Luminescence: types, methods, application. Thermally stimulated luminescence - what is it? Franck-Condon principle and laws of fluorescence. Luminescence of biologically important molecules. Mechanisms of energy migration The luminescence spectrum depends on

Luminescence: basic concepts ■ The mention of luminescence dates back to the 15th century, when the luminescence of inorganic crystals was described. Many associate the emergence of luminescence with the publication of the work of David Brewster, who in 1833 described the red fluorescence of chlorophyll. ■ The Hound of the Baskervilles (Conan Doyle Arthur).

Luminescence: basic concepts ■ So, what is luminescence? The definition of this concept is rather complicated and proceeds from a comparison of the properties of luminescent radiation and the laws of thermal equilibrium radiation. Thermal radiation is understood as electromagnetic radiation caused by the excitation of particles of matter (atoms, molecules, ions) due to their thermal motion. To cause the luminescence of a substance, a certain amount of energy must be supplied to it from the outside. ■ Luminescence is the glow of atoms, molecules and other more complex complexes, resulting from the electronic transition in these particles when they return from an excited state to a normal one (VL Levshin).

Luminescence: basic concepts ■ Luminescence is radiation (B`v, T), which is an excess over thermal radiation (Bv, T) of a substance at a given temperature and has a duration (>10 -10 s) significantly exceeding the period of light waves (Wiedemann - Vavilov).

Src="https://present5.com/presentation/37574361_76674408/image-5.jpg" alt="(!LANG: Classification of types of luminescence n According to the duration of luminescence: fluorescence (~10 -8 s), phosphorescence (>10 - 6"> Классификация видов люминесценции n По длительности свечения: флуоресценция (~10 -8 c), фосфоресценция (>10 -6 с). n По способу возбуждения (таблица). n По механизму свечения: свечение дискретных центров – поглощающими и излучающими центрами являются одни и те же частицы (атомы, молекулы, ионы); рекомбинационное свечение – процессы поглощения и излучения разделены во времени и в пространстве. В процессе возбуждения происходит разделение частицы вещества на две противоположно заряженные части. Последующая их рекомбинация сопровождается выделением энергии.!}

Main characteristics of luminescence n Absorption spectra: A = f(λ); A = f(v); T, % = f(λ); T, % = f(v). n Luminescence spectra: I = f(λ); I = f(v). n Excitation spectra: dependences of the luminescence intensity (I) on the frequency (wave number) or wavelength of the exciting light; for particles that luminesce according to the type of discrete centers, the excitation spectra are identical to the absorption spectra. n Energy yield of luminescence. n Quantum yield of luminescence. n Lifetime of an excited luminescent center.

Luminescence yield n The ability of a substance to luminesce in a given medium is characterized by the magnitude of the luminescence yield. n Distinguish between the absolute quantum and energy yields of luminescence and the relative yield of luminescence. n The absolute quantum yield of luminescence (φkv) is the ratio of the number of quanta Nl emitted by a substance to the number of absorbed quanta of exciting light Np: φkv = Nl / Np ■ φkv is determined by the ratio between the probabilities of radiative (α) and nonradiative (β): φkv = α / α + β

Luminescence yield n The absolute energy yield of luminescence (φen) is the ratio of the energy radiated by the substance El to the absorbed excitation energy En: φen = El / En (vl / vp) or φen = φkv (λp / λl); φkv = φeng (λl / λp) ■ Measurement of absolute luminescence yields is a difficult task, therefore, in practice, relative luminescence yields are often measured.

The lifetime of an excited luminescent center n In the case of discrete luminescent centers, the number of excited centers n after excitation ceases in the absence of nonradiative deactivation processes will decrease with time: -dn/dt = k 1 n, where k 1 is the rate constant of the monomolecular radiative process. ■ The average radiative lifetime (τ0) of a luminescent center is given by: τ0 = 1/ k 1

Lifetime of an excited luminescent center n For rough estimates, the relation is applicable: 10 -4 τ0 ≈ ---- ε(λmax) n n Since nonradiative processes take place, the measured lifetimes τ are always less than τ0: 1 τ = ------ k 1 + k 2 + k 3

Energy transitions in the n molecule At room temperature, the molecule is usually in the n n ground S 0 singlet state. When energy is absorbed, the molecule is in an excited electronic state S 2. Then, almost instantly (~10 -12 s), as a result of vibrational relaxation (CR), an unexcited vibrational level S 2 is reached. Then, also almost instantly (~ 10 -11 s) due to internal conversion the molecule will go to a lower electronically excited state S 1. The transition S 1 → S 0 with the emission of a photon (10 -6 - 10 -9 s) - fluorescence.

Energy transitions in a molecule ■ Radiative transition S 1 → T 1 with a change in the electron spin - intercombination conversion. n Transition T 1 → S 0 with photon emission (>10 -4 s) – phosphorescence.

Delayed fluorescence n In addition to fluorescence and phosphorescence, there is another type of luminescence - delayed fluorescence. n This type of molecular luminescence is observed in very limited ranges of temperatures, viscosities and concentrations of solutions. n Compared to fluorescence and phosphorescence, its intensity is low and reaches maximum values at room and higher temperatures, significantly weakening with decreasing temperature. n Distinguish delayed fluorescence E - type.

Delayed fluorescence E - type n Delayed fluorescence E - type: due to thermal activation of molecules in the T 1 state, they move to higher vibrational levels, which can overlap with vibrational levels S 1 and the transition T 1 → S 1 becomes possible.

Delayed fluorescence n Delayed P-type fluorescence (observed in pyrene molecules and other aromatic compounds): occurs when energy is transferred as a result of collisions

Potential energy diagram n When considering luminescence, it is useful to consider the potential energy diagram. n Let us confine ourselves to two-dimensional diagrams related, strictly speaking, to the case of a diatomic molecule.

Potential energy diagram n The potential energy curves of states S 1 and T 1 intersect at some point. n At this point, the position and momenta of the atomic nuclei are the same, i.e., the S 1 → T 1 transition is possible. n In complex polyatomic molecules, multidimensional potential surfaces can intersect at many points, which increases the likelihood of IR. n Franck-Condon principle. According to this principle, electronic transitions are such fast processes (10 -13 s) in comparison with the movement of nuclei (10 -12 s) that during the electronic transition the nuclei do not have time to change either their speed or their relative position.

Franck-Condon principle n Therefore, the former position of the nuclei will correspond to the forces that have changed as a result of the electronic transition only if the molecule makes sufficient vibrations. n Thus, upon electronic excitation of a molecule, the bond strength instantly weakens, and the nuclei at the first moment continue to occupy their former position close to each other (compressed molecule). n Such a discrepancy leads to the fact that the molecule begins to oscillate. n For a short lifetime of the excited state (10 -9 s), the excess vibrational energy has time to be distributed between numerous vibrations of the molecule or transferred to the environment.

Franck-Condon principle n As a result, a molecule from a non-equilibrium Frank-Condon state passes into an equilibrium one, in which the nuclei, in accordance with the weakened bond, are separated from each other and oscillate relative to this position. n Further, when a luminescence quantum is emitted, the strength of the bond in the molecule instantly increases, while the nuclei at the first moment continue to occupy their former, far from each other position (stretched molecule). n And again, the transition from the non-equilibrium Frank-Condon state to the equilibrium state is carried out as a result of oscillations.

Franck-Condon principle n So, according to the Franck-Condon principle, intramolecular bonds, as a rule, are weakened during electronic excitation. n This leads to the fact that the minimum of the potential curve of the excited state is located at a slightly larger internuclear distance than that of the ground state. n As follows from quantum mechanics, the most probable internuclear distance for a molecule with zero vibrational energy corresponds to the midpoint AB or CD.

Franck-Condon principle n The transitions corresponding to vertical lines drawn from the middle of segments AB (absorption) or CD (emission) to the intersection with the corresponding potential curves will be the most probable:

Photoluminescence n The ability of substances to luminescence, as well as to absorb radiation, is associated with their electronic structure. n For example, if the lowest excited singlet state of an organic molecule is due to the π → π* transition, then it often has high yields of both fluorescence and phosphorescence. n In cases where the lowest excited singlet state occurs as a result of the n → π* transition, the molecule usually has a low fluorescence yield, but may have a high phosphorescence yield at low temperature. n Usually the n → π* transition is the longest wavelength transition.

Photoluminescence n The probability of such a transition is small (ε λmax ~ (1 - 2) 103 M -1 cm-1), and the lifetime of the excited singlet state n , π*, and hence the probability of nonradiative deactivation are high. n It has been experimentally established that the difference in energies S 1 ↔ T 1 for the state n , π* is 2 - 4 times less than for the state π, π*. n All this leads to the fact that often compounds containing n - electrons fluoresce weakly or not at all, but strongly phosphorescent.

Structure and optical properties of molecules n It has been noted that symmetrical molecules with an extended system of conjugated bonds, prone to the formation of ortho- and para-quinoid rings, have the greatest ability to luminescence. n One of the most important factors that determine luminescence is the requirement for a rigid and flat structure. n Apparently, the relative rotation of parts of a "flexible" molecule perturbs the electron shells and facilitates nonradiative transitions. n For example, the well-known hormone adrenaline does not luminesce, but when oxidized it turns into a brightly luminescent trioxidone.

The structure and optical properties of molecules n Luminescent fluorescein differs from non-luminescent phenolphthalein only in that the oxygen bridge in the fluorescein molecule rigidly holds two rings in the same plane: fluorescein phenolphthalein

Basic laws of molecular luminescence n Kasha's rule: the shape of the luminescence spectrum does not depend on the wavelength of the exciting light. n Stokes - Lommel law: the luminescence spectrum as a whole and its maximum is shifted with the absorption spectrum and its maximum to the long wavelength region. n Levshin's rule (mirror symmetry rule): normalized absorption and fluorescence spectra, presented in the form of graphs ε = f(v) and I/v = f(v), are mirror-symmetrical with respect to a straight line perpendicular to the frequency axis and passing through the intersection point of the spectra v0.

Basic regularities of molecular luminescence n Levshin's rule: va + vf = 2 v 0, where va, vf are symmetrical frequencies of absorption and fluorescence; v 0 is the frequency of a purely electronic transition, i.e., the transition between zero vibrational levels S 0 ↔ S 1; ∆v = va - vf = 2(va - v 0)

The main regularities of molecular luminescence n Vavilov's law: as λv increases, the energy yield of fluorescence increases, remains constant, and then decreases.

Luminescence decay law n For the luminescence intensity Il, determined by the rate of emission of luminescence quanta, we have: cessation of arousal. n Thus, the luminescence intensity of a discrete center decreases with time according to an exponential law. n The decay of the recombination glow occurs according to a more complex hyperbolic law.

Dependence of the luminescence intensity on the concentration n With stationary (continuous) excitation of the sample and the absence of quenching: Il = k 1 φkv Np (Np is the number of absorbed quanta); Np \u003d k 2 (I 0 - I); I \u003d I 0 10 -εℓC; Il \u003d k φkv I 0 (1 - 10 -εℓC), where k is the coefficient of proportionality; Expanding 10 -εℓC into a series gives: (2, 3εℓC) 2 (2, 3εℓC)3 1 - 2, 3εℓC + ---- - ---- + ……. ; 2! 3!

Dependence of luminescence intensity on concentration ■ At εℓC ≤ 10 -2 the contribution of the third and subsequent terms of expansion is insignificant: Il = 2, 3 k φkv I 0 ε ℓ C; Il \u003d k C; usually ε ~ 103 - 104, then at ℓ = 1 cm Сi = 10 -5 - 10 -6 M

Reasons for the deviation of the dependence Il = k. C from linearity ■ The effect of the internal filter is related to the absorption of part of the excitation radiation when passing through the phosphor layer; ■ Self-absorption - absorption of part of the luminescent radiation by the phosphor; ■ Luminescence quenching: concentration quenching (formation of non-luminescent aggregates, energy migration from excited molecules to unexcited ones); temperature quenching (an intramolecular process due to a significant increase in vibrational energy with an increase in T);

Luminescence quenching ■ Luminescence quenching: quenching by foreign substances (heavy ions: I-, Br-, Cs+, Cu+; paramagnetic Mn 2+, O 2; solvent molecules); static quenching (an impurity substance forms non-luminescent products with an unexcited phosphor); dynamic quenching (an impurity substance forms non-luminescent products with an excited phosphor).

Luminescence quenching ■ Stern-Volmer equation: φkv(Q) = k 1 / (k 1 + k 2 + k 3 [Q];

Practical application of luminescence connections); fluorescence of complex compounds of metal ions with organic reagents. ■ Phosphorimetric determinations. ■ Time selection. ■ Synchronous scanning of spectra (derivative spectra). ■ Chemiluminescent analysis. ■

Synchronous spectra ■ Synchronous spectra are obtained by simultaneous (synchronous) scanning (changing) of the excitation and emission wavelengths with a constant shift Δλ between them. ■ In this case, there is a significant simplification of the luminescence spectra of complex molecules, a narrowing of their bands and, as a result, an increase in the selectivity of determinations, as well as a decrease in the background glow due to the suppression of the Rayleigh and Raman scattering of the solvent. ■ The optimal condition for achieving the most intense signal and the smallest line half-width is synchronous scanning with the condition: Δλ = λexp (max) - λex (max)

3D spectra ■ 3D spectra show the dependence of the luminescence intensity on both the excitation wavelength and the emission wavelength. ■ Three-dimensional spectra look like a "mountain range". Each row of such a ridge represents the emission spectrum, and each column represents the excitation spectrum. ■ Such spectra are obtained from a large number (usually at least 50) of individual luminescence spectra recorded at certain intervals of excitation wavelengths. ■ Three-dimensional spectra provide a complete picture of the spectral properties of the sample being examined.

Contour (2D) Spectra ■ The use of 3D spectra to analyze mixtures containing more than three components and having broad smeared bands in the same spectral region is an unsolvable problem. ■ In this case, the use of contour spectra is more promising - the result of a section of a three-dimensional spectrum by planes parallel to the plane XOU, followed by combining the obtained sections in one XOU plane. ■ The resulting images resemble contour maps(contour spectra), which are the "fingerprints" of an individual compound.

Chemiluminescence analysis ■ Chemiluminescence analysis is based on the phenomenon of chemiluminescence (CL). This type of glow does not require an external source of excitation, but arises due to the energy of exothermic chemical processes: A + B → P* + C P* → P + hvcl n In CL solutions, it is observed mainly in oxidation reactions organic matter oxygen or hydrogen peroxide. n The formation of reaction products occurs most often by a complex radical chain mechanism. n So, many believe that the oxidation of luminol (I) proceeds with the participation of radicals HO 2 *, HO *, O 2 *.

Chemiluminescent analysis ■ The main groups of analytes: chemiluminescent compounds that emit light during oxidation (luminol, lucigenin, lofin, etc.); oxidizing agents (hydrogen peroxide, hypochlorites, hypobromites, persulfates, potassium permanganate, molecular oxygen, etc.); catalysts for indicator reactions (copper, cobalt, manganese, nickel, iron ions, etc.); inhibitors of indicator reactions (aromatic compounds containing phenolic and amino groups); compounds that change p. H medium (alkalis, carbonates, organic bases, etc.). ■ Varietal CL analysis and indicator methods.

Chemiluminescent analysis ■ Varietal CL analysis is used in testing wines, fruit and vegetable juices, meat extracts, etc. So, by the oxidation reaction of luminol in the presence of a catalyst - a complex of copper ions with α-amino acids contained in potato juice, it is possible to capture varietal differences potatoes: varieties differ in amino acid content. ■ Indicator methods of CL analysis include various types of titration using chemiluminescent indicators (CLI). Unlike fluorescent indicators, no excitation source is required to work with CLI.

Chemiluminescent analysis (analytical characteristics) ■ Most CL-determinations are highly sensitive: detection limits 10 -10 - 10 -4 g/ml with a final volume of 2 - 5 ml. ■ The selectivity of CL-determinations, as a rule, is low, since many substances affect the rate of the indicator reaction. However, varying the conditions of determination or the use of masking agents makes it possible to "mitigate" this shortcoming. ■ The simplicity, availability and cheapness of the equipment used in CL, combined with the possibility of express, highly sensitive, and under certain conditions, selective determination of a large range of compounds, determines the prevalence of CL.

The glow of a substance (i.e., the emission of visible light) due to the transitions of atoms and molecules of a substance from higher energy levels to lower ones, is called luminescence, or cold

glow. Luminescence must be preceded by the excitation of atoms and molecules of the substance. After elimination of the pathogen, luminescence continues for a certain period of time, depending on the nature of the luminescent substance and varying over a wide range: from billionths of a second to many hours and even days. According to the duration of the "afterglow", luminescence is divided into fluorescence (short-term "afterglow") and phosphorescence (long-term "afterglow"). However, this division is very conditional.

The glow due to the thermal motion of atoms and molecules (i.e., thermal radiation) does not apply to luminescence. It also does not include the reflection and scattering of light and some other types of luminescence of the body, which cease simultaneously with the elimination of the cause that caused them.

To distinguish luminescence from these types of luminescence, it can be given the following definition: luminescence is the luminescence of a substance that is in excess of the thermal radiation of this substance at a given temperature and has a finite duration (i.e., does not stop simultaneously with the elimination of the cause that caused it).

Substances that have a pronounced ability to luminesce are called phosphors.

There are several types of luminescence depending on the method of excitation of luminescence.

1. Photoluminescence is excited by visible and ultraviolet radiation. An example of photoluminescence is the glow of a watch dial and hands painted with the corresponding phosphor.

2. X-ray luminescence is excited by X-rays; it can be observed, for example, on the screen of an x-ray machine.

3. Radioluminescence is excited by radioactive radiation (see § 139); observed, for example, on the screen of scintillation counters (see § 140).

4. Cathodoluminescence is excited by an electron beam; observed on the screens of an oscilloscope, TV, radar and other cathode ray devices. Zinc and cadmium sulfides and selenides are mainly used as the phosphor covering the screen.

5. Electroluminescence is excited by an electric field; takes place, for example, in gas-discharge tubes.

6. Chemiluminescence is excited chemical processes in substance. Such, for example, are the glow of white phosphorus, decaying wood, as well as the glow of certain spore plants, insects, marine animals and bacteria.

Thus, luminescence is a kind of generator (quantum generator) that directly converts energy electromagnetic waves of various lengths, as well as mechanical, electrical and chemical energy into the energy of visible light.

The degree of conversion of absorbed energy into luminescence energy is characterized by the luminescence energy yield:

The luminescence spectrum depends on the nature of the luminescent substance and the type of luminescence.

Of all the listed types of luminescence, let us consider in more detail only photoluminescence, which has great practical application.

An experimental study of the photoluminescence spectra showed that, as a rule, they differ from the spectra of exciting radiation.

The luminescence spectrum and its maximum are shifted towards longer wavelengths relative to the spectrum used for excitation.

This pattern, called the Stokes rule, can be easily explained on the basis of quantum theory. The energy of the absorbed quantum is partially converted into other forms of energy, such as heat. Therefore, the energy of the luminescence quantum must be less Therefore, where are the wavelengths corresponding to the emitted and absorbed quanta.

Sometimes so-called anti-Stokes luminescence can take place, in which this happens when the quantum is absorbed by an already excited molecule. Then the luminescence quantum includes not only a part of the energy of the absorbed quantum, but also the excitation energy of the molecule. It is clear that in this case

An essential feature of liquid and solid phosphors is the independence of their luminescence spectrum from the wavelength of the exciting light. Due to this, the nature of the substance of liquid and solid luminophores can be judged from the photoluminescence spectrum.

The energy yield of luminescence can under certain conditions be very large, reaching 0.8; in liquids and solids, it depends on the wavelength of the exciting light. According to Vavilov's law,

the energy yield of luminescence first increases in proportion to the wavelength of the exciting light and then (having reached a maximum) drops sharply to zero.

On fig. 365 shows a graph of the dependence on obtained by Vavilov for a solution of fluorescein.

Like the Stokes rule, Vavilov's law is explained by the quantum properties of light. Indeed, let us imagine the most favorable case when each quantum of exciting light leads to the formation of a luminescence quantum. Then

the energy yield of luminescence is obviously equal to the ratio of these quanta:

But X does not depend on (for liquid and solid phosphors). Consequently, in the last formula, when changing, only the energy output will change, i.e., the energy output will be proportional. The breakdown of the energy output curve occurs at large wavelengths, which correspond to too small quanta that are no longer able to excite luminescence.

Luminescence is widely used in lighting technology: for example, a fluorescent lamp is based on it. A fluorescent lamp consists of a glass tube, in which the inner surface of the walls is covered with a thin layer of phosphor (Fig. 366). Electrodes are soldered into the ends of the tube. The tube is filled with mercury vapor and argon; the partial pressure of mercury vapor is about 1 Pa, the partial pressure of argon is 400 Pa.

The fluorescent lamp is connected to the mains in series with the throttle and the starter (which serves to preheat the electrodes).

The gas discharge arising in the lamp causes electroluminescence of mercury vapor. In the spectrum of this luminescence, along with visible light, there is ultraviolet radiation (with a wavelength, it excites the photoluminescence of the phosphor deposited on the walls of the lamp. Thus, a double energy conversion takes place in a fluorescent lamp: Electric Energy turns into the energy of ultraviolet radiation of mercury vapor, which in turn turns into the energy of visible radiation of the phosphor.

By changing the composition of the phosphor, it is possible to manufacture lamps with the required photoluminescence spectