotation of the nucleus and electron around a common center of mass.

As a result, the energy of the atom acquires a slightly different value, which leads to a change in the Rydberg constant

where the value of the Rydberg constant corresponding to the fixed nucleus

Thus, depends on and, consequently, the frequency of the lines must depend on The latter circumstance served as the basis for the spectroscopic discovery of heavy hydrogen. In 1932, Urey, Maffey, and Brickwid discovered weak companions of the Balmer series line in the hydrogen spectrum.

Assuming that these satellites correspond to lines of a heavy hydrogen isotope with an atomic weight of two, they calculated, using (1), the wavelengths and compared them with experimental data.

According to formula (1), for elements with medium and large atomic weights, the isotope effect should be vanishingly small.

This conclusion is confirmed experimentally for elements with medium weights, but, oddly enough, is in sharp contradiction with the data for heavy elements. Heavy elements clearly exhibit an isotopic hyperfine structure. According to the available theory, in this case, it is no longer the mass that plays a role, but the finite dimensions of the nucleus.

The definition of the meter in the SI system (GOST 9867-61) takes into account the role of the hyperfine structure by indicating the isotope of krypton: "The meter is a length equal to 1650763.73 wavelengths in the vacuum of radiation corresponding to the transition between the levels of the krypton atom 86".

The second type of hyperfine structure is not associated with the presence of a mixture of isotopes; in particular, a hyperfine structure of this type is observed in bismuth, which has only one isotope.

The second type of hyperfine structure has a different shape for different spectral lines of the same element. The second type of hyperfine structure was explained by Pauli, who attributed to the nucleus its own mechanical torque (spin), a multiple of

Rice. 268. Origin of the hyperfine structure of the yellow lines of sodium.

The total rotational moment of an atom is equal to the vector sum of the nuclear moment and the moment of the electron shell. The total torque must be quantized, as are all atomic moments. Therefore, spatial quantization again arises - only certain orientations of the nuclear torque with respect to the electron shell torque are allowed. Each orientation corresponds to a certain sublevel of atomic energy. As in multiplets, here different sublevels correspond to a different amount of magnetic energy of the atom. But the mass of the nucleus is thousands of times greater than the mass of the electron, and therefore the magnetic moment of the nucleus is approximately the same number of times less than the magnetic moment of the electron. Thus, changes in the orientation of the nuclear moment should cause only very small changes in energy, which show up in the hyperfine structure of the lines. On fig. 268 shows diagrams of the hyperfine structure of sodium. To the right of each energy level is a number characterizing the total torque. The spin of the atomic nucleus of sodium turned out to be equal to

As can be seen from the figure, each of the yellow sodium lines consists of a large number of components, which, with insufficient resolution, look like two narrow doublets. The rotational moments of nuclei determined from the analysis of the hyperfine structure (in particular, for nitrogen) turned out to be in conflict with the hypothesis of the existence of electrons in the composition of the nucleus, which was used by D. D. Ivanenko to assert that the nuclei consist of protons and neutrons (§ 86).

Subsequently (since 1939), the much more accurate Rabi radiospectrographic method began to be used to determine nuclear moments.

Rabi's radio spectroscopic scheme for determining nuclear magnetic moments is, as it were, two Stern-Gerlach facilities (p. 317) arranged in series with mutually opposite directions of inhomogeneous magnetic fields. The molecular beam penetrates both installations in succession. If in the first setup the molecular beam is deflected, for example, to the right, then in the second setup it is deflected to the left. The effect of one setting compensates for the effect of another. Between these two settings is a device that violates the compensation. It consists of an electromagnet that creates a uniform magnetic field, and electrodes connected to a generator of high-frequency oscillations. The uniform magnetic field is directed parallel to the magnetic field in the first Stern-Gerlach installation.

A particle with a magnetic moment directed at an angle to the direction of the field has potential energy (vol. II, § 58). The same angle determines the amount of beam deflection in the first Stern-Gerlach setup. Under the action of a high-frequency field, the orientation of the magnetic moment can change and the magnetic energy becomes equal. This change in magnetic energy must be equal to the energy of the photon that caused the transition (absorption or forced transition, § 73):

Possible values ​​are determined by the spatial quantization law. Beam deflection in the second setup depends on the angle Since the angle is not equal to the angle, this deflection will not be equal to the deflection in the first setup and the compensation will be violated. Violation of the compensation of deviations is observed only at frequencies that satisfy the specified ratio; in other words, the observed effect is a resonance effect, which greatly improves the accuracy of the method. From the measured frequencies, the magnetic moments of the nuclei are calculated with great accuracy.

However, conventional optical spectroscopy retains its full value for the study of isotopic effects, where radiospectroscopy is fundamentally inapplicable. Isotopic effects are of particular interest for the theory of nuclear forces and intranuclear processes.

In recent years, spectroscopists have again returned to a thorough study of the spectrum of hydrogen. The spectrum of hydrogen turned out to be a literally inexhaustible source of new discoveries.

In § 59 it was already said that, when examined with high resolution equipment, each line of the hydrogen spectrum turns out to be double. It has long been believed that the theory of these subtle details of the hydrogen spectrum is in excellent agreement with experimental data. But, beginning in 1934, spectroscopists began to carefully point out the existence of small discrepancies between theory and experience. The discrepancies were within the measurement accuracy. The smallness of the effects can be judged by the following figures: the line, according to the theory, should basically consist of two lines with the following wave numbers: 15233.423 and The theoretical difference of the wave numbers is only a thousandth of a percent of each wave number. The experiment gave a value for this difference, about 2% less Michelson once said that "we should look for our future discoveries in the sixth decimal place." Here we are talking about the discrepancy in the eighth decimal place. In 1947, Lamb and Riserford returned to the same problem, but using the latest advances in physical experiment technology. The old theory led to a scheme of lower energy levels for the line shown in fig. 269.

