Table of molecular spectra. Molecular spectra

While atomic spectra consist of individual lines, molecular spectra, when observed with an instrument of average resolving power, appear to consist of (see Fig. 40.1, which shows a section of the spectrum resulting from a glow discharge in air).

When using high-resolution instruments, it is discovered that the bands consist of a large number of closely spaced lines (see Fig. 40.2, which shows the fine structure of one of the bands in the spectrum of nitrogen molecules).

In accordance with their nature, the spectra of molecules are called striped spectra. Depending on the change in which types of energy (electronic, vibrational or rotational) causes the emission of a photon by a molecule, three types of bands are distinguished: 1) rotational, 2) vibrational-rotational and 3) electronic-vibrational. Stripes in Fig. 40.1 belong to the electronic vibrational type. This type of stripe is characterized by the presence of a sharp edge called the edge of the stripe. The other edge of such a strip turns out to be blurred. The edging is caused by the condensation of lines forming a strip. Rotational and oscillatory-rotational bands do not have an edge.

We will limit ourselves to considering the rotational and vibrational-rotational spectra of diatomic molecules. The energy of such molecules consists of electronic, vibrational and rotational energies (see formula (39.6)). In the ground state of the molecule, all three types of energy have a minimum value. When a molecule is given a sufficient amount of energy, it goes into an excited state and then, making a transition allowed by the selection rules to one of the lower energy states, emits a photon:

(it must be borne in mind that both and differ for different electronic configurations of the molecule).

In the previous paragraph it was stated that

Therefore, with weak excitations, it changes only with stronger ones - and only with even stronger excitations does the electronic configuration of the molecule change, i.e.

Rotational stripes. Photons that correspond to transitions of a molecule from one rotational state to another have the lowest energy (the electronic configuration and vibrational energy do not change):

Possible changes in the quantum number are limited by the selection rule (39.5). Therefore, the frequencies of lines emitted during transitions between rotational levels can have the following values:

where is the quantum number of the level to which the transition occurs (it can have the values: 0, 1, 2, ...), and

In Fig. Figure 40.3 shows a diagram of the occurrence of a rotational band.

The rotational spectrum consists of a series of equally spaced lines located in the very far infrared region. By measuring the distance between the lines, you can determine the constant (40.1) and find the moment of inertia of the molecule. Then, knowing the masses of the nuclei, one can calculate the equilibrium distance between them in a diatomic molecule.

The distance between the Lie lines is of the order of magnitude, so that for the moments of inertia of molecules, values ​​of the order of magnitude are obtained. For example, for a molecule, which corresponds to .

Vibrational-rotational bands. In the case when both the vibrational and rotational state of the molecule changes during the transition (Fig. 40.4), the energy of the emitted photon will be equal to

For the quantum number v the selection rule (39.3) applies, for J the rule (39.5) applies.

Since photon emission can be observed not only at and at . If the photon frequencies are determined by the formula

where J is the rotational quantum number of the lower level, which can take the following values: 0, 1, 2, ; B - value (40.1).

If the formula for the photon frequency has the form

where is the rotational quantum number of the lower level, which can take the values: 1, 2, ... (in this case it cannot have the value 0, since then J would be equal to -1).

Both cases can be covered by one formula:

The set of lines with frequencies determined by this formula is called a vibrational-rotational band. The vibrational part of the frequency determines the spectral region in which the band is located; the rotational part determines the fine structure of the strip, i.e., the splitting of individual lines. The region in which the vibrational-rotational bands are located extends from approximately 8000 to 50000 A.

From Fig. 40.4 it is clear that the vibrational-rotational band consists of a set of relatively symmetrical lines spaced apart from each other by only in the middle of the band the distance is twice as large, since a line with frequency does not appear.

The distance between the components of the vibrational-rotational band is related to the moment of inertia of the molecule by the same relationship as in the case of the rotational band, so that by measuring this distance, the moment of inertia of the molecule can be found.

Note that, in full accordance with the conclusions of the theory, rotational and vibrational-rotational spectra are observed experimentally only for asymmetrical diatomic molecules (i.e., molecules formed by two different atoms). For symmetric molecules, the dipole moment is zero, which leads to the prohibition of rotational and vibrational-rotational transitions. Electronic vibrational spectra are observed for both asymmetric and symmetric molecules.

molecular spectra, optical emission and absorption spectra, as well as Raman scattering, belonging to free or loosely connected molecules. M. s. have a complex structure. Typical M. s. - striped, they are observed in emission and absorption and in Raman scattering in the form of a set of more or less narrow bands in the ultraviolet, visible and near infrared regions, which break up with sufficient resolving power of the spectral instruments used into a set of closely spaced lines. The specific structure of M. s. is different for different molecules and, generally speaking, becomes more complex as the number of atoms in the molecule increases. For very complex molecules, the visible and ultraviolet spectra consist of a few broad continuous bands; the spectra of such molecules are similar to each other.

M. s. arise when quantum transitions between energy levels E' And E'' molecules according to the ratio

h n= E‘ - E‘’, (1)

Where h n - energy of emitted absorbed photon frequency n ( h -Planck's constant ). With Raman scattering h n is equal to the difference between the energies of the incident and scattered photons. M. s. much more complex than line atomic spectra, which is determined by the greater complexity of internal motions in a molecule than in atoms. Along with the movement of electrons relative to two or more nuclei in molecules, vibrational motion of the nuclei (together with the internal electrons surrounding them) occurs around equilibrium positions and rotational motion of the molecule as a whole. These three types of motion - electronic, vibrational and rotational - correspond to three types of energy levels and three types of spectra.

According to quantum mechanics, the energy of all types of motion in a molecule can take only certain values, i.e. it is quantized. Total energy of a molecule E can be approximately represented as the sum of quantized energy values ​​of three types of its motion:

E = E email + E count + E rotate (2)

By order of magnitude

Where m is the mass of the electron, and the magnitude M has the order of mass of atomic nuclei in a molecule, i.e. m/M~ 10 -3 -10 -5, therefore:

E email >> E count >> E rotate (4)

Usually E el about several ev(several hundred kJ/mol), E count ~ 10 -2 -10 -1 eV, E rotation ~ 10 -5 -10 -3 ev.

In accordance with (4), the system of energy levels of a molecule is characterized by a set of electronic levels far apart from each other (different values E el at E count = E rotation = 0), vibrational levels located much closer to each other (different values E count at a given E l and E rotation = 0) and even more closely spaced rotational levels (different values E rotation at given E el and E count).

Electronic energy levels ( E el in (2) correspond to the equilibrium configurations of the molecule (in the case of a diatomic molecule, characterized by the equilibrium value r 0 internuclear distance r. Each electronic state corresponds to a certain equilibrium configuration and a certain value E el; the lowest value corresponds to the basic energy level.

The set of electronic states of a molecule is determined by the properties of its electron shell. In principle the values E el can be calculated using methods quantum chemistry, however, this problem can only be solved using approximate methods and for relatively simple molecules. The most important information about the electronic levels of a molecule (the location of the electronic energy levels and their characteristics), determined by its chemical structure, is obtained by studying its molecular structure.

A very important characteristic of a given electronic energy level is the value quantum number S, characterizing the absolute value of the total spin moment of all electrons of the molecule. Chemically stable molecules usually have an even number of electrons, and for them S= 0, 1, 2... (for the main electronic level the typical value is S= 0, and for excited ones - S= 0 and S= 1). Levels with S= 0 are called singlet, with S= 1 - triplet (since the interaction in the molecule leads to their splitting into c = 2 S+ 1 = 3 sublevels) . WITH free radicals have, as a rule, an odd number of electrons, for them S= 1 / 2, 3 / 2, ... and the value is typical for both the main and excited levels S= 1 / 2 (doublet levels splitting into c = 2 sublevels).

