Molecular spectra. Structure and spectra of molecules Optical spectra of molecules

Studies of molecular spectra make it possible to determine the forces acting between atoms in a molecule, the dissociation energy of a molecule, its geometry, internuclear distances, etc. , i.e. provide extensive information about the structure and properties of the molecule.

The molecular spectrum, in a broad sense, is understood as the probability distribution of transitions between two separate energy levels of a molecule (see Figure 9) depending on the transition energy. Since in what follows we will talk about optical spectra, each such transition must be accompanied by the emission or absorption of a photon with energy

E n = hn = E 2 - E 1, 3.1

where E 2 and E 1 are the energies of the levels between which the transition occurs.

If the radiation, consisting of photons emitted by gas molecules, is passed through a spectral device, then the emission spectrum of the molecule will be obtained, consisting of separate bright (maybe colored) lines. Moreover, each line will correspond to the corresponding transition. In turn, the brightness and position of the line in the spectrum depend on the transition probability and energy (frequency, wavelength) of the photon, respectively.

If, on the contrary, radiation consisting of photons of all wavelengths (continuous spectrum) is passed through this gas, and then through a spectral device, then an absorption spectrum will be obtained. In this case, this spectrum will be a set of dark lines against the background of a bright continuous spectrum. The contrast and position of the line in the spectrum here also depend on the transition probability and the photon energy.

Based on the complex structure of the energy levels of a molecule (see Fig. 9), all transitions between them can be divided into separate types, which give a different nature of the spectrum of molecules.

The spectrum consisting of lines corresponding to transitions between rotational levels (see Fig. 8) without changing the vibrational and electronic states of the molecule is called the rotational spectrum of the molecule. Since the energy of rotational motion lies in the range of 10 -3 -10 -5 eV, the frequency of the lines in these spectra should lie in the microwave region of radio frequencies (far infrared region).

A spectrum consisting of lines corresponding to transitions between rotational levels belonging to different vibrational states of a molecule in the same electronic state is called the vibrational-rotational or simply vibrational spectrum of a molecule. These spectra, at vibrational energies of 10 -1 -10 -2 eV, lie in the infrared frequency range.

Finally, a spectrum consisting of lines corresponding to transitions between rotational levels belonging to different electronic and vibrational states of the molecule is called the electronic-vibrational-rotational or simply the electronic spectrum of the molecule. These spectra lie in the visible and ultraviolet frequency ranges, because the energy of electronic motion is several electron volts.

Since the emission (or absorption) of a photon is an electromagnetic process, its necessary condition is the presence or, more precisely, a change in the electric dipole moment associated with the corresponding quantum transition in the molecule. Hence it follows that rotational and vibrational spectra can be observed only in molecules with an electric dipole moment, i.e. consisting of dissimilar atoms.

1. In contrast to optical line spectra with their complexity and diversity, the X-ray characteristic spectra of various elements are simple and uniform. With the growth of the atomic number Z element, they are monotonously shifted to the shortwave side.

2. The characteristic spectra of different elements are of a similar nature (of the same type) and do not change if the element of interest to us is in conjunction with others. This can only be explained by the fact that the characteristic spectra appear during transitions of electrons to internal parts atom, parts having a similar structure.

3. Characteristic spectra consist of several series: TO,L, M, ... Each series consists of a small number of lines: TO a , TO β , TO γ , ... L a , L β , L y , ... etc. in decreasing order of wavelength λ .

Analysis of the characteristic spectra led to the understanding that a system of X-ray terms is inherent in atoms TO,L, M, ...(Figure 13.6). The same figure shows a diagram of the appearance of characteristic spectra. Excitation of an atom occurs when one of the internal electrons is removed (under the action of electrons or photons of sufficiently high energy). If one of the two electrons escapes K-level (n= 1), then the vacant place can be occupied by an electron from some higher level: L, M, N, and so on. As a result, there is K-series. Other series arise in the same way: L, M,...

Series TO, as can be seen from Fig. 13.6, it is certainly accompanied by the appearance of the remaining series, since when its lines are emitted, electrons are released at levels L, M and others, which in turn will be filled with electrons from higher levels.

Molecular spectra. Types of bonds in molecules, the energy of a molecule, the energy of vibrational and rotational motion.

Molecular spectra.

Molecular spectra are optical emission and absorption spectra, as well as Raman scattering of light (See. Raman light scattering), owned by free or loosely coupled Molecule m. 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 decay 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 complicated with an increase in the number of atoms in a molecule. For highly complex molecules, the visible and ultraviolet spectra consist of a few broad continuous bands; the spectra of such molecules are similar to each other.