Light is electromagnetic radiation with a wavelength l from 10–3 to 10–8 m. This wavelength range includes infrared (IR), visible and ultraviolet (UV) regions. Infrared interval of the spectrum ( l\u003d 1 mm ø 750 nm) is divided into far (1 mm ø 50 µm), middle (50 ø 2.5 µm) and near (2.5 µm ø 750 nm) regions. At room temperature, any material body radiates in the far infrared region, at a white heat temperature, the radiation shifts to the near infrared, and then to the visible part of the spectrum. The visible spectrum extends from 750 nm (red border) to 400 nm (violet border). The light of these wavelengths is perceived by the human eye, and it is in this region that a large number of spectral lines of atoms fall. The range from 400 to 200 nm corresponds to the ultraviolet region, then vacuum ultraviolet follows up to about 1 × 10 nm. RANGE.

THEORETICAL BASIS

Each atom and molecule has a unique structure, which corresponds to its own unique spectrum.

The structure of the spectrum of an atom, molecule, or the macrosystem formed by them is determined by their energy levels. According to the laws of quantum mechanics, each energy level corresponds to a certain quantum state. Electrons and nuclei in this state perform characteristic periodic motions, for which the energy, orbital angular momentum and other physical quantities are strictly defined and quantized, i.e. take only allowed discrete values ​​corresponding to integer and half-integer values ​​of quantum numbers. If the forces that bind electrons and nuclei into a single system are known, then, according to the laws of quantum mechanics, one can calculate its energy levels and quantum numbers, as well as predict the intensities and frequencies of spectral lines. On the other hand, by analyzing the spectrum of a particular system, one can determine the energies and quantum numbers of states, as well as draw conclusions about the forces acting in it. Thus, spectroscopy is the main source of information about quantum mechanical quantities and about the structure of atoms and molecules.

In an atom, the strongest interaction between the nucleus and electrons is due to electrostatic, or Coulomb, forces. Each electron is attracted to the nucleus and repelled by all other electrons. This interaction determines the structure of the energy levels of electrons. External (valence) electrons, moving from level to level, emit or absorb radiation in the near infrared, visible and ultraviolet regions. The transition energies between the levels of the inner shells correspond to the vacuum ultraviolet and X-ray regions of the spectrum. Weaker is the effect of the electric field on the magnetic moments of electrons. This leads to the splitting of the electronic energy levels and, accordingly, each spectral line into components (fine structure). In addition, a nucleus with a nuclear moment can interact with the electric field of orbiting electrons, causing an additional hyperfine splitting of energy levels.

When two or more atoms approach each other, forces of mutual attraction and repulsion begin to act between their electrons and nuclei. The resulting balance of forces can lead to a decrease in the total energy of the system of atoms - in this case, a stable molecule is formed. The structure of a molecule is mainly determined by the valence electrons of atoms, and molecular bonds obey the laws of quantum mechanics. In a molecule, ionic and covalent bonds are most often found MOLECULE STRUCTURE) . The atoms in the molecule experience continuous vibrations, and the molecule itself rotates as a whole, so it has new energy levels that are absent in isolated atoms. Rotational energies are less than vibrational energies, and vibrational energies are less than electronic ones. Thus, in a molecule, each electronic energy level is split into a number of closely spaced vibrational levels, and each vibrational level, in turn, into closely spaced rotational sublevels. As a result, vibrational transitions in molecular spectra have a rotational structure, while electronic transitions have a vibrational and rotational structure. Transitions between rotational levels of the same vibrational state fall into the far infrared and microwave regions, and transitions between vibrational levels of the same electronic state correspond in frequency to the infrared region. Due to the splitting of vibrational levels into rotational sublevels, each transition breaks up into many vibrational-rotational transitions, forming bands. Similarly, the electronic spectra of molecules are a series of electronic transitions split by closely spaced sublevels of vibrational and rotational transitions.

Since each atom is a quantum system (i.e., obeys the laws of quantum mechanics), its properties, including the frequencies and intensities of spectral lines, can be calculated if its Hamiltonian is given for a given system. Hamiltonian H is the total energy of the atom (kinetic plus potential), presented in operator form. (A quantum mechanical operator is a mathematical expression by which physical quantities are calculated.) The kinetic energy of a particle with mass t and moment R is equal to R 2 /2m. The potential energy of the system is equal to the sum of the energies of all interactions linking the system into a single whole. If the Hamiltonian is given, then the energy E of each quantum state can be found by solving the Schrödinger equation Нy = Еy, where y is the wave function describing the quantum state of the system.

SPECTRA AND STRUCTURE OF ATOMS

Hydrogen atom.

From the point of view of quantum mechanics, a hydrogen atom and any hydrogen-like ion (for example, He ++, etc.) are the simplest system consisting of one electron with a mass m and charge -e, which moves in the Coulomb field of the nucleus, which has mass M and charge + Ze(Z is the ordinal number of the element). If we take into account only the electrostatic interaction, then the potential energy of an atom is - Ze 2 /r, and the Hamiltonian will have the form H=p 2 /2m - Ze 2 /r, where m = tm/(m+ M) @ m. In differential form, the operator p 2 equals - ћ 2 C 2, where ћ = h/2p . Thus, the Schrödinger equation takes the form

The solution of this equation determines the energies of the stationary states ( E 0) water-like atom:

As m/M@ 1/2000 and m close to m, then

E n = –RZ 2 /n 2 .

where R is the Rydberg constant equal to R= me 4 /2ћ 2 @ 13.6 eV (or @ 109678 cm - 1); in X-ray spectroscopy, the rydberg is often used as a unit of energy. The quantum states of an atom are determined by quantum numbers n,l and m l. Principal quantum number P takes integer values ​​1, 2, 3.... Azimuthal quantum number l determines the magnitude of the angular momentum of the electron relative to the nucleus (orbital momentum); given P it can take the values ​​l = 0, 1, 2,..., P- 1. The square of the orbital momentum is equal to l(l+l) ћ 2. Quantum number m l determines the value of the projection of the orbital momentum on a given direction, it can take the values m l= 0, ± 1, ± 2,..., ± l. The projection of the orbital momentum itself is equal to m l ћ. Values l= 0, 1, 2, 3, 4, ... is usually denoted by letters s,p,d,f,g,.... Therefore, level 2 R hydrogen has quantum numbers n = 2 and l = 1.

Generally speaking, spectral transitions can by no means occur between all pairs of energy levels. Electric dipole transitions, accompanied by the strongest spectral manifestations, take place only under certain conditions (selection rules). Transitions that satisfy the selection rules are called allowed, the probability of other transitions is much less, they are difficult to observe and are considered forbidden.

In the hydrogen atom, transitions between states plm l and Pў lў m l¢ are possible if the number l changes by one, and the number m l remains constant or changes by one. Thus, the selection rules can be written:

D l = l – lў = ± 1, D m l = m lў = 0, ± 1.

For numbers P and P¢ There are no selection rules.

In a quantum transition between two levels with energies E n¢ and E n an atom emits or absorbs a photon whose energy is D E = E nў - E n . Since the frequency of the photon n=D E/h, frequencies of the spectral lines of the hydrogen atom ( Z= 1) are determined by the formula

and the corresponding wavelength is l = with/n. For values Pў = 2, P= 3, 4, 5,... the line frequencies in the emission spectrum of hydrogen correspond to the Balmer series (visible light and near ultraviolet region) and are in good agreement with the empirical Balmer formula l n = 364,56 n 2 /(n 2 - 4) nm. From comparing these two expressions, one can determine the value R. Spectroscopic studies of atomic hydrogen are an excellent example of theory and experiment that have made a huge contribution to fundamental science.

Fine structure of the hydrogen atom.

The relativistic quantum mechanical theory of levels discussed above was mainly confirmed by the analysis of atomic spectra, but did not explain the splitting and fine structure of the energy levels of the hydrogen atom. The fine structure of the levels of atomic hydrogen can be explained by taking into account two specific relativistic effects: the spin-orbit interaction and the dependence of the electron mass on velocity. The concept of the electron spin, which originally arose from the analysis of experimental data, received a theoretical justification in the relativistic theory developed by P. Dirac, from which it followed that the electron has its own angular momentum, or spin, and the corresponding magnetic moment. Spin quantum number s is equal to 1/2, and the projection of the spin onto the fixed axis takes the values m s= ±1/2. An electron, moving in orbit in the radial electric field of the nucleus, creates a magnetic field. The interaction of the intrinsic magnetic moment of the electron with this field is called the spin-orbit interaction.

An additional contribution to the fine structure comes from the relativistic correction to the kinetic energy due to the high orbital velocity of the electron. This effect was first discovered by N. Bohr and A. Sommerfeld, who showed that a relativistic change in the mass of an electron should cause the precession of its orbit.

Accounting for the spin-orbit interaction and the relativistic correction to the electron mass gives the following expression for the energy of fine level splitting:

where a= e 2 /sc» 1/137. The total angular momentum of an electron is + s. For a given value l quantum number j takes positive values j= l ± s (j= 1/2 for l= 0). According to the spectroscopic nomenclature, the state with quantum numbers n, l, s, j denoted as n 2s+ l lj. This means that 2 p hydrogen level with n= 2 and j= 3/2 will be written as 2 2 p 3/2. Value 2 s+ 1 is called multiplicity; it shows the number of states associated with a given value s. Note that the level splitting energy for a given n depends only on j but not from l or s separately. Thus, according to the above formula 2 2 s 1/2 and 2 2 p 1/2 levels of the fine structure are degenerate in energy. The levels 3 2 p 3/2 and 3 2 d 3/2. These results agree with the conclusions of the Dirac theory, if we neglect the terms a Z higher order. Allowed transitions are determined by the selection rules for j:D j= 0, ± 1 (excluding j= 0 ® 0).

Spectra of alkali metals.

In the alkali metal atoms Li, Na, K, Rb, Cs, and Fr, there is one valence electron in the outer orbit, which is responsible for the formation of the spectrum. All other electrons are located on inner closed shells. Unlike the hydrogen atom, in alkali metal atoms the field in which the outer electron moves is not a point charge field: the inner electrons shield the nucleus. The degree of screening depends on the nature of the orbital motion of the outer electron and its distance from the nucleus. Shielding is most effective at large values l and least effective for s-states where the electron is closest to the nucleus. At large n and l the system of energy levels is similar to that of hydrogen.