For molecules whose equilibrium configuration has symmetry, the electronic levels can be further classified. In the case of diatomic and linear triatomic molecules having an axis of symmetry (of infinite order) passing through the nuclei of all atoms , electronic levels are characterized by the values ​​of the quantum number l, which determines the absolute value of the projection of the total orbital momentum of all electrons onto the axis of the molecule. Levels with l = 0, 1, 2, ... are designated S, P, D..., respectively, and the value of c is indicated by the index at the top left (for example, 3 S, 2 p, ...). For molecules with a center of symmetry, for example CO 2 and C 6 H 6 , all electronic levels are divided into even and odd, designated by indices g And u(depending on whether the wave function retains its sign when inverted at the center of symmetry or changes it).

Vibrational energy levels (values E count) can be found by quantizing the oscillatory motion, which is approximately considered harmonic. In the simplest case of a diatomic molecule (one vibrational degree of freedom, corresponding to a change in the internuclear distance r) it is considered as harmonic oscillator; its quantization gives equally spaced energy levels:

E count = h n e (u +1/2), (5)

where n e is the fundamental frequency of harmonic vibrations of the molecule, u is the vibrational quantum number, taking the values ​​0, 1, 2, ... For each electronic state of a polyatomic molecule consisting of N atoms ( N³ 3) and having f vibrational degrees of freedom ( f = 3N- 5 and f = 3N- 6 for linear and nonlinear molecules, respectively), it turns out f so-called normal vibrations with frequencies n i ( i = 1, 2, 3, ..., f) and a complex system of vibrational levels:

Where u i = 0, 1, 2, ... are the corresponding vibrational quantum numbers. The set of frequencies of normal vibrations in the ground electronic state is a very important characteristic of a molecule, depending on its chemical structure. All or part of the atoms of the molecule participate in a certain normal vibration; the atoms perform harmonic vibrations with the same frequency v i, but with different amplitudes that determine the shape of the vibration. Normal vibrations are divided according to their shape into stretching (in which the lengths of bond lines change) and bending (in which the angles between chemical bonds - bond angles - change). The number of different vibration frequencies for molecules of low symmetry (without symmetry axes of order higher than 2) is equal to 2, and all vibrations are non-degenerate, while for more symmetric molecules there are doubly and triply degenerate vibrations (pairs and triplets of vibrations that match in frequency). For example, in a nonlinear triatomic molecule H 2 O f= 3 and three non-degenerate vibrations are possible (two stretching and one bending). The more symmetrical linear triatomic CO 2 molecule has f= 4 - two non-degenerate vibrations (stretching) and one doubly degenerate (deformation). For a flat highly symmetrical molecule C 6 H 6 it turns out f= 30 - ten non-degenerate and 10 doubly degenerate oscillations; of these, 14 vibrations occur in the plane of the molecule (8 stretching and 6 bending) and 6 out-of-plane bending vibrations - perpendicular to this plane. The even more symmetrical tetrahedral CH 4 molecule has f = 9 - one non-degenerate vibration (stretching), one doubly degenerate (deformation) and two triply degenerate (one stretching and one deformation).

Rotational energy levels can be found by quantizing the rotational motion of a molecule, treating it as a solid with certain moments of inertia. In the simplest case of a diatomic or linear polyatomic molecule, its rotational energy

Where I is the moment of inertia of the molecule relative to an axis perpendicular to the axis of the molecule, and M- rotational moment of momentum. According to the quantization rules,

where is the rotational quantum number J= 0, 1, 2, ..., and therefore for E rotation received:

where the rotational constant determines the scale of distances between energy levels, which decreases with increasing nuclear masses and internuclear distances.

Various types of M. s. arise during various types of transitions between energy levels of molecules. According to (1) and (2)

D E = E‘ - E'' = D E el + D E count + D E rotate, (8)

where changes D E el, D E count and D E rotation of electronic, vibrational and rotational energies satisfy the condition:

D E el >> D E count >> D E rotate (9)

[distances between levels are of the same order as the energies themselves E el, E ol and E rotation, satisfying condition (4)].

At D E el ¹ 0, electronic microscopy is obtained, observable in the visible and ultraviolet (UV) regions. Usually at D E el ¹ 0 simultaneously D E number 0 and D E rotation ¹ 0; different D E count for a given D E el correspond to different vibrational bands, and different D E rotation at given D E el and d E count - individual rotational lines into which this strip breaks up; a characteristic striped structure is obtained.

Rotational splitting of the electron-vibrational band 3805 of the N 2 molecule

A set of stripes with a given D E el (corresponding to a purely electronic transition with a frequency v el = D E email/ h) called the strip system; individual bands have different intensities depending on the relative probabilities of transitions, which can be approximately calculated by quantum mechanical methods. For complex molecules, the bands of one system corresponding to a given electronic transition usually merge into one wide continuous band; several such wide bands can overlap each other. Characteristic discrete electronic spectra observed in frozen solutions of organic compounds . Electronic (more precisely, electronic-vibrational-rotational) spectra are studied experimentally using spectrographs and spectrometers with glass (for the visible region) and quartz (for the UV region) optics, in which prisms or diffraction gratings are used to decompose light into a spectrum .

At D E el = 0, and D E count ¹ 0, oscillatory magnetic resonances are obtained, observed in close range (up to several µm) and in the middle (up to several tens µm) infrared (IR) region, usually in absorption, as well as in Raman scattering of light. As a rule, simultaneously D E rotation ¹ 0 and at a given E The result is a vibrational band that breaks up into separate rotational lines. They are most intense in oscillatory M. s. stripes corresponding to D u = u’ - u'' = 1 (for polyatomic molecules - D u i = u i' - u i ''= 1 at D u k = u k ’ - u k '' = 0, where k¹i).

For purely harmonic vibrations these selection rules, prohibiting other transitions are carried out strictly; for anharmonic vibrations, bands appear for which D u> 1 (overtones); their intensity is usually low and decreases with increasing D u.

Vibrational (more precisely, vibrational-rotational) spectra are studied experimentally in the IR region in absorption using IR spectrometers with prisms transparent to IR radiation or with diffraction gratings, as well as Fourier spectrometers and in Raman scattering using high-aperture spectrographs ( for the visible region) using laser excitation.

At D E el = 0 and D E count = 0, purely rotational magnetic systems are obtained, consisting of individual lines. They are observed in absorption at a distance (hundreds of µm)IR region and especially in the microwave region, as well as in Raman spectra. For diatomic and linear polyatomic molecules (as well as for fairly symmetrical nonlinear polyatomic molecules), these lines are equally spaced (on the frequency scale) from each other with intervals Dn = 2 B in absorption spectra and Dn = 4 B in Raman spectra.

Pure rotational spectra are studied in absorption in the far IR region using IR spectrometers with special diffraction gratings (echelettes) and Fourier spectrometers, in the microwave region using microwave (microwave) spectrometers , as well as in Raman scattering using high-aperture spectrographs.

Methods of molecular spectroscopy, based on the study of microorganisms, make it possible to solve various problems in chemistry, biology, and other sciences (for example, determining the composition of petroleum products, polymer substances, etc.). In chemistry according to MS. study the structure of molecules. Electronic M. s. make it possible to obtain information about the electronic shells of molecules, determine excited levels and their characteristics, and find the dissociation energies of molecules (by the convergence of the vibrational levels of a molecule to the dissociation boundaries). Study of oscillatory M. s. allows you to find the characteristic vibration frequencies corresponding to certain types of chemical bonds in the molecule (for example, simple double and triple C-C bonds, C-H, N-H, O-H bonds for organic molecules), various groups of atoms (for example, CH 2 , CH 3 , NH 2), determine the spatial structure of molecules, distinguish between cis- and trans-isomers. For this purpose, both infrared absorption spectra (IR) and Raman spectra (RSS) are used. The IR method has become especially widespread as one of the most effective optical methods for studying the structure of molecules. It provides the most complete information in combination with the SKR method. The study of rotational magnetic resonances, as well as the rotational structure of electronic and vibrational spectra, makes it possible to use experimentally found values ​​of the moments of inertia of molecules [which are obtained from the values ​​of rotational constants, see (7)] to find with great accuracy (for simpler molecules, for example H 2 O) parameters of the equilibrium configuration of the molecule - bond lengths and bond angles. To increase the number of determined parameters, the spectra of isotopic molecules (in particular, in which hydrogen is replaced by deuterium) having the same parameters of equilibrium configurations, but different moments of inertia, are studied.

As an example of the use of M. s. To determine the chemical structure of molecules, consider the benzene molecule C 6 H 6 . Studying her M. s. confirms the correctness of the model, according to which the molecule is flat, and all 6 C-C bonds in the benzene ring are equivalent and form a regular hexagon with a sixth-order symmetry axis passing through the center of symmetry of the molecule perpendicular to its plane. Electronic M. s. absorption band C 6 H 6 consists of several systems of bands corresponding to transitions from the ground even singlet level to excited odd levels, of which the first is triplet, and the higher ones are singlets. The system of stripes is most intense in the area of ​​1840 ( E 5 - E 1 = 7,0 ev), the system of bands is weakest in the region of 3400 ( E 2 - E 1 = 3,8ev), corresponding to the singlet-triplet transition, which is prohibited by the approximate selection rules for the total spin. Transitions correspond to the excitation of the so-called. p electrons delocalized throughout the benzene ring ; The level diagram obtained from electronic molecular spectra is in agreement with approximate quantum mechanical calculations. Oscillatory M. s. C 6 H 6 correspond to the presence of a center of symmetry in the molecule - vibrational frequencies that appear (active) in the IRS are absent (inactive) in the SRS and vice versa (the so-called alternative prohibition). Of the 20 normal vibrations of C 6 H 6 4 are active in the ICS and 7 are active in the SCR, the remaining 11 are inactive in both the ICS and the SCR. Measured frequency values ​​(in cm -1): 673, 1038, 1486, 3080 (in ICS) and 607, 850, 992, 1178, 1596, 3047, 3062 (in TFR). Frequencies 673 and 850 correspond to non-plane vibrations, all other frequencies correspond to plane vibrations. Particularly characteristic of planar vibrations are the frequency 992 (corresponding to the stretching vibration of C-C bonds, consisting of periodic compression and stretching of the benzene ring), frequencies 3062 and 3080 (corresponding to the stretching vibrations of C-H bonds) and frequency 607 (corresponding to the bending vibration of the benzene ring). The observed vibrational spectra of C 6 H 6 (and similar vibrational spectra of C 6 D 6) are in very good agreement with theoretical calculations, which made it possible to give a complete interpretation of these spectra and find the shapes of all normal vibrations.

In the same way, you can use M. s. determine the structure of various classes of organic and inorganic molecules, up to very complex ones, such as polymer molecules.

Lecture 12. Nuclear physics. The structure of the atomic nucleus.

Core- this is the central massive part of the atom around which electrons revolve in quantum orbits. The mass of the nucleus is approximately 4·10 3 times greater than the mass of all the electrons included in the atom. The kernel size is very small (10 -12 -10 -13 cm), which is approximately 10 5 times less than the diameter of the entire atom. The electric charge is positive and in absolute value is equal to the sum of the charges of atomic electrons (since the atom as a whole is electrically neutral).

The nucleus was discovered by E. Rutherford (1911) in experiments on the scattering of alpha particles as they passed through matter. Having discovered that a-particles are scattered at large angles more often than expected, Rutherford suggested that the positive charge of the atom is concentrated in a small nucleus (before this, the ideas of J. Thomson prevailed, according to which the positive charge of the atom was considered uniformly distributed throughout its volume) . Rutherford's idea was not immediately accepted by his contemporaries (the main obstacle was the belief in the inevitable fall of atomic electrons onto the nucleus due to the loss of energy to electromagnetic radiation when moving in orbit around the nucleus). The famous work of N. Bohr (1913), which laid the foundation for the quantum theory of the atom, played a major role in its recognition. Bohr postulated the stability of orbits as the initial principle of quantization of the motion of atomic electrons and from it then derived the laws of line optical spectra that explained extensive empirical material (Balmer's series, etc.). Somewhat later (at the end of 1913), Rutherford's student G. Moseley experimentally showed that the shift of the short-wave boundary of the line X-ray spectra of atoms when the atomic number Z of an element in the periodic system of elements changes corresponds to Bohr's theory, if we assume that the electric charge of the nucleus (in units of electron charge) is equal to Z. This discovery completely broke the barrier of mistrust: a new physical object - the nucleus - turned out to be firmly connected with a whole range of seemingly heterogeneous phenomena, which have now received a unified and physically transparent explanation. After Moseley's work, the fact of the existence of the atomic nucleus was finally established in physics.

Kernel composition. At the time of the discovery of the nucleus, only two elementary particles were known - the proton and the electron. Accordingly, it was considered probable that the nucleus consists of them. However, at the end of the 20s. 20th century The proton-electron hypothesis encountered a serious difficulty, called the “nitrogen catastrophe”: according to the proton-electron hypothesis, the nitrogen nucleus should contain 21 particles (14 protons and 7 electrons), each of which had a spin of 1/2. The spin of the nitrogen nucleus should have been half-integer, but according to the data on the measurement of optical molecular spectra, the spin turned out to be equal to 1.

The composition of the nucleus was clarified after the discovery by J. Chadwick (1932) neutron. The mass of the neutron, as it turned out from Chadwick’s first experiments, is close to the mass of the proton, and the spin is equal to 1/2 (established later). The idea that the nucleus consists of protons and neutrons was first expressed in print by D. D. Ivanenko (1932) and immediately after this was developed by W. Heisenberg (1932). The assumption about the proton-neutron composition of the nucleus was later fully confirmed experimentally. In modern nuclear physics, the proton (p) and neutron (n) are often combined under the common name nucleon. The total number of nucleons in a nucleus is called the mass number A, the number of protons is equal to the charge of the nucleus Z (in units of electron charge), the number of neutrons N = A - Z. U isotopes same Z, but different A And N, the nuclei have the same isobars A and different Z and N.

In connection with the discovery of new particles heavier than nucleons, the so-called. nucleon isobars, it turned out that they should also be part of the nucleus (intranuclear nucleons, colliding with each other, can turn into nucleon isobars). In the simplest kernel - deuteron , consisting of one proton and one neutron, nucleons should remain in the form of nucleon isobars ~ 1% of the time. A number of observed phenomena testify in favor of the existence of such isobaric states in nuclei. In addition to nucleons and nucleon isobars, in nuclei periodically for a short time (10 -23 -10 -24 sec) appear mesons , including the lightest of them - p-mesons. The interaction of nucleons comes down to multiple acts of emission of a meson by one of the nucleons and its absorption by another. Emerging ie. exchange meson currents affect, in particular, the electromagnetic properties of nuclei. The most distinct manifestation of meson exchange currents was found in the reaction of deuteron splitting by high-energy electrons and g-quanta.