From the solution of the Schrödinger equation for hydrogen molecules under the above assumptions, the dependence of the energy eigenvalues on the distance is obtained R between the cores, i.e. E =E(R).

Molecule energy

where E el - energy of motion of electrons relative to nuclei; E count - energy of vibrations of nuclei (as a result of which the relative position of nuclei periodically changes); E rotation - the energy of rotation of nuclei (as a result of which the orientation of the molecule in space periodically changes).

In formula (13.45), the energy of translational motion of the center of mass of molecules and the energy of atomic nuclei in a molecule are not taken into account. The first of them is not quantized; therefore, its changes cannot lead to the appearance of a molecular spectrum, and the second can be ignored if the hyperfine structure of spectral lines is not considered.

It is proved that E e-mail >> E count >> E rotate, while E el ≈ 1 - 10 eV. Each of the energies included in expression (13.45) is quantized and a set of discrete energy levels corresponds to them. During the transition from one energy state to another, energy is absorbed or emitted Δ E = hν... It follows from theory and experiment that the distance between the rotational energy levels Δ E rotation is much less than the distance between vibrational levels Δ E count, which, in turn, is less than the distance between electronic levels Δ E e-mail

The structure of molecules and the properties of their energy levels are manifested in molecular spectra - emission (absorption) spectra arising from quantum transitions between the energy levels of molecules. The emission spectrum of a molecule is determined by the structure of its energy levels and the corresponding selection rules (for example, the change in quantum numbers corresponding to both vibrational and rotational motion should be equal to ± 1). Different types of transitions between levels give rise to different types of molecular spectra. The frequencies of spectral lines emitted by molecules can correspond to transitions from one electronic level to another ( electronic spectra ) or from one vibrational (rotational) level to another [ vibrational (rotational) spectra ].

In addition, transitions with the same values are also possible. E count and E rotate to levels that have different values for all three components, resulting in electronic vibrational and vibrational-rotational spectra ... Therefore, the spectrum of molecules is rather complex.

Typical molecular spectra - striped , are a combination of more or less narrow bands in the ultraviolet, visible and infrared regions. By using high-resolution spectral instruments, it can be seen that the bands are so closely spaced lines that they are difficult to resolve.

The structure of molecular spectra is different for different molecules and becomes more complicated with an increase in the number of atoms in a molecule (only continuous broad bands are observed). Only polyatomic molecules have vibrational and rotational spectra, while diatomic ones do not. This is explained by the fact that diatomic molecules do not have dipole moments (during vibrational and rotational transitions, there is no change in the dipole moment, which is a necessary condition for the transition probability to differ from zero).

Molecular spectra are used to study the structure and properties of molecules, are used in molecular spectral analysis, laser spectroscopy, quantum electronics, etc.

TYPES OF BONDS IN MOLECULES Chemical bond- the phenomenon of interaction atoms overlapping electronic clouds binding particles, which is accompanied by a decrease full energy systems. Ionic bond- durable chemical bond formed between atoms with a large difference electronegativities at which the total electron pair completely passes to the atom with greater electronegativity. This is the attraction of ions as oppositely charged bodies. Electronegativity (χ)- the fundamental chemical property of the atom, a quantitative characteristic of the ability atom v molecule shift to oneself common electronic pairs. Covalent bond(atomic bond, homeopolar bond) - chemical bond formed by the overlap (socialization) of the pair valence electronic clouds... The electronic clouds (electrons) that provide communication are called common electronic pair.Hydrogen bond- connection between electronegative atom and hydrogen atom H related covalently with another electronegative atom. Metal bond - chemical bond due to the presence of relatively free electrons... Typical for both clean metals and their alloys and intermetallic compounds.

Raman scattering of light.

this is the scattering of light by a substance, accompanied by a noticeable change in the frequency of the scattered light. If the source emits a line spectrum, then at K. p. with. additional lines are found in the scattered light spectrum, the number and location of which are closely related to the molecular structure of the substance. With K. p. with. the transformation of the primary luminous flux is usually accompanied by the transition of scattering molecules to other vibrational and rotational levels , moreover, the frequencies of new lines in the scattering spectrum are combinations of the frequency of the incident light and the frequencies of vibrational and rotational transitions of scattering molecules - hence the name. "TO. R. with.".

To observe the spectra of K. p. with. it is necessary to concentrate an intense beam of light on the object under study. As a source of exciting light, a mercury lamp is most often used, and since the 60s. - laser ray. The scattered light is focused and enters the spectrograph, where the spectrum of the K. p. with. recorded by photographic or photoelectric methods.

Lecture number 6

Molecule energy

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

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 called an electrically charged particle formed by the loss or acquisition of electrons from atoms.

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

Molecules are made up of the same or different atoms connected by interatomic chemical bonds.

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

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

If the atoms are at a great distance from each other, then they do not interact with each other. When atoms approach each other, the forces of their mutual attraction increase. At distances comparable to the size of atoms, forces of mutual repulsion are manifested, 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 gravity. This means that with an increase in the distance between atoms, the repulsive forces decrease faster than the attractive forces.

The graph of the dependence of the force of attraction, the repulsive force and the resulting force of interaction between atoms as a function of distance has the form:

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 of nuclei.

Then it represents the force of interaction of 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 dissociation energy of the molecule or communication 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 outside the range of interatomic forces. The dissociation energy is equal to the energy released during the formation of a 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 movement 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, translational energy has a continuous spectrum and its average value is, that is.

Rotational energy has a discrete spectrum and can take the values

where I is the rotational quantum number;

J is the moment of inertia of the molecule.

Oscillatory motion energy also has a discrete spectrum and can take the values

where is the vibrational quantum number;

- natural frequency of this type of vibration.

At the lowest vibrational level has zero energy

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

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

The main types of interatomic bonds

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

Ionic bond takes place in those cases when the electrons in the molecule are arranged in such a way that an excess is formed near one of the nuclei, and a shortage of them near the other. Thus, the molecule, as it were, consists of two ions of opposite signs, attracted to each other. An example of molecules with ionic bonds are NaCl, KCl, RbF, CsJ etc. formed by the connection of atoms of elements I th and Vii-th group of Mendeleev's periodic system. In this case, an atom that has attached one or more electrons to itself acquires a negative charge and becomes a negative ion, and an atom that gives up 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 the ionic bond to take place, it is necessary that the energy of electron detachment, that is, the work of creating a positive ion, would 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 amount of work in the case when there is a detachment of electrons located in the electron shell that has begun to build up.

On the other hand, the greatest energy is released when an electron is attached to halogen atoms, which lack one electron until the electron shell is filled. Therefore, the ionic bond is formed in such a transfer of electrons, which leads to the creation of the formed ions of filled electron shells.

Another type of connection is covalent bond.

With the formation of molecules consisting of identical atoms, the appearance of oppositely charged ions is impossible. Therefore, ionic bond is impossible. However, in nature there are substances whose molecules are formed from identical atoms. H 2, O 2, N 2 etc. The bond in substances of this type is called covalent or homeopolar(homeo - different [Greek]). In addition, a covalent bond is also observed in molecules with different atoms: hydrogen fluoride HF, nitric oxide NO, methane CH 4 etc.

The nature of the covalent bond 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 the atom does not break off abruptly with increasing distance from the center of the atom, but gradually decreases. When atoms approach each other, the diffuse electron clouds of external electrons partially overlap, which leads to their deformation. An accurate calculation of the change in the state of electrons requires the solution of the Schrödinger wave equation for the system of all particles participating in the interaction. The complexity and cumbersomeness of this path force us to confine ourselves here to only a qualitative consideration of the phenomena.

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

Pauli's principle allows two electrons to exist in the same state with oppositely directed 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 alternately belong to one or the other nucleus.

Calculations show that the exchange energy of a molecule is positive if the spins of the 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 the ionic bond it was a question of the transfer of electrons from one atom to another, then here the bond is carried out by the generalization of electrons and the creation of a common space for their movement.

Molecular Spectra

Molecular spectra are very different from atomic ones. While atomic spectra are made up of individual lines, molecular spectra are made up of bands that are sharp at one end and blurred 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. The spectrum contains a number of series.

Quantum mechanics explains the nature of molecular spectra. The theoretical interpretation of the spectra of polyatomic molecules is very complicated. We will restrict ourselves to considering only diatomic molecules.

Earlier, we noted that the energy of a molecule depends on the nature of the motion 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 motion 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 the translational energy cannot lead to the appearance of a spectral line in the molecular spectrum; therefore, we shall exclude this type of energy in the further consideration of molecular spectra. Then

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

Experience and theoretical studies have shown that

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

Rotational spectrum of molecules

Let's start to investigate 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. By gradually increasing the frequency, we will reach quanta capable of lifting a molecule from one rotational step to another. This occurs in the infrared wavelength range 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 of the rotational absorption spectrum. As the wavelength decreases (i.e., the number changes), new lines of the absorption spectrum appear in this region. The set of all lines gives an idea of the distribution of the rotational energy states of the molecule.

We have so far considered the absorption spectrum of a 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 the masses of the atoms, it is possible to determine the distances between the atoms. For a diatomic molecule

Vibrational-rotational spectrum of molecules

The absorption of electromagnetic waves in the infrared region with a wavelength of microns by a substance causes transitions between vibrational energy levels and leads to the appearance of the vibrational spectrum of the molecule. However, when the vibrational energy levels of a molecule change, its rotational energy states also change. Transitions between two vibrational energy levels are accompanied by a change in rotational energy states. This gives rise to the vibrational-rotational spectrum of the molecule.

If a molecule vibrates and rotates at the same time, 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., the 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 fulfilled only for molecules formed by two different atoms, i.e. for asymmetric molecules.

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

Vibrational spectrum of molecules

The absorption of electromagnetic waves in the visible and ultraviolet ranges leads to transitions of the molecule between different electronic energy levels, i.e. to the emergence 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 a variety of vibrational energy levels.

The transition between two electronic levels is accompanied by many accompanying transitions between vibrational levels. This is how the electronic-vibrational spectrum of the molecule appears, 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 you to understand the detailed structure of molecules and has wide application for chemical analysis.

Raman light scattering

This phenomenon consists 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 scattering molecules.

The Raman scattering phenomenon has a simple quantum mechanical explanation. The scattering of light by molecules can be viewed as an inelastic collision of photons with molecules. Upon collision, a photon can give to a molecule or receive from it only such amounts of energy that are equal to the differences between its two energy levels. If, upon collision with a photon, a molecule passes from a state with a lower energy to a state with a higher energy, then it loses its energy and its frequency decreases. This creates a line in the spectrum of the molecule, shifted relative to the main line towards longer wavelengths. If, after colliding with a photon, the molecule passes from a state with a higher energy to a state with a 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 on the structure of molecules. Using this method, the natural vibration frequencies of molecules are easily and quickly determined. It also allows one 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 there is a glow of these bodies or luminescence.

There are two types of luminescence: fluorescence and phosphorescence.

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

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 sec.).

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

During phosphorescence, the molecule passes from an excited state to a metastable level. Metastable such a level is called, the transition from which to a lower level is unlikely. Radiation in this case can occur if the molecule returns to the excited level.

The transition from a metastable state to an excited state is possible only in the presence of additional excitation. This additional causative agent can be the temperature of the substance. At high temperatures, this transition occurs quickly, at low temperatures - slowly.

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

Quantum amplifiers and radiation generators

In the mid-1950s, the rapid development of quantum electronics began. In 1954, the works of Academicians N.G. Basov and A.M. Prokhorov, who described 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 for visible and infrared light that appeared in the 60s was named optical quantum generators or lasers(light amplification by stimulated emission of radiation).

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

Let us dwell on 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 are carried out spontaneously (or spontaneously). However, under the action of incident radiation, such transitions are possible both in the forward and reverse directions. These transitions are called forced or induced... When a forced transition from one of the excited levels to a low energy level occurs, 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, therefore, of all stimulated radiation coincides with the direction of propagation of the external radiation that caused the transition, i.e. stimulated emission is strictly coherent with stimulating emission.

Thus, the new photon, which appears as a result of the stimulated emission, amplifies the light passing through the medium. However, simultaneously with the induced radiation, the process of absorption of light occurs, since a stimulating radiation photon is absorbed by an atom at a low energy level, and the atom moves to a higher energy level. and

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

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

Consider a device using such media, used as a wave generator in the optical range, or laser.

Its main part is a crystal of artificial ruby, which is alumina, in which some of the aluminum atoms are replaced by chromium atoms. When a ruby crystal is irradiated with light with a wavelength of 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 pass into a metastable state. The ions are at this level for a longer time than at the upper one. As a result, the inverse state of the metastable level is achieved.

The return of ions to the ground state is accompanied by the emission of two red lines: and. This return occurs like an avalanche under the action of photons of the same wavelength, i.e. with forced radiation. This return is much faster than with spontaneous emission, so the light is amplified.

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 ground and silver-plated so that they form two opposite mirrors, one of which is translucent. The entire ruby rod is located near a pulsed vacuum tube, with the help of which the medium is optically pumped. Photons, the directions of movement of which 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 the 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 sufficiently intense, part of it goes out through the semitransparent end of the crystal.