The fine structure of the levels of alkali metal atoms is also similar to that of hydrogen. Each electronic state splits into two close components. The allowed transitions in both cases are determined by the same selection rules. Therefore, the spectra of alkali metal atoms are similar to the spectrum of atomic hydrogen. However, for alkali metals, the splitting of spectral lines at small P greater than that of hydrogen, and increases rapidly with increasing Z.

Multi-electron atoms.

For atoms containing more than one valence electron, the Schrödinger equation can only be solved approximately. The central field approximation assumes that each electron moves in a centrally symmetric field created by the nucleus and other electrons. In this case, the state of the electron is completely determined by quantum numbers P, l,m l and m s (m s is the projection of the spin onto a fixed axis). Electrons in a multi-electron atom form shells, the energies of which increase as the quantum number increases P. Shells with n= 1, 2, 3... are denoted by letters K, L, M... etc. According to the Pauli principle, there cannot be more than one electron in each quantum state, i.e. no two electrons can have the same set of quantum numbers P, l,m l and m s. This leads to the fact that the shells in a multi-electron atom are filled in a strictly defined order, and each shell corresponds to a strictly defined number of electrons. Electron with quantum numbers P and l denoted by the combination ps, if l= 0, combination etc, if l= 1, etc. The electrons successively fill the shells with the lowest possible energy. First of all, two s filled with electrons K-shell with minimum energy; its configuration is denoted 1 s 2. Next to be filled L-shell: first two 2 s electrons, then six 2 R electrons (closed shell configuration 2 s 2 2R 6). As the ordinal number of the element grows, the shells that are more and more distant from the core are filled. The filled shells have a spherically symmetric charge distribution, zero orbital momentum, and strongly bound electrons. The outer, or valence, electrons are much weaker bound; they determine the physical, chemical, and spectral properties of the atom. The structure of the periodic system of elements is well explained by the order in which the shells of atoms in the ground states are filled.

In the central field approximation, it is assumed that all quantum states belonging to a given configuration have the same energy. In reality, these states are split by two main perturbations: spin-orbit and residual Coulomb interactions. These interactions relate the spin and orbital moments of individual electrons in the outer shell in different ways. In the case when the residual Coulomb interaction predominates, we have LS type of bond, and if the spin-orbit interaction prevails, then jj connection type.

When LS-bonds, the orbital moments of the outer electrons form the total orbital moment, and the spin moments form the total spin moment. Addition gives the total momentum of the atom. When jj- communication orbital and spin moments of an electron with number i, adding up, form the total moment of the electron , and when adding all vectors the total angular momentum of the atom is obtained. The total number of quantum states for both types of bond is naturally the same.

In multielectron atoms, the selection rules for allowed transitions depend on the type of bond. In addition, there is a parity selection rule: in allowed electric dipole transitions, the parity of the quantum state must change. (Parity is a quantum number that indicates whether the wavefunction is even (+1) or odd (–1) when reflected from the origin.) The parity selection rule is a basic requirement for an electric dipole transition in an atom or molecule.

Superfine structure.

Such characteristics of atomic nuclei as mass, volume, magnetic and quadrupole moments affect the structure of electronic energy levels, causing them to split into very closely spaced sublevels, called hyperfine structure.

Interactions that cause hyperfine splitting of electronic levels, which depend on the electron-nuclear orientation, can be magnetic or electric. In atoms, magnetic interactions predominate. In this case, the hyperfine structure arises as a result of the interaction of the nuclear magnetic moment with the magnetic field, which is created in the region of the nucleus by the spins and orbital motion of electrons. The interaction energy depends on the total angular momentum of the system , where is the nuclear spin, and I is the corresponding quantum number. The hyperfine magnetic splitting of energy levels is given by

where BUT is the hyperfine structure constant proportional to the magnetic moment of the nucleus. Frequencies from hundreds of megahertz to gigahertz are usually observed in the spectrum. They are maximum for s-electrons whose orbits are closest to the nucleus.

The charge distribution in the nucleus, the degree of asymmetry of which is characterized by the quadrupole moment of the nucleus, also affects the splitting of energy levels. The interaction of the quadrupole moment with the electric field in the region of the nucleus is very small, and the splitting frequencies caused by it are several tens of megahertz.

The hyperfine structure of the spectra can be due to the so-called isotopic shift. If an element contains several isotopes, then weakly separated or overlapping lines are observed in its spectrum. In this case, the spectrum is a collection of sets of spectral lines slightly shifted relative to each other belonging to different isotopes. The intensity of the lines of each isotope is proportional to its concentration.

STRUCTURE AND SPECTRA OF MOLECULES

Molecular spectra are much more complex and diverse than atomic ones. This is due to the fact that molecules have additional degrees of freedom and along with the movement of electrons around the nuclei of atoms that form the molecule, the nuclei themselves oscillate relative to the equilibrium position, as well as the rotation of the molecule as a whole. The nuclei in the molecule form a linear, planar, or three-dimensional configuration. Planar and three-dimensional molecules, consisting of N atoms, have 3N–6 vibrational and three rotational degrees of freedom, while linear molecules have 3N–5 vibrational and two rotational degrees of freedom. Thus, in addition to electronic energy, a molecule has vibrational and rotational internal energies, as well as new systems of levels.

rotational spectra.