Interaction of nucleons. The forces that hold nucleons in the nucleus are called nuclear . These are the strongest interactions known in physics. The nuclear forces acting between two nucleons in a nucleus are an order of magnitude one hundred times more intense than the electrostatic interaction between protons. An important property of nuclear forces is their. independence from the charge state of nucleons: the nuclear interactions of two protons, two neutrons, or a neutron and a proton are the same if the states of relative motion of these pairs of particles are the same. The magnitude of nuclear forces depends on the distance between nucleons, on the mutual orientation of their spins, on the orientation of the spins relative to the orbital angular momentum and the radius vector drawn from one particle to another. Nuclear forces are characterized by a certain range of action: the potential of these forces decreases with distance r between particles faster than r-2, and the forces themselves are faster than r-3. From consideration of the physical nature of nuclear forces it follows that they should decrease exponentially with distance. The radius of action of nuclear forces is determined by the so-called. Compton wavelength r 0 mesons exchanged between nucleons during interaction:

here m, is the meson mass, is Planck’s constant, With- speed of light in vacuum. The forces caused by the exchange of p-mesons have the greatest radius of action. For them r 0 = 1.41 f (1 f = 10 -13 cm). Internucleon distances in nuclei are of precisely this order of magnitude, but exchanges of heavier mesons (m-, r-, w-mesons, etc.) also contribute to nuclear forces. The exact dependence of the nuclear forces between two nucleons on the distance and the contribution of nuclear forces due to the exchange of mesons of different types has not been established with certainty. In multinucleon nuclei, forces are possible that cannot be reduced to the interaction of only pairs of nucleons. The role of these so-called many-particle forces in the structure of nuclei remains unclear.

Kernel sizes depend on the number of nucleons they contain. The average density of the number p of nucleons in a nucleus (their number per unit volume) for all multinucleon nuclei (A > 0) is almost the same. This means that the volume of the nucleus is proportional to the number of nucleons A, and its linear size ~A 1/3. Effective core radius R is determined by the relation:

R = a A 1/3 , (2)

where is the constant A close to Hz, but differs from it and depends on in what physical phenomena it is measured R. In the case of the so-called charge radius of the nucleus, measured by the scattering of electrons on nuclei or by the position of energy levels m- mesoatoms : a = 1,12 f. Effective radius determined from interaction processes hadrons (nucleons, mesons, a-particles, etc.) with nuclei slightly larger than the charge: from 1.2 f up to 1.4 f.

The density of nuclear matter is fantastically high compared to the density of ordinary substances: it is approximately 10 14 G/cm 3. In the core, r is almost constant in the central part and decreases exponentially towards the periphery. For an approximate description of empirical data, the following dependence of r on the distance r from the center of the nucleus is sometimes accepted:

.

Effective core radius R equal to R 0 + b. The value b characterizes the blurring of the nucleus boundary; it is almost the same for all nuclei (» 0.5 f). The parameter r 0 is the double density at the “border” of the nucleus, determined from the normalization condition (equality of the volume integral of p to the number of nucleons A). From (2) it follows that the sizes of nuclei vary in order of magnitude from 10 -13 cm until 10 -12 cm for heavy nuclei (atom size ~ 10 -8 cm). However, formula (2) describes the increase in the linear dimensions of nuclei with an increase in the number of nucleons only roughly, with a significant increase A. The change in the size of the nucleus in the case of the addition of one or two nucleons to it depends on the details of the structure of the nucleus and can be irregular. In particular (as shown by measurements of the isotopic shift of atomic energy levels), sometimes the radius of the nucleus even decreases when two neutrons are added.

MOLECULAR SPECTRA

Emission, absorption and Raman spectra of light belonging to free or weakly bound molecules. Typical microscopic systems are striped; they are observed in the form of a set of more or less narrow bands in the UV, visible, and IR regions of the spectrum; with sufficient resolution of spectral devices mol. the stripes break up into a collection of closely spaced lines. Structure of M. s. different for different molecules and becomes more complex as the number of atoms in a molecule increases. The visible and UV spectra of very complex molecules are similar to each other and consist of a few broad continuous bands. M. s. arise during quantum transitions between energy levels?" and?" molecules according to the ratio:

where hv is the energy of the emitted or absorbed photon of frequency v. In Raman scattering, hv is equal to the difference in the energies of the incident and scattered photons. M. s. much more complex than atomic spectra, which is determined by the greater complexity of the internal movements in the molecule, because in addition to the movement of electrons relative to two or more nuclei, oscillation occurs in the molecule. the movement of the nuclei (together with the internal electrons surrounding them) around the equilibrium position and rotate. its movements as a whole. Electronic, oscillating and rotate. The movements of a molecule correspond to three types of energy levels? el, ?col and?vr and three types of M. s.

According to quant. mechanics, the energy of all types of motion in a molecule can only take on certain values ​​(quantized). Total energy of a molecule? can be approximately represented as a sum of quantized energy values ​​corresponding to its three types of internal energy. movements:

??el +?col+?vr, (2) and in order of magnitude

El:?col:?vr = 1: ?m/M:m/M, (3)

where m is the mass of the electron, and M is of the order of the mass of the nuclei of atoms in the molecule, i.e.

El -> ?count ->?vr. (4) Usually? el order several. eV (hundreds of kJ/mol), ?col = 10-2-10-1 eV, ?vr=10-5-10-3 eV.

The system of energy levels of a molecule is characterized by sets of electronic energy levels far apart from each other (disag. ?el at?col=?vr=0). vibrational levels located much closer to each other (differential values ​​for a given el and volt = 0) and even closer to each other rotational levels (values ​​of volt for a given el and tyr).

Electronic energy levels a to b in Fig. 1 correspond to the equilibrium configurations of the molecule. Each electronic state corresponds to a certain equilibrium configuration and a certain value?el; the smallest value corresponds to basic. electronic state (basic electronic energy level of the molecule).

Rice. 1. Diagram of energy levels of a diatomic molecule, a and b - electronic levels; v" and v" are quantum. number of oscillations levels; J" and J" - quantum. numbers are rotated. levels.

The set of electronic states of a molecule is determined by the properties of its electronic shell. In principle, the values ​​of ?el can be calculated using quantum methods. chemistry, however, this problem can only be solved approximately and for relatively simple molecules. Important information about the electronic levels of molecules (their location and their characteristics), determined by its chemical. structure is obtained by studying M. s.

A very important characteristic of the electronic energy level is the value of the quantum number 5, which determines the abs. the value of the total spin moment of all electrons. Chemically stable molecules, as a rule, have an even number of electrons, and for them 5 = 0, 1, 2, . . .; for main electronic level is typically 5=0, for excited levels - 5 = 0 and 5=1. Levels with S=0 are called. singlet, with S=1 - triplet (since their multiplicity is c=2S+1=3).

In the case of diatomic and linear triatomic molecules, electronic levels are characterized by quantum values. number L, which determines the abs. the magnitude of the projection of the total orbital momentum of all electrons onto the axis of the molecule. Levels with L=0, 1, 2, ... are designated S, P, D, respectively. . ., and and is indicated by an index at the top left (for example, 3S, 2P). For molecules with a center of symmetry (for example, CO2, CH6), all electronic levels are divided into even and odd (g and u, respectively) depending on whether or not the wave function that defines them retains its sign when inverted at the center of symmetry.

Vibrational energy levels can be found by quantizing the vibrations. movements that are approximately considered harmonic. A diatomic molecule (one vibrational degree of freedom corresponding to a change in the internuclear distance r) can be considered as a harmonic. oscillator, quantization of which gives equally spaced energy levels:

where v - main. harmonic frequency vibrations of the molecule, v=0, 1, 2, . . .- oscillate quantum. number.

For each electronic state of a polyatomic molecule consisting of N? 3 atoms and having f Oscillation. degrees of freedom (f=3N-5 and f=3N-6 for linear and nonlinear molecules, respectively), it turns out / so-called. normal oscillations with frequencies vi(ill, 2, 3, ..., f) and a complex system of oscillations. energy levels:

The set of frequencies is normal. fluctuations in the main electronic state of phenomena. an important characteristic of a molecule, depending on its chemical. buildings. In a certain sense. vibrations involve either all the atoms of the molecule or part of them; atoms perform harmonic oscillations with the same frequency vi, but with different amplitudes that determine the shape of the vibration. Normal vibrations are divided according to their shape into valence (the lengths of chemical bonds change) and deformation (the angles between chemical bonds change - bond angles). For molecules of lower symmetry (see SYMMETRY OF A MOLECULE) f=2 and all vibrations are non-degenerate; for more symmetrical molecules there are doubly and triply degenerate vibrations, i.e., pairs and triplets of vibrations matching in frequency.

Rotational energy levels can be found by quantizing the rotation. movement of a molecule, considering it as a TV. a body with certain moments of inertia. In the case of a diatomic or linear triatomic molecule, its rotational energy is? moment of quantity of movement. According to the quantization rules,

M2=(h/4pi2)J(J+1),

where f=0, 1,2,. . .- rotational quantum. number; for?v we get:

Вр=(h2/8pi2I)J(J+1) = hBJ(J+1), (7)

where they rotate. constant B=(h/8piI2)I

determines the scale of distances between energy levels, which decreases with increasing nuclear masses and internuclear distances.

Diff. types of M. s. arise when different types of transitions between energy levels of molecules. According to (1) and (2):

D?=?"-?"==D?el+D?col+D?vr,

and similarly to (4) D?el->D?count->D?time. At D?el?0, electronic microscopy is obtained, observable in the visible and UV regions. Usually at D??0 both D?number?0 and D?time?0; diff. D? count at a given D? el correspond to diff. oscillate stripes (Fig. 2), and decomposition. D?vr for given D?el and D?number of dep. rotate lines into which oscillations break up. stripes (Fig. 3).

Rice. 2. Electroino-oscillation. spectrum of the N2 molecule in the near UV region; groups of stripes correspond to diff. values ​​Dv= v"-v".

A set of bands with a given D?el (corresponding to a purely electronic transition with a frequency nel=D?el/h) is called. strip system; stripes have different intensity depending on relative transition probabilities (see QUANTUM TRANSITION).

Rice. 3. Rotate. electron-colsbat splitting. stripes 3805.0 ? N2 molecules.

For complex molecules, the bands of one system corresponding to a given electronic transition usually merge into one broad continuous band; can overlap each other and several times. such stripes. Characteristic discrete electronic spectra are observed in frozen organic solutions. connections.

Electronic (more precisely, electronic-vibrational-rotational) spectra are studied using spectral instruments with glass (visible region) and quartz (UV region, (see UV RADIATION)) optics. When D?el = 0, and D?col?0, oscillations are obtained. MS observed in the near-IR region is usually in the absorption and Raman spectra. As a rule, for a given D? count D? time? 0 and oscillation. the strip breaks up into sections. rotate lines. Most intense during vibrations. M. s. bands satisfying the condition Dv=v"- v"=1 (for polyatomic molecules Dvi=v"i- v"i=1 with Dvk=V"k-V"k=0; here i and k determine different normal vibrations). For purely harmonious fluctuations, these selection rules are strictly followed; for anharmonic bands appear for vibrations, for which Dv>1 (overtones); their intensity is usually low and decreases with increasing Dv. Oscillation M. s. (more precisely, vibrational-rotational) are studied using IR spectrometers and Fourier spectrometers, and Raman spectra are studied using high-aperture spectrographs (for the visible region) using laser excitation. With D?el=0 and D?col=0, pure rotation is obtained. spectra consisting of separate lines. They are observed in absorption spectra in the far IR region and especially in the microwave region, as well as in Raman spectra. For diatomic, linear triatomic molecules and fairly symmetrical nonlinear molecules, these lines are equally spaced (on the frequency scale) from each other.

Rotate cleanly. M. s. studied using IR spectrometers with special diffraction gratings (echelettes), Fourier spectrometers, spectrometers based on a backward wave lamp, microwave (microwave) spectrometers (see SUBMILLIMETER SPECTROSCOPY, MICROWAVE SPECTROSCOPY), and rotate. Raman spectra - using high-aperture spectrometers.

Methods of molecular spectroscopy, based on the study of microscopy, make it possible to solve various problems in chemistry. Electronic M. s. provide information about electronic shells, excited energy levels and their characteristics, about the dissociation energy of molecules (by the convergence of energy levels to the dissociation boundary). Study of oscillations. spectra allows you to find the characteristic vibration frequencies corresponding to the presence of certain types of chemicals in the molecule. bonds (for example, double and triple C-C bonds, C-H, N-H bonds for organic molecules), determine spaces. structure, distinguish between cis- and trans-isomers (see ISOMERISTICS OF MOLECULES). Particularly widespread are the methods of infrared spectroscopy - one of the most effective optical methods. methods for studying the structure of molecules. They provide the most complete information in combination with Raman spectroscopy methods. The study will rotate. spectra, and also rotate. structures of electronic and vibrations. M. s. allows using experimentally found moments of inertia of molecules to find with great accuracy the parameters of equilibrium configurations - bond lengths and bond angles. To increase the number of parameters determined, the isotopic spectra are studied. molecules (in particular, molecules in which hydrogen is replaced by deuterium) having the same parameters of equilibrium configurations, but different. moments of inertia.

M. s. They are also used in spectral analysis to determine the composition of a substance.

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MOLECULAR SPECTRA- absorption, emission or scattering spectra arising from quantum transitions molecules from one energy. states to another. M. s. determined by the composition of the molecule, its structure, the nature of the chemical. communication and interaction with external fields (and, therefore, with the atoms and molecules surrounding it). Naib. characteristic are M. s. rarefied molecular gases when there is no broadening of spectral lines pressure: such a spectrum consists of narrow lines with Doppler width.

Rice. 1. Diagram of energy levels of a diatomic molecule: a And b-electronic levels; u" And u"" - oscillatory quantum numbers; J" And J"" - rotational quantum numbers.

In accordance with three systems of energy levels in a molecule - electronic, vibrational and rotational (Fig. 1), M. s. consist of a set of electronic vibrations. and rotate. spectra and lie in a wide range of el-magn. waves - from radio frequencies to x-rays. areas of the spectrum. Frequencies of transitions between rotations. energy levels usually fall into the microwave region (on a wavenumber scale of 0.03-30 cm -1), the frequencies of transitions between oscillations. levels - in the IR region (400-10,000 cm -1), and the frequencies of transitions between electronic levels - in the visible and UV regions of the spectrum. This division is conditional, because it is often rotated. transitions also fall into the IR region, oscillations. transitions - in the visible region, and electronic transitions - in the IR region. Typically, electronic transitions are accompanied by changes in vibrations. energy of the molecule, and with vibrations. transitions changes and rotates. energy. Therefore, most often the electronic spectrum represents systems of electron vibrations. bands, and with high resolution spectral equipment their rotation is detected. structure. Intensity of lines and stripes in M. s. is determined by the probability of the corresponding quantum transition. Naib. intense lines correspond to a transition allowed selection rules.To M. s. also include Auger spectra and X-ray spectra. spectra of molecules (not considered in the article; see Auger effect, Auger spectroscopy, X-ray spectra, X-ray spectroscopy).

Electronic spectra. Purely electronic M.s. arise when the electronic energy of molecules changes, if the vibrations do not change. and rotate. energy. Electronic M.s. are observed both in absorption (absorption spectra) and emission (luminescence spectra). During electronic transitions, the electrical energy usually changes. dipole moment of the molecule. Ele-ktric. dipole transition between the electronic states of a molecule of symmetry type G " and G "" (cm. Symmetry of molecules) is allowed if the direct product Г " G "" contains the symmetry type of at least one of the components of the dipole moment vector d . In absorption spectra, transitions from the ground (fully symmetric) electronic state to excited electronic states are usually observed. It is obvious that for such a transition to occur, the symmetry types of the excited state and the dipole moment must coincide. Because electric Since the dipole moment does not depend on the spin, then during an electronic transition the spin must be conserved, i.e., only transitions between states with the same multiplicity are allowed (inter-combination prohibition). This rule, however, is broken

for molecules with strong spin-orbit interactions, which leads to intercombination quantum transitions. As a result of such transitions, for example, phosphorescence spectra appear, which correspond to transitions from the excited triplet state to the ground state. singlet state.