A lot 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 monochromaticity;

3. high power;

4. the narrowness of the beam.

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 is found to modulate and demodulate light, a huge amount of information can be transmitted. Thus, in terms of the amount of information transmitted, 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, a spot of light 3 km in diameter can be obtained on the lunar surface. The high power and narrowness of the beam allows, when focusing with 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, for influencing the course of chemical reactions, etc.

The above does not exhaust all the possibilities 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.

Chemical bonds and molecular structure.

Molecule - the smallest particle of a substance, consisting of the same or different atoms connected to each other chemical bonds, and is the carrier of its basic chemical and physical properties. Chemical bonds are due to the interaction of external, valence electrons of atoms. Most often, there are two types of bonds in molecules: ionic and covalent.

Ionic bond (for example, in molecules NaCl, KBr) is carried out by the electrostatic interaction of atoms during the transition of an electron from one atom to another, i.e. with the formation of positive and negative ions.

A covalent bond (for example, in H2, C 2, CO molecules) occurs when the valence electrons are shared by two neighboring atoms (the spins of the valence electrons must be antiparallel). The covalent bond is explained on the basis of the principle of indistinguishability of identical particles, for example, electrons in a hydrogen molecule. The indistinguishability of particles leads to exchange interaction.

A molecule is a quantum system; it is described by the Schrödinger equation, which takes into account the motion of electrons in a molecule, vibrations of atoms in a molecule, and rotation of a molecule. Solving this equation is a very difficult problem, which usually breaks down into two: for electrons and nuclei. Isolated molecule energy:

where is the energy of motion of electrons relative to the nuclei, is the energy of vibrations of nuclei (as a result of which the relative position of nuclei changes periodically), is the energy of rotation of nuclei (as a result of which the orientation of the molecule in space periodically changes). In formula (13.1), the energy of translational motion of the center of mass of the molecule and the energy of the nuclei of atoms in the molecule are not taken into account. The first of them is not quantized; therefore, its changes cannot lead to the appearance of a molecular spectrum, and the second can be ignored if the hyperfine structure of spectral lines is not considered. It is proved that eV, eV, eV, therefore >>>>.

Each of the energies included in expression (13.1) is quantized (a set of discrete energy levels corresponds to it) and is determined by quantum numbers. During the transition from one energy state to another, energy D is absorbed or emitted E = hv. During such transitions, the energy of motion of electrons, the energies of vibrations and rotation change simultaneously. It follows from theory and experiment that the distance between rotational energy levels D is much less than the distance between vibrational levels D, which, in turn, is less than the distance between electronic levels D. Figure 13.1 schematically shows the energy levels of a diatomic molecule (for example, only two electronic levels are considered - shown in bold lines).

The structure of molecules and the properties of their energy levels are manifested in molecular spectra– emission (absorption) spectra arising from quantum transitions between the energy levels of molecules. The emission spectrum of a molecule is determined by the structure of its energy levels and the corresponding selection rules.

So, for different types of transitions between levels, different types of molecular spectra arise. The frequencies of spectral lines emitted by molecules can correspond to transitions from one electronic level to another (electronic spectra) or from one vibrational (rotational) level to another ( vibrational (rotational) spectra In addition, transitions with the same values are also possible and to levels that have different values for all three components, resulting in vibrational and vibrational-rotational spectra.

Typical molecular spectra are striped, representing a combination of more or less narrow bands in the ultraviolet, visible and infrared regions.

By using high-resolution spectral instruments, it can be seen that the bands are so closely spaced lines that they are difficult to resolve. The structure of molecular spectra is different for different molecules and becomes more complicated with an increase in the number of atoms in a molecule (only continuous broad bands are observed). Only polyatomic molecules have vibrational and rotational spectra, while diatomic ones do not. This is explained by the fact that diatomic molecules do not have dipole moments (during vibrational and rotational transitions, there is no change in the dipole moment, which is a necessary condition for the transition probability to differ from zero). Molecular spectra are used to study the structure and properties of molecules, are used in molecular spectral analysis, laser spectroscopy, quantum electronics, etc.

Spectrum is called the sequence of quanta of energy of electromagnetic radiation, absorbed, released, scattered or reflected by matter during the transitions of atoms and molecules from one energy state to another.

Depending on the nature of the interaction of light with matter, the spectra can be divided into absorption (absorption) spectra; emissions (emission); scattering and reflection.

For the objects under study, optical spectroscopy, i.e. spectroscopy in the wavelength range 10 -3 ÷ 10 -8 m subdivided into atomic and molecular.

Atomic spectrum is a sequence of lines, the position of which is determined by the energy of the transition of electrons from one level to another.

The energy of the atom can be represented as the sum of the kinetic energy of translational motion and electronic energy:

where is the frequency, is the wavelength, is the wave number, is the speed of light, is the Planck constant.

Since the energy of an electron in an atom is inversely proportional to the square of the principal quantum number, then for a line in the atomic spectrum we can write the equation:

(4.12)

Here - electron energies at higher and lower levels; - Rydberg constant; - spectral terms, expressed in units of measurement of wave numbers (m -1, cm -1).

All lines of the atomic spectrum converge in the short-wavelength region to the limit determined by the ionization energy of the atom, after which there is a continuous spectrum.

Molecule energy in the first approximation can be considered as the sum of translational, rotational, vibrational and electronic energies:

(4.15)

For most molecules, this condition is fulfilled. For example, for H2 at 291K, the individual components of the total energy differ by an order of magnitude or more:

309,5 kJ / mol,

=25,9 kJ / mol,

2,5 kJ / mol,

=3,8 kJ / mol.

The energy values of quanta in different spectral regions are compared in Table 4.2.

Table 4.2 - Energy of absorbed quanta of different regions of the optical spectrum of molecules

The concepts of "vibrations of nuclei" and "rotation of molecules" are conditional. In reality, such types of motion only very approximately convey the idea of the distribution of nuclei in space, which is of the same probabilistic nature as the distribution of electrons.

A schematic system of energy levels in the case of a diatomic molecule is shown in Figure 4.1.

Transitions between rotational energy levels give rise to rotational spectra in the far IR and microwave regions. Transitions between vibrational levels within one electronic level give vibrational-rotational spectra in the near-IR region, since a change in the vibrational quantum number inevitably entails a change in the rotational quantum number. Finally, transitions between electronic levels cause the appearance of electronic-vibrational-rotational spectra in the visible and UV regions.

In the general case, the number of transitions can be very large, but in fact, not all of them manifest themselves in the spectra. The number of transitions is limited selection rules .

Molecular spectra provide rich information. They can be used:

For the identification of substances in a qualitative analysis, since each substance has its own spectrum inherent only to it;

For quantitative analysis;

For structural group analysis, since certain groups, such as, for example,> C = O, _ NH 2, _ OH, etc. give characteristic bands in the spectra;

To determine the energy states of molecules and molecular characteristics (internuclear distance, moment of inertia, natural vibration frequencies, dissociation energies); a comprehensive study of molecular spectra makes it possible to draw conclusions about the spatial structure of molecules;

In kinetic studies, including the study of very fast reactions.

- energy of electronic levels;

Energies of vibrational levels;

Rotational energy

Figure 4.1 - Schematic arrangement of energy levels of a diatomic molecule

Bouguer-Lambert-Beer law

Quantitative molecular analysis using molecular spectroscopy is based on Bouguer-Lambert-Beer law linking the intensity of incident and transmitted light with the concentration and thickness of the absorbing layer (Figure 4.2):

or with a coefficient of proportionality:

Integration result:

(4.19)

(4.20)

With a decrease in the intensity of the incident light by an order of magnitude

(4.21)

If = 1 mol / L, then, i.e. the absorption coefficient is equal to the reciprocal of the layer thickness, in which, at a concentration equal to 1, the incident light intensity decreases by an order of magnitude.

The absorption coefficients and depend on the wavelength. The type of this dependence is a kind of "fingerprint" of molecules, which is used in qualitative analysis to identify a substance. This dependence is characteristic and individual for a particular substance and reflects the characteristic groups and bonds included in the molecule.

Optical density D

expressed in%

4.2.3 Rotational energy of a diatomic molecule in the rigid rotator approximation. Rotational spectra of molecules and their application to determine molecular characteristics

The appearance of rotational spectra is associated with the fact that the rotational energy of a molecule is quantized, i.e.

The energy of rotation of a molecule around the axis of rotation

Since the point O is the center of gravity of the molecule, then:

Introduction of the designation of the reduced mass:

(4.34)

leads to the equation

(4.35)

Thus, a diatomic molecule (Figure 4.7 a) rotating around an axis or passing through the center of gravity can be simplified to be regarded as a particle with mass that describes a circle with a radius around the point O(figure 4.7 b).

The rotation of the molecule around the axis gives the moment of inertia, practically equal to zero, since the radii of the atoms are much less than the internuclear distance. Rotation about the axes or, mutually perpendicular to the bond line of the molecule, leads to equal moments of inertia:

where is a rotational quantum number taking only integer values

0, 1, 2…. In accordance with selection rule for the rotational spectrum In a diatomic molecule, a change in the rotational quantum number upon absorption of an energy quantum is possible only by one, i.e.

converts equation (4.37) into the form:

the wave number of the line in the rotational spectrum corresponding to the absorption of a quantum upon transition from j energy level per level j+1 can be calculated using the equation:

Thus, the rotational spectrum in the approximation of the rigid rotator model is a system of lines located at the same distance from each other (Figure 4.5b). Examples of rotational spectra of diatomic molecules estimated in the rigid rotator model are shown in Figure 4.6.

a b

Figure 4.6 - Rotational spectra HF (a) and CO(b)

For molecules of hydrogen halides, this spectrum is shifted to the far-IR region of the spectrum, for heavier molecules - to the microwave.

Based on the obtained regularities of the appearance of the rotational spectrum of a diatomic molecule, in practice, first determine the distance between adjacent lines in the spectrum, from which they are further found, and according to the equations:

(4.45)

where - centrifugal distortion constant , is related to the rotational constant by the approximate relation ... The correction should be taken into account only for very large j.

For polyatomic molecules, in the general case, the existence of three different moments of inertia is possible ... In the presence of symmetry elements in a molecule, the moments of inertia may coincide or even be equal to zero. For example, for linear polyatomic molecules(CO 2, OCS, HCN, etc.)

where - position of the line corresponding to the rotational transition in an isotope-substituted molecule.

To calculate the value of the isotopic shift of the line, it is necessary to sequentially calculate the reduced mass of the isotope-substituted molecule taking into account the change in the atomic mass of the isotope, the moment of inertia, the rotational constant, and the position of the line in the spectrum of the molecule according to equations (4.34), (4.35), (4.39) and (4.43), respectively , or estimate the ratio of the wave numbers of lines corresponding to the same transition in isotope-substituted and non-isotopic molecules, and then determine the direction and magnitude of the isotopic shift using equation (4.50). If the internuclear distance is approximately constant , then the ratio of the wavenumbers corresponds to the inverse ratio of the reduced masses:

where is the total number of particles, is the number of particles per i- that energy level at temperature T, k- Boltzmann constant, - statistical ve forcefully degree of degeneration i-th energy level, characterizes the probability of finding particles at a given level.

For a rotational state, the level population is usually characterized by the ratio of the number of particles per j- that energy level to the number of particles at the zero level:

(4.53)

where - statistical weight j-th rotational energy level, corresponds to the number of projections of the momentum of a rotating molecule on its axis - the bond line of the molecule, , the energy of the zero rotational level ... The function passes through a maximum when increasing j, as Figure 4.7 illustrates for the example of the CO molecule.

The extremum of the function corresponds to the level with the maximum relative population, the value of the quantum number of which can be calculated by the equation obtained after determining the derivative of the function at the extremum:

(4.54)

Figure 4.7 - Relative population of rotational energy levels

molecules CO at temperatures of 298 and 1000 K

Example. In the HI rotational spectrum, the distance between adjacent lines is determined cm -1... Calculate the rotational constant, moment of inertia and equilibrium internuclear distance in the molecule.

Solution

In the approximation of the rigid rotator model, in accordance with equation (4.45), we determine the rotational constant:

cm -1.

The moment of inertia of the molecule is calculated from the value of the rotational constant according to the equation (4.46):

kg . m 2.

To determine the equilibrium internuclear distance, we use equation (4.47), taking into account that the masses of the hydrogen nuclei and iodine expressed in kg:

Example. In the far IR region of the spectrum of 1 H 35 Cl, lines were found, the wavenumbers of which are:

Determine the average values of the moment of inertia and internuclear distance of the molecule. Assign the observed lines in the spectrum to rotational transitions.

Solution

According to the rigid rotator model, the difference between the wave numbers of adjacent lines of the rotational spectrum is constant and equal to 2. Let us determine the rotational constant from the average distance between adjacent lines in the spectrum:

cm -1,

cm -1

Find the moment of inertia of the molecule (equation (4.46)):

We calculate the equilibrium internuclear distance (equation (4.47)), taking into account that the masses of the hydrogen nuclei and chlorine (expressed in kg):

Using equation (4.43), we estimate the position of the lines in the rotational spectrum of 1 H 35 Cl:

Let us compare the calculated values of the wave numbers of the lines with the experimental ones. It turns out that the lines observed in the rotational spectrum of 1 H 35 Cl correspond to the transitions:

N line
, cm -1	85.384	106.730	128.076	149.422	170.768	192.114	213.466
	3 4	4 5	5 6	6 7	7 8	8 9	9 10

Example. Determine the magnitude and direction of the isotopic shift of the absorption line corresponding to the transition from energy level in the rotational spectrum of the 1 H 35 Cl molecule with the substitution of the chlorine atom for the 37 Cl isotope. The internuclear distance in molecules of 1 H 35 Cl and 1 H 37 Cl is considered the same.

Solution

To determine the value of the isotopic shift of the line corresponding to the transition , we calculate the reduced mass of the 1 H 37 Cl molecule taking into account the change in the atomic mass of 37 Cl:

then we calculate the moment of inertia, rotational constant and position of the line in the spectrum of the 1 H 37 Cl molecule and the isotopic shift according to equations (4.35), (4.39), (4.43), and (4.50), respectively.

Otherwise, the isotope shift can be estimated from the ratio of the wave numbers of lines corresponding to the same transition in molecules (the internuclear distance is assumed to be constant) and then the position of the line in the spectrum using equation (4.51).

For 1 H 35 Cl and 1 H 37 Cl molecules, the ratio of the wavenumbers of a given transition is:

To determine the wave number of the line of an isotope-substituted molecule, we substitute the value of the wave number of the transition found in the previous example j → j+1 (3→4):

We conclude: the isotopic shift in the low-frequency or long-wave region is

85.384-83.049 = 2.335 cm -1.

Example. Calculate the wavenumber and wavelength of the most intense spectral line of the rotational spectrum of the 1 H 35 Cl molecule. Match the line with the corresponding rotational transition.

Solution

The most intense line in the rotational spectrum of the molecule is associated with the maximum relative population of the rotational energy level.

Substitution of the value of the rotational constant found in the previous example for 1 H 35 Cl ( cm -1) into equation (4.54) allows you to calculate the number of this energy level:

We calculate the wavenumber of the rotational transition from this level using the equation (4.43):

We find the transition wavelength from the transformed with respect to equation (4.11):

4.2.4 Multivariate task No. 11 "Rotational spectra of diatomic molecules"

1. Write a quantum mechanical equation for calculating the rotational energy of a diatomic molecule as a rigid rotator.

2. Derive an equation for calculating the change in the rotational energy of a diatomic molecule as a rigid rotator when it moves to a neighboring, higher quantum level .

3. Derive the equation for the dependence of the wave number of rotational lines in the absorption spectrum of a diatomic molecule on the rotational quantum number.

4. Derive an equation for calculating the difference between the wave numbers of adjacent lines in the rotational absorption spectrum of a diatomic molecule.

5. Calculate the rotational constant (in cm -1 and m -1) of the diatomic molecule A by the wavenumbers of two adjacent lines in the long-wave infrared region of the rotational absorption spectrum of the molecule (see Table 4.3).

6. Determine the rotation energy of the molecule A at the first five quantum rotational levels (J).

7. Draw schematically the energy levels of the rotational motion of a diatomic molecule as a rigid rotator.

8. Draw the rotational quantum levels of a molecule that is not a rigid rotator on this diagram with a dotted line.

9. Derive an equation for calculating the equilibrium internuclear distance based on the difference in the wave numbers of adjacent lines in the rotational absorption spectrum.

10. Determine the moment of inertia (kg.m 2) of a diatomic molecule A.

11. Calculate the reduced mass (kg) of the molecule A.

12. Calculate the equilibrium internuclear distance () of the molecule A... Compare the received value with the reference data.

13. Assign the observed lines in the rotational spectrum of the molecule A to rotary transitions.

14. Calculate the wavenumber of the spectral line corresponding to the rotational transition from the level j for a molecule A(see table 4.3).

15. Calculate the reduced mass (kg) of the isotopically substituted molecule B.

16. Calculate the wavenumber of the spectral line associated with the rotational transition from the level j for a molecule B(see table 4.3). Internuclear distances in molecules A and B considered equal.

17. Determine the magnitude and direction of the isotope shift in the rotational spectra of molecules A and B for the spectral line corresponding to the transition to the rotational level j.

18. Explain the reason for the nonmonotonic change in the intensity of absorption lines as the rotation energy of the molecule increases

19. Determine the quantum number of the rotational level corresponding to the highest relative population. Calculate the wavelengths of the most intense spectral lines of the rotational spectra of molecules A and B.