A diatomic molecule can be simplistically considered as a rigid rotator with moment of inertia I. The solution of the Schrödinger equation for a rigid rotator gives the following allowed energy levels:

where J- a quantum number that characterizes the rotational momentum of the momentum of a molecule. The selection rule for allowed transitions is: D J= ± 1. Consequently, the purely rotational spectrum consists of a series of equidistant lines with frequencies

The rotational spectra of polyatomic molecules have a similar structure.

Vibrational-rotational spectra.

In reality, molecular bonds are not rigid. In the simplest approximation, the motion of the nuclei of a diatomic molecule can be considered as vibrations of particles with a reduced mass m relative to the equilibrium position in the potential well with a harmonic potential. If the harmonic potential has the form V(x)= kx 2 /2, where x is the deviation of the internuclear distance from the equilibrium, and k- coefficient of elasticity, then solving the Schrödinger equation gives the following possible energy levels: E v = hn(v+ 1/2). Here n is the oscillation frequency defined by the formula , and v is the vibrational quantum number, which takes the values v= 1, 2, 3.... Selection rule for allowed (infrared) transitions: D v= ± 1. Thus, for vibrational transitions there is a single frequency n. But since vibrations and rotation occur simultaneously in the molecule, a vibrational-rotational spectrum arises in which a “comb” of rotational lines is superimposed on the vibrational frequency of the molecule.

Electronic spectra.

Molecules have a large number of excited electronic levels, transitions between which are accompanied by a change in vibrational and rotational energy. As a result, the structure of the electronic spectra of molecules becomes much more complicated, since: 1) electronic transitions often overlap; 2) the selection rule for vibrational transitions is not observed (there is no restriction on D v); 3) the selection rule D is preserved J= 0, ± 1 for allowed rotational transitions. The electronic spectrum is a series of vibrational bands, each containing tens or hundreds of rotational lines. As a rule, several electronic transitions are observed in molecular spectra in the near infrared, visible and ultraviolet regions. For example, in the spectrum of the iodine molecule ( J 2) there are about 30 electronic transitions.

With the advent of lasers, the study of the electronic spectra of molecules, especially polyatomic ones, has reached a new level. Widely tunable high-intensity laser radiation is used in high-resolution spectroscopy to accurately determine molecular constants and potential surfaces. Visible, infrared, and microwave lasers are used in double resonance experiments to investigate new transitions.

Infrared spectra and Raman spectra.

Molecular absorption spectra are due to electrical dipole transitions. An electric dipole is a collection of two point electric charges that are equal in magnitude, opposite in sign and located at some distance from each other. The product of a positive charge and the distance between charges is called an electric dipole moment. The larger the dipole moment, the stronger the system can absorb and radiate electromagnetic energy. In polar molecules, such as HBr, which have a large dipole moment and strongly absorb at the corresponding frequencies, vibrational-rotational spectra are observed. On the other hand, non-polar molecules, such as H 2 , O 2 and N 2 , do not have a permanent dipole moment, and therefore cannot emit or absorb electromagnetic energy when rotating, therefore they do not have rotational spectra. In addition, the vibrations of such molecules are so symmetrical that they do not lead to the appearance of a dipole moment. This is due to the absence of their infrared vibrational spectrum.

An important spectroscopic method for studying the structure of molecules is the study of light scattering. Scattering of light is a process in which, under the action of incident light in an atom or molecule, oscillations of the dipole moment are excited, accompanied by the emission of the received energy. Reemission occurs mainly at the frequency of the incident light (elastic scattering), but weak inelastic scattering can be observed at shifted (combination) frequencies. Elastic scattering is called Rayleigh, while inelastic scattering is called Raman or Raman. The lines corresponding to Raman scattering are shifted relative to the line of incident light by the frequency of molecular vibrations of the scattering sample. Since the molecule can also rotate, rotational frequencies are superimposed on the displacement frequency.

Molecules with a homeopolar bond that do not have an infrared spectrum should be studied by Raman scattering. In the case of polyatomic molecules with several vibrational frequencies, part of the spectral information can be obtained from infrared absorption spectra, and part from Raman spectra (depending on the vibrational symmetry). The information obtained complements each other, since, due to different selection rules, they contain information about different molecular vibrations.

Infrared and Raman spectroscopy of polyatomic molecules is a powerful analytical technique similar to the spectrochemical analysis of atoms. Each molecular bond corresponds to a characteristic vibrational pattern in the spectrum, which can be used to identify a molecule or determine its structure.

Zeeman and Stark effects.

External electric and magnetic fields are successfully used to study the nature and properties of energy levels.

SPECTRAL LINE BROADENING

In accordance with the laws of quantum mechanics, spectral lines always have a finite width characteristic of a given atomic or molecular transition. An important characteristic of a quantum state is its radiative lifetime t, i.e. the time during which the system remains in this state without transitioning to lower levels. From the point of view of classical mechanics, radiation is a train of waves with a duration t, whence it follows that the width of the emission line D n equals 1/2 pt. The shorter the lifetime t, the wider the line.

The radiative lifetime depends on the transition dipole moment and the radiation frequency. The largest transition moments correspond to electric dipole transitions. In atoms and molecules for strong electronic transitions in the visible region of the spectrum t» 10 ns, which corresponds to a line width of 10 to 20 MHz. For excited vibrational states emitting in the infrared range, the transition times are weaker and the wavelength is longer, so their radiative lifetimes are measured in milliseconds.

The radiative lifetime determines the minimum width of the spectral line. However, in the overwhelming majority of cases the spectral lines can be much wider. The reasons for this are chaotic thermal motion (in a gas), collisions between radiating particles, and strong perturbations in the frequency of ions due to their random arrangement in the crystal lattice. There are a number of methods for minimizing the linewidth, allowing you to measure the center frequencies with the highest possible accuracy.

SPECTRAL INSTRUMENTS

A spectroscope is the simplest optical instrument designed to decompose light into spectral components and visually observe the spectrum. Modern spectroscopes equipped with devices for measuring wavelengths are called spectrometers. Quantometers, polychromators, quants, etc. also belong to the family of spectrographs. In spectrographs, the spectrum is recorded simultaneously in a wide range of wavelengths; photographic plates and multichannel detectors (photodiode arrays, photodiode arrays) are used to record the spectra. In spectrophotometers, photometry is carried out, i.e. comparison of the measured radiation flux with the reference one, and the spectra are electronically recorded. An emission spectrometer usually consists of a radiation source (emitted sample), a slit diaphragm, a collimating lens or collimating mirror, a dispersing element, a focusing system (lens or mirror), and a detector. The slit cuts out a narrow beam of light from the source, the collimating lens expands it and converts it into a parallel one. The dispersing element decomposes the light into spectral components. The focusing lens creates an image of a slit in the focal plane where the detector is placed. When studying absorption, a source with a continuous spectrum is used, and a cell with an absorbing sample is placed at certain points along the path of the light flux.

Sources.

The sources of continuous IR radiation are silicon carbide rods (globars) heated to high temperatures, which have intense radiation with l> 3 µm. For obtaining a continuous spectrum in the visible, near-IR and near-UV regions, incandescent solids are considered to be the best conventional sources. In the vacuum UV region, hydrogen and helium discharge lamps are used. Electric arcs, sparks, and discharge tubes are traditional sources of line spectra of neutral and ionized atoms.

Excellent sources are lasers that generate intense monochromatic collimated coherent radiation in the entire optical range. Among them, sources with a wide frequency tuning range deserve special attention. So, for example, diode IR lasers can be tuned in the range from 3 to 30 μm, dye lasers can be tuned within the visible and near IR regions. Frequency conversion expands the tuning range of the latter from the mid-IR to the far UV region. There are a large number of laser sources tunable in narrower ranges, and a large family of lasers with a fixed frequency that can cover the entire spectrum from the far IR to the UV region. Frequency-converting laser sources of vacuum UV radiation generate radiation with a wavelength of only a few nanometers. Fixed-frequency lasers operating in the X-ray range have also been developed.

Spectral decomposition methods.

The spectral decomposition of light is carried out by three methods: dispersion due to refraction in prisms, diffraction on periodic gratings, and using interference. Prisms for the infrared region are made from various inorganic crystals, for visible and UV radiation - from glass and quartz, respectively. In most modern instruments, instead of prisms, diffraction gratings with a large number of closely spaced grooves are used. Spectrometers with diffraction gratings allow measurements in the entire optical range. The decomposition of light into spectral components in them is more uniform than in prism spectrometers. The grating strokes are often applied directly to focusing mirrors, eliminating the need for lenses. Currently, holographic diffraction gratings are being used more and more widely, providing a higher resolution than conventional gratings. In interference spectrometers, a beam of light is split into two beams that follow different paths and then recombine to form an interference pattern. Interferometers provide the highest resolution and are used to study the fine and hyperfine structure of spectra, as well as to measure relative wavelengths. The Fabry-Perot interferometer is used as a standard for measuring wavelengths in spectrometers.

Recently, Fourier spectrometers have been used instead of traditional prism and diffraction instruments in the IR region. The Fourier spectrometer is a two-beam interferometer with a variable length of one arm. As a result of the interference of two beams, a modulated signal arises, the Fourier transform of which gives the spectrum. Fourier spectrometers differ from conventional spectrometers in their greater luminosity and higher resolution. In addition, they allow the use of modern computer methods for collecting and processing data.

Detectors.

The methods for recording spectra are very diverse. The human eye has a very high sensitivity. However, being high for green light ( l\u003d 550 nm), the sensitivity of the human eye quickly drops to zero at the borders of the infrared and ultraviolet regions. (We note, by the way, that Raman scattering, usually very weak, was detected with the naked eye.) Until the 1950s, various photographic plates were widely used to record spectra. Their sensitivity allowed measurements over the entire wavelength range from the near-IR (1.3 μm) to the vacuum UV region (100 nm or less). Later, photographic plates were replaced by electronic detectors and photodiode arrays.

In the IR region, bolometers, radiometers, and thermocouples have been and remain traditional radiometric detectors. Then came various types of fast-response and sensitive photocells and photoresistors. Photomultipliers are extremely sensitive in the visible and UV regions of the spectrum. They have low inertia, low dark current and low noise level. Fast-response sensitive multichannel detectors are also used. These include photodiode arrays with microchannel plates and charge-coupled devices. Like photographic plates, multichannel detectors record the entire spectrum at once; data from them can be easily entered into a computer.

Data collection and information processing.

At present, computer data collection and processing are used in spectroscopy. Wavelength scanning of the spectrum is usually carried out by a stepper motor, which, with each pulse from the computer, rotates the diffraction grating by a certain angle. At each position, the signal received from the detector is converted into a digital code and entered into the computer's memory. If necessary, the received information can be displayed on the screen. For quick comparison of data, reference spectrochemical information, as well as reference infrared and Raman spectra, are usually stored on diskettes.

SPECTROSCOPIC METHODS

Fluorescence spectroscopy.

Fluorescence spectroscopy is a very sensitive method for analyzing the chemical composition of a sample, which makes it possible to detect trace amounts of substances and even their individual molecules. Lasers are especially effective as sources of exciting radiation.

Absorption spectroscopy.

Absorption spectroscopy is indispensable for studies in those regions of the spectrum where fluorescence is weak or absent altogether. The absorption spectrum is recorded by direct measurement of the light transmitted through the sample or by one of the many indirect methods. To observe weak and forbidden transitions, long or multipass cells are used. The use of tunable lasers as radiation sources makes it possible to dispense with slit diaphragms and diffraction gratings.

Registration methods.

There are a number of sensitive methods that allow you to register changes that occur in the samples under study under the action of light. These include, in particular, laser-induced fluorescence, laser photoionization, and photodissociation. The optical-acoustic transducer measures the absorption of the modulated light from the intensity of the resulting sound wave. Photovoltaic cells control the current in a gas discharge when studying the populations of high-lying levels selectively excited by a tunable laser.

Saturation spectroscopy.

Irradiation of the sample with intense monochromatic laser radiation causes an increased population of the upper level of the transition and, as a consequence, a decrease in absorption (saturation of the transition). In low-pressure vapors, selective saturation occurs in those molecules whose velocity is such that resonance with laser radiation is achieved due to the Doppler shift. Selective saturation virtually eliminates the Doppler broadening of the lines and makes it possible to observe very narrow resonant peaks.

Raman Spectroscopy.

Raman spectroscopy is a two-photon spectroscopy based on inelastic scattering, in which a molecule goes into a lower excited state, exchanging two photons with a radiation field. In this process, a pump photon is absorbed and a Raman photon is emitted. In this case, the frequency difference of two photons is equal to the transition frequency. In the case of equilibrium population (the population of the initial state is greater than that of the final state), the frequency of the Raman transition is lower than that of the pump photon; it is called the Stokes frequency. Otherwise (the population of the combination levels is inverted), "anti-Stokes" radiation with a higher frequency is emitted. Since, in the case of a two-photon transition, the parity of the initial and final states must be the same, Raman scattering provides additional information with respect to IR absorption spectra, which requires a change in parity.

KAKR.

The method of coherent anti-Stokes Raman scattering (CAS) uses the emission of coherent light. During the CAS process, two intense light waves incident on the sample with frequencies n 1 and n 2 cause the emission of radiation with a frequency of 2 n 1 – n 2. The process is sharply enhanced when the frequency difference n 1 – n 2 is equal to the frequency of the Raman transition. This makes it possible to measure the difference between the energies of the combination levels. The KKR method is highly sensitive.

APPLIED SPECTROSCOPY

Spectral analysis has long been used in chemistry and materials science to determine trace amounts of elements. Spectral analysis methods are standardized, information about the characteristic lines of most elements and many molecules is stored in computer databases, which greatly speeds up the analysis and identification of chemicals.

An extremely effective method of monitoring the state of the air is laser spectroscopy. It allows you to measure the size and concentration of particles in the air, determine their shape, as well as obtain data on the temperature and pressure of water vapor in the upper atmosphere. Such studies are carried out by the method of lidar (laser location of the infrared range).

Spectroscopy has opened up wide opportunities for obtaining information of a fundamental nature in many fields of science. Thus, in astronomy, spectral data collected with the help of telescopes on atoms, ions, radicals and molecules located in stellar matter and interstellar space contributed to the deepening of our knowledge of such complex cosmological processes as the formation of stars and the evolution of the Universe at an early stage of development.

Until now, the spectroscopic method for measuring the optical activity of substances has been widely used to determine the structure of biological objects. As before, when studying biological molecules, their absorption spectra and fluorescence are measured. Dyes that fluoresce under laser excitation are used to determine the pH and ionic strengths in cells, as well as to study specific sites in proteins. With the help of resonant Raman scattering, the structure of cells is probed and the conformation of protein and DNA molecules is determined. Spectroscopy has played an important role in the study of photosynthesis and the biochemistry of vision. Increasingly, laser spectroscopy is also being used in medicine. Diode lasers are used in an oximeter, a device that determines blood oxygen saturation by absorbing radiation from two different frequencies in the near-IR region of the spectrum. The possibility of using laser-induced fluorescence and Raman scattering for the diagnosis of cancer, arterial disease and a number of other diseases is being studied.

Literature:

Zaidel A.N., Ostrovskaya G.V., Ostrovsky Yu.I. . Technique and practice of spectroscopy. M., 1972
Letokhov V.S., Chebotarev V.P. Principles of Nonlinear Laser Spectroscopy. M., 1975
Elyashevich M.A. Spectroscopy. Physical Encyclopedic Dictionary. M., 1995



The study of the spectrum of the hydrogen atom using spectral instruments with high resolution and large dispersion showed that the spectral lines of hydrogen have a fine structure, i.e. consist of several lines with very similar wavelengths. For example, the head line of the Balmer series H is a quintet (consisting of five separate lines) with a wavelength difference of nm.

The fine structure of the spectral lines of a hydrogen-like atom is explained by an additional interaction between the charge of the atomic nucleus and the spin magnetic moment of the electron. This interaction is called spin-orbit.

The total angular momentum of an electron is the sum of the orbital and spin moments. The addition of these moments occurs according to quantum mechanical laws so that the quantum number of the total angular momentum j can take two
,
, if
) or one (
, if
) meaning .

Taking into account the spin-orbit interaction of the state of the atom with different values j have different energies, so the energy levels with
split into two sublevels called doublets. Non-split levels with
and
called singlets.

The splitting value is determined by the wave relativistic Dirac equation, which gives a correction to the energy (5.2):

, (5.4)

where
is the fine structure constant. Energy E nj spin-orbit interaction is approximately
part of the energy of an electron E n. The relative difference between the components of the fine structure of the spectral lines has the same order of smallness. In this laboratory work, the resolution of the instruments does not allow us to observe such a small splitting of the spectral lines of the hydrogen atom.

3. Multielectron atoms

A multi-electron atom consists of a nucleus with a charge Ze and the electron shell surrounding the nucleus with Z electrons (for a mercury atom
). The exact determination of the wave function of the entire electron shell of an atom is impossible due to the large number of particles Z. Usually, an atom model is used for calculations, in which the idea of ​​the individual state of an electron in an atom is preserved. In this approach, called one-particle approximation, the state of individual electrons is described using four quantum numbers n, l, m, m s. At the same time, according to the Pauli principle, no more than one electron can be in one quantum state. Electrons of an atom with a given value of the principal quantum number n form a shell (layer). Set of electrons with given values ​​of quantum numbers n and l forms a subshell. Subshells are denoted by letters: s, p, d, f, … , which correspond to the values
The maximum number of electrons in a subshell is
. AT s subshell this number is 2, in p shell - 6, in d shell - 10, in f shell - 14, etc.

Electronic configuration called the distribution of electrons in an atom over single-particle states with different n and l. For example, for a mercury atom, the designation of the electronic configuration is: , where the numbers above the symbols of the subshell indicate the number of electrons in this state. The arrangement of electron shells and subshells in a configuration is determined by the order in which single-particle electronic states are filled. The filling of the states starts from the lower energy levels. In the mercury atom, the first four shells are completely filled, while the fifth and sixth are not completely filled. In the ground state of the mercury atom, two valence electrons are at 6 s subshell.

For a multielectron atom, the total angular momentum of completely filled inner shells and subshells is equal to zero. Therefore, the total angular momentum of such an atom is determined by the orbital and spin moments of the outer, valence, electrons. Valence electrons are in the centrally symmetric field of the nucleus and electrons of closed shells, so their total angular momentum is a conserved quantity. For light and medium atoms, the interaction of electrons, due to their orbital and spin moments, leads to the fact that these moments add up separately, i.e. the orbital momentum of all the electrons add up to the total orbital momentum of the atom
, and the spin moments of the electrons add up to the spin moment of the atom
. In this case, we say that between the electrons L-S connection or Rössel–Saunders connection.

quantum numbers L and S orbital and spin moments of an atom are determined by the general quantum-mechanical rules for adding angular momenta. For example, if two valence electrons have quantum numbers l 1 and l 2 , then L can take the following integer values:
. Applying a similar rule for the spin, and taking into account that the spin number of the electron
, we get the possible values S for two valence electrons:
.

Energy level corresponding to certain values ​​of quantum numbers L and S, is called spectral term. In spectroscopy, it is customary to denote the term by the symbol
, where instead of values
put letters S, P, D, F, … respectively. Number
called multiplicity terma.

Taking into account the spin-orbit interaction, the energy level, or term, is split into a number of sublevels, which correspond to different values ​​of the total angular momentum of the atom. Such a splitting of a term is called thin or multiplet. For given numbers L and S total angular momentum of an atom
determined by the quantum number J, which can take values: . Fine structure components or energy sublevels corresponding to given values L, S and J denoted by the symbol
.

If the spin number of two valence electrons of a mercury atom
, then the only possible value
. In this case, the multiplicity of the term is equal to
, i.e. all levels are singlet. Their spectral designations are: ,,
,etc.

R is. 5.3

If a
, a
, then three cases are possible:
. In this case, the multiplicity is
, i.e. all levels are triplet. And finally, if
, then the only value
, and the level of this state is singlet. In accordance with this, the following possible energy levels in the mercury atom are obtained: ,,,,
,
,
,
,,
etc.

All the listed energy levels are determined by various admissible sets of quantum states in which the valence electrons of the mercury atom can be.

An analysis of the emission and absorption spectra of mercury in the ultraviolet, visible and infrared regions made it possible to draw up a complete scheme of possible energy levels and transitions between them (Fig. 5.3). The diagram shows the wavelengths of the spectral lines of mercury in nanometers, as well as the quantum number n for each level .

The scheme shows the values ​​of the principal quantum number near the corresponding energy levels. On fig. 5.3 also indicates the transitions between levels and the wavelengths of the spectral lines of mercury corresponding to these transitions. Possible transitions are determined by the selection rules:
;
and
, and the transition from the state
into a state
impossible. From requirement
it follows that transitions between levels of the same multiplicity (singlet-singlet and triplet-triplet transitions) are allowed. However, as can be seen from Fig. 5.3, transitions forbidden by the selection rules (five singlet-triplet transitions) are also observed. The existence of transitions forbidden by the selection rules takes place for atoms with large atomic numbers. When studying the scheme of levels and transitions of mercury atoms, it is necessary to pay attention to the following circumstance: for large atomic numbers, the multiplet splitting due to the spin-orbit interaction is of great importance. So, the triplet level of mercury
has a splitting (the difference between the maximum and minimum energies) of the order of one electron volt, which is approximately one tenth of the energy of the ground state of the mercury atom. In this sense, the splitting of the energy level can no longer be considered "subtle".