Molecules in different electronic states often have different geoms. symmetry. In such cases, condition G " G "" G d must be performed for a point group with a low-symmetry configuration. However, when using a permutation-inversion (PI) group, this problem does not arise, since the PI group for all states can be chosen to be the same.

For linear molecules of symmetry With xy type of dipole moment symmetry Г d= S + (d z)-P( d x , d y), therefore, for them only transitions S + - S +, S - - S -, P - P, etc. are allowed with the transition dipole moment directed along the axis of the molecule, and transitions S + - P, P - D, etc. d. with the moment of transition directed perpendicular to the axis of the molecule (for designations of states, see Art. Molecule).

Probability IN electric dipole transition from the electronic level T to the electronic level P, summed over all oscillatory-rotational. electronic level levels T, is determined by the f-loy:

dipole moment matrix element for transition n - m, y ep and y em- wave functions of electrons. Integral coefficient absorption, which can be measured experimentally, is determined by the expression

Where Nm- number of molecules in the beginning condition m, vnm- transition frequency TP. Often electronic transitions are characterized by the strength of the oscillator

Where e And i.e.- charge and mass of the electron. For intense transitions f nm ~ 1. From (1) and (4) avg is determined. lifetime of the excited state:

These formulas are also valid for oscillations. and rotate. transitions (in this case, the matrix elements of the dipole moment should be redefined). For allowed electronic transitions, the coefficient is usually absorption for several orders of magnitude greater than for oscillations. and rotate. transitions. Sometimes the coefficient absorption reaches a value of ~10 3 -10 4 cm -1 atm -1, i.e. electronic bands are observed at very low pressures (~10 -3 - 10 -4 mm Hg) and small thicknesses (~10-100 cm) layer of substance.

Vibrational spectra observed when fluctuations change. energy (electronic and rotational energy should not change). Normal vibrations of molecules are usually represented as a set of non-interacting harmonics. oscillators. If we restrict ourselves only to the linear terms of the expansion of the dipole moment d (in the case of absorption spectra) or polarizability a (in the case of Raman scattering) along normal coordinates Qk, then allowed oscillations. only transitions with a change in one of the quantum numbers u are considered transitions k per unit. Such transitions correspond to the basic oscillate stripes, they fluctuate. spectra max. intense.

Basic oscillate bands of a linear polyatomic molecule corresponding to transitions from the basic. oscillate states can be of two types: parallel (||) bands, corresponding to transitions with the transition dipole moment directed along the axis of the molecule, and perpendicular (1) bands, corresponding to transitions with the transition dipole moment perpendicular to the axis of the molecule. The parallel strip consists only of R- And R-branches, and in the perpendicular strip there are

also resolved Q-branch (Fig. 2). Spectrum absorption bands of a symmetrical top-type molecule also consists of || And | stripes, but rotate. the structure of these stripes (see below) is more complex; Q-branch in || the lane is also not allowed. Allowed oscillations. stripes indicate vk. Band intensity vk depends on the square of the derivative ( dd/dQ To ) 2 or ( d a/ dQk) 2 . If the band corresponds to a transition from an excited state to a higher one, then it is called. hot.

Rice. 2. IR absorption band v 4 molecules SF 6, obtained on a Fourier spectrometer with a resolution of 0.04 cm -1 ; the niche shows the fine structure lines R(39), measured with a diode laser spectrometer with a resolution of 10 -4 cm -1.

Taking into account the anharmonicity of vibrations and nonlinear terms in the expansions d and a by Qk transitions prohibited by the selection rule for u also become possible k. Transitions with a change in one of the numbers u k on 2, 3, 4, etc. called. overtone (Du k=2 - first overtone, Du k=3 - second overtone, etc.). If two or more of the numbers u change during the transition k, then such a transition is called. combinational or total (if all u To increase) and difference (if some of u k decrease). Overtone bands are designated 2 vk, 3vk, ..., total bands vk + v l, 2vk + v l etc., and the difference bands vk - v l, 2vk - e l etc. Band intensities 2u k, vk + v l And vk - v l depend on the first and second derivatives d By Qk(or a by Qk) and cubic. anharmonicity coefficients potential. energy; the intensities of higher transitions depend on the coefficient. higher degrees of decomposition d(or a) and potential. energy by Qk.

For molecules that do not have symmetry elements, all vibrations are allowed. transitions both during absorption of excitation energy and during combination. scattering of light. For molecules with an inversion center (for example, CO 2, C 2 H 4, etc.), transitions allowed in absorption are prohibited for combinations. scattering, and vice versa (alternative prohibition). Transition between oscillations energy levels of symmetry types Г 1 and Г 2 is allowed in absorption if the direct product Г 1 Г 2 contains the symmetry type of the dipole moment, and is allowed in combination. scattering, if the product Г 1

Г 2 contains the symmetry type of the polarizability tensor. This selection rule is approximate, since it does not take into account the interaction of vibrations. movements with electronic and rotate. movements. Taking these interactions into account leads to the appearance of bands that are forbidden according to pure vibrations. selection rules.

Study of oscillations. M. s. allows you to install harmon. vibration frequencies, anharmonicity constants. According to fluctuations The spectra are subject to conformation. analysis

Lecture No. 6

Molecule Energy

Atom The smallest particle of a chemical element that has its chemical properties is called.

An atom consists of a positively charged nucleus and electrons moving in its field. The charge of the nucleus is equal to the charge of all electrons. Ion of a given atom is an electrically charged particle formed when atoms lose or gain electrons.

Molecule is the smallest particle of a homogeneous substance that has its basic chemical properties.

Molecules consist of identical or different atoms connected to each other by interatomic chemical bonds.

In order to understand the reasons why electrically neutral atoms can form a stable molecule, we will limit ourselves to considering the simplest diatomic molecules, consisting of two identical or different atoms.

The forces that hold an atom in a molecule are caused by the interaction of external electrons. When atoms combine into a molecule, the electrons of the inner shells remain in their previous states.

If atoms are at a great distance from each other, then they do not interact with each other. As atoms come closer together, the forces of their mutual attraction increase. At distances comparable to the sizes of atoms, mutual repulsion forces appear, which do not allow the electrons of one atom to penetrate too deeply into the electron shells of another atom.

Repulsive forces are more “short-range” than attractive forces. This means that as the distance between atoms increases, the repulsive forces decrease faster than the attractive forces.

The graph of the attractive force, the repulsive force and the resulting interaction force between atoms as a function of distance looks like this:

The interaction energy of electrons in a molecule is determined by the mutual arrangement of atomic nuclei and is a function of distance, that is

The total energy of the entire molecule also includes the kinetic energy of the moving nuclei.

Hence,

.

This means that it is the potential energy of interaction between nuclei.

Then represents the force of interaction between atoms in a diatomic molecule.

Accordingly, the graph of the dependence of the potential energy of interaction of atoms in a molecule on the distance between atoms has the form:

The equilibrium interatomic distance in a molecule is called connection length. The quantity D is called molecular dissociation energy or bond energy. It is numerically equal to the work that must be done in order to break the chemical bonds of atoms into molecules and remove them beyond the action of interatomic forces. The dissociation energy is equal to the energy released during the formation of the molecule, but is opposite in sign. The dissociation energy is negative, and the energy released during the formation of a molecule is positive.

The energy of a molecule depends on the nature of the motion of the nuclei. This movement can be divided into translational, rotational and oscillatory. At small distances between atoms in a molecule and a sufficiently large volume of the vessel provided to the molecules, forward energy has a continuous spectrum and its average value is equal to , that is.

Rotational energy has a discrete spectrum and can take values

,

where I is the rotational quantum number;

J is the moment of inertia of the molecule.

Energy of vibrational motion also has a discrete spectrum and can take values

,

where is the vibrational quantum number;

– natural frequency of this type of oscillation.

When the lowest vibrational level has zero energy

The energy of rotational and translational motion corresponds to the kinetic form of energy, the energy of oscillatory motion corresponds to the potential form. Consequently, the energy steps of the vibrational motion of a diatomic molecule can be represented on a graph.

The energy steps of the rotational motion of a diatomic molecule are located in a similar way, only the distance between them is much smaller than that of the same steps of vibrational motion.

Main types of interatomic bonds

There are two types of atomic bonds: ionic (or heteropolar) and covalent (or homeopolar).

Ionic bond occurs in cases where electrons in a molecule are arranged in such a way that an excess is formed near one of the nuclei, and a deficiency near the other. Thus, the molecule seems to consist of two ions of opposite signs, attracted to each other. Examples of molecules with ionic bonds are NaCl, KCl, RbF, CsJ etc. formed by combining atoms of elements I-oh and VII-th group of Mendeleev's periodic system. In this case, an atom that has added one or more electrons to itself acquires a negative charge and becomes a negative ion, and an atom that donates the corresponding number of electrons turns into a positive ion. The total sum of the positive and negative charges of the ions is zero. Therefore, ionic molecules are electrically neutral. The forces that ensure the stability of the molecule are electrical in nature.

For an ionic bond to take place, it is necessary that the energy of electron removal, that is, the work of creating a positive ion, be less than the sum of the energy released during the formation of negative ions and the energy of their mutual attraction.

It is quite obvious that the formation of a positive ion from a neutral atom requires the least work in the case when electrons located in the electron shell that has begun to build up occur.

On the other hand, the greatest energy is released when an electron attaches to halogen atoms, which lack one electron before filling the electron shell. Therefore, an ionic bond is formed through the transfer of electrons, which leads to the creation of filled electron shells in the resulting ions.

Another type of connection - covalent bond.

When molecules consisting of identical atoms are formed, the formation of oppositely charged ions is impossible. Therefore, ionic bonding is not possible. However, in nature there are substances whose molecules are formed from identical atoms H 2, O 2, N 2 etc. Bonding in substances of this type is called covalent or homeopolar(homeo – different [Greek]). In addition, covalent bonds are also observed in molecules with different atoms: hydrogen fluoride HF, nitric oxide NO, methane CH 4 etc.

The nature of covalent bonds can only be explained on the basis of quantum mechanics. The quantum mechanical explanation is based on the wave nature of the electron. The wave function of the outer electrons of an atom does not stop abruptly as the distance from the center of the atom increases, but gradually decreases. As atoms approach each other, the fuzzy electron clouds of outer electrons partially overlap, causing them to deform. An accurate calculation of the change in state of electrons requires solving the Schrödinger wave equation for the system of all particles participating in the interaction. The complexity and cumbersomeness of this path force us to limit ourselves here to only a qualitative consideration of phenomena.

In the simplest case s- state of an electron, the electron cloud is a sphere of a certain radius. If both electrons in a covalent molecule exchange places so that electron 1, previously belonging to the nucleus " A", will move to the place of electron 2, which belonged to the nucleus " b", and electron 2 makes a reverse transition, then nothing will change in the state of the covalent molecule.

The Pauli principle allows for the existence of two electrons in the same state with opposite spins. The merging of regions where both electrons can be located means the emergence between them of a special quantum mechanical exchange interaction. In this case, each of the electrons in the molecule can belong alternately to one or another nucleus.

As calculations show, the exchange energy of a molecule is positive if the spins of interacting electrons are parallel, and negative if they are not parallel.

So, the covalent type of bond is provided by a pair of electrons with opposite spins. If in an ionic bond we were talking about the transfer of electrons from one atom to another, then here the connection is carried out by generalizing electrons and creating a common space for their movement.

Molecular spectra

Molecular spectra are very different from atomic spectra. While atomic spectra consist of individual lines, molecular spectra consist of bands that are sharp at one end and blurry at the other. Therefore, molecular spectra are also called striped spectra.

Bands in molecular spectra are observed in the infrared, visible and ultraviolet frequency ranges of electromagnetic waves. In this case, the stripes are arranged in a certain sequence, forming a series of stripes. There are a number of series in the spectrum.

Quantum mechanics provides an explanation for the nature of molecular spectra. The theoretical interpretation of the spectra of polyatomic molecules is very complex. We will limit ourselves to considering only diatomic molecules.

Earlier, we noted that the energy of a molecule depends on the nature of the movement of atomic nuclei and identified three types of this energy: translational, rotational and vibrational. In addition, the energy of a molecule is also determined by the nature of the movement of electrons. This type of energy is called electronic energy and is a component of the total energy of the molecule.

Thus, the total energy of the molecule is:

A change in translational energy cannot lead to the appearance of a spectral line in the molecular spectrum, therefore we will exclude this type of energy in further consideration of molecular spectra. Then

According to Bohr's frequency rule ( III– Bohr's postulate) the frequency of the quantum emitted by a molecule when its energy state changes is equal to

.

Experience and theoretical studies have shown that

Therefore, with weak excitations it changes only, with stronger ones -, with even stronger ones -. Let us discuss in more detail the different types of molecular spectra.

Rotational spectrum of molecules

Let's start exploring the absorption of electromagnetic waves with small portions of energy. Until the value of the energy quantum becomes equal to the distance between the two nearest levels, the molecule will not absorb. Gradually increasing the frequency, we will reach quanta capable of raising a molecule from one rotational step to another. This occurs in the region of infrared waves of the order of 0.1 -1 mm.

,

where and are the values ​​of the rotational quantum number at the -th and -th energy levels.

Rotational quantum numbers and can have values, i.e. their possible changes are limited by the selection rule

The absorption of a quantum by a molecule transfers it from one rotational energy level to another, higher one, and leads to the appearance of a spectral line in the rotational absorption spectrum. As the wavelength decreases (i.e., the number changes), more and more new lines of the absorption spectrum appear in this region. The totality of all lines gives an idea of ​​the distribution of rotational energy states of the molecule.

We have so far considered the absorption spectrum of the molecule. The emission spectrum of the molecule is also possible. The appearance of lines in the rotational emission spectrum is associated with the transition of the molecule from the upper rotational energy level to the lower one.

Rotational spectra make it possible to determine interatomic distances in simple molecules with great accuracy. Knowing the moment of inertia and mass of atoms, it is possible to determine the distances between atoms. For a diatomic molecule

Vibrational-rotational spectrum of molecules

Absorption of electromagnetic waves by a substance in the infrared region with a wavelength of microns causes transitions between vibrational energy levels and leads to the appearance of a vibrational spectrum of the molecule. However, when the vibrational energy levels of a molecule change, its rotational energy states simultaneously change. Transitions between two vibrational energy levels are accompanied by changes in rotational energy states. In this case, a vibrational-rotational spectrum of the molecule appears.

If a molecule simultaneously vibrates and rotates, then its energy will be determined by two quantum numbers and:

.

Taking into account the selection rules for both quantum numbers, we obtain the following formula for the frequencies of the vibrational-rotational spectrum (the previous formula /h and discard the previous energy level, i.e. terms in brackets):

.

In this case, the sign (+) corresponds to transitions from a lower to a higher rotational level, and the sign (-) corresponds to the opposite position. The vibrational part of the frequency determines the spectral region in which the band is located; the rotational part determines the fine structure of the strip, i.e. splitting of individual spectral lines.

According to classical concepts, rotation or vibration of a diatomic molecule can lead to the emission of electromagnetic waves only if the molecule has a nonzero dipole moment. This condition is satisfied only for molecules formed by two different atoms, i.e. for asymmetric molecules.

A symmetrical molecule formed by identical atoms has a zero dipole moment. Therefore, according to classical electrodynamics, vibration and rotation of such a molecule cannot cause radiation. Quantum theory leads to similar results.

Electronic vibrational spectrum of molecules

Absorption of electromagnetic waves in the visible and ultraviolet range leads to transitions of the molecule between different electronic energy levels, i.e. to the appearance of the electronic spectrum of the molecule. Each electronic energy level corresponds to a certain spatial distribution of electrons, or, as they say, a certain configuration of electrons with discrete energy. Each configuration of electrons corresponds to many vibrational energy levels.

A transition between two electronic levels is accompanied by many accompanying transitions between vibrational levels. This is how the electronic vibrational spectrum of the molecule arises, consisting of groups of close lines.

A system of rotational levels is superimposed on each vibrational energy state. Therefore, the frequency of a photon during an electronic-vibrational transition will be determined by a change in all three types of energy:

.

Frequency - determines the position of the spectrum.

The entire electronic vibrational spectrum is a system of several groups of bands, often overlapping each other and making up a wide band.

The study and interpretation of molecular spectra allows one to understand the detailed structure of molecules and is widely used for chemical analysis.

Raman scattering

This phenomenon lies in the fact that in the scattering spectrum that occurs when light passes through gases, liquids or transparent crystalline bodies, along with the scattering of light with a constant frequency, a number of higher or lower frequencies appear, corresponding to the frequencies of vibrational or rotational transitions of scattering molecules.

The phenomenon of Raman scattering has a simple quantum mechanical explanation. The process of light scattering by molecules can be considered as an inelastic collision of photons with molecules. During a collision, a photon can give or receive from a molecule only such amounts of energy that are equal to the differences between its two energy levels. If, when colliding with a photon, a molecule moves from a state with lower energy to a state with higher energy, it loses its energy and its frequency decreases. This creates a line in the spectrum of the molecule, shifted relative to the main one towards longer wavelengths. If, after a collision with a photon, a molecule passes from a state with higher energy to a state with lower energy, a line is created in the spectrum that is shifted relative to the main one towards shorter wavelengths.

Raman scattering studies provide information about the structure of molecules. Using this method, the natural vibrational frequencies of molecules are easily and quickly determined. It also allows us to judge the nature of the symmetry of the molecule.

Luminescence

If the molecules of a substance can be brought into an excited state without increasing their average kinetic energy, i.e. without heating, then the glow of these bodies or luminescence occurs.

There are two types of luminescence: fluorescence And phosphorescence.

Fluorescence called luminescence, which stops immediately after the end of the action of the luminescence exciter.

With fluorescence, a spontaneous transition of molecules from an excited state to a lower level occurs. This type of glow has a very short duration (about 10 -7 seconds).

Phosphorescence called luminescence, which retains its glow for a long time after the action of the luminescence exciter.

During phosphorescence, a molecule moves from an excited state to a metastable level. Metastable This is a level from which a transition to a lower level is unlikely. Emission can occur if the molecule returns to the excited level again.

The transition from a metastable state to an excited one is possible only in the presence of additional excitation. Such an additional pathogen may be the temperature of the substance. At high temperatures this transition occurs quickly, at low temperatures it occurs slowly.

As we have already noted, luminescence under the influence of light is called photoluminescence, under the influence of electron bombardment – cathodoluminescence, under the influence of an electric field – electroluminescence, under the influence of chemical transformations - chemiluminescence.

Quantum amplifiers and radiation generators

In the mid-50s of our century, the rapid development of quantum electronics began. In 1954, the works of academicians N.G. Basov and A.M. appeared in the USSR. Prokhorov, in which a quantum generator of ultrashort radio waves in the centimeter range, called maser(microware amplification by stimulated emission of radiation). A series of generators and amplifiers of light in the visible and infrared regions, which appeared in the 60s, were called optical quantum generators or lasers(light amplification by stimulated emission of radiation).

Both types of devices operate based on the effect of stimulated or stimulated radiation.

Let's look at this type of radiation in more detail.

This type of radiation is the result of the interaction of an electromagnetic wave with the atoms of the substance through which the wave passes.

In atoms, transitions from higher energy levels to lower ones occur spontaneously (or spontaneously). However, under the influence of incident radiation, such transitions are possible in both the forward and reverse directions. These transitions are called forced or induced. During a forced transition from one of the excited levels to a low energy level, the atom emits a photon that is additional to the photon under the influence of which the transition was made.

In this case, the direction of propagation of this photon and, consequently, of all stimulated radiation coincides with the direction of propagation of external radiation that caused the transition, i.e. stimulated emission is strictly coherent with the driving emission.

Thus, the new photon resulting from stimulated emission amplifies the light passing through the medium. However, simultaneously with the induced emission, the process of light absorption occurs, because The driving photon is absorbed by an atom located at a low energy level, and the atom moves to a higher energy level. And

The process of transferring the environment to an inverse state is called pumped enhancing environment. There are many methods for pumping a gain medium. The simplest of them is optical pumping of a medium, in which atoms are transferred from a lower level to an upper excited level by irradiating light of such a frequency that .

In a medium with an inverse state, stimulated emission exceeds the absorption of light by atoms, as a result of which the incident beam of light will be amplified.

Let us consider a device that uses such media, used as a wave generator in the optical range or laser.

Its main part is a crystal of artificial ruby, which is an aluminum oxide in which some aluminum atoms are replaced by chromium atoms. When a ruby ​​crystal is irradiated with light of wavelength 5600, chromium ions move to the upper energy level.

The return transition to the ground state occurs in two stages. At the first stage, excited ions give up part of their energy to the crystal lattice and enter a metastable state. The ions remain at this level for a longer time than at the upper level. As a result, an inverse state of a metastable level is achieved.

The ruby ​​used in the laser has the form of a rod with a diameter of 0.5 cm and a length of 4-5 cm. The flat ends of this rod are polished and silvered so that they form two mirrors facing each other, one of them being translucent. The entire ruby ​​rod is located near a pulsed electron tube, which is used to optically pump the medium. Photons whose directions of motion form small angles with the axis of the ruby ​​experience multiple reflections from its ends.

Therefore, their path in the crystal will be very long, and cascades of photons in this direction will receive the greatest development.

Photons emitted spontaneously in other directions exit the crystal through its side surface without causing further radiation.

When the axial beam becomes intense enough, part of it exits through the translucent end of the crystal to the outside.

A large amount of heat is generated inside the crystal. Therefore, it has to be intensively cooled.

Laser radiation has a number of features. It is characterized by:

1. temporal and spatial coherence;

2. strict monochromatic;

3. high power;

4. beam narrowness.

The high coherence of radiation opens up broad prospects for the use of lasers for radio communications, in particular for directional radio communications in space. If a way to modulate and demodulate light is found, it will be possible to transmit a huge amount of information. Thus, in terms of the volume of transmitted information, one laser could replace the entire communication system between the east and west coasts of the United States.

The angular width of the laser beam is so small that, using telescopic focusing, it is possible to obtain a spot of light with a diameter of 3 km on the lunar surface. The high power and narrowness of the beam allows, when focusing using a lens, to obtain an energy flux density 1000 times higher than the energy flux density that can be obtained by focusing sunlight. Such beams of light can be used for machining and welding, to influence the course of chemical reactions, etc.

The above does not exhaust all the capabilities of the laser. It is a completely new type of light source and it is still difficult to imagine all the possible areas of its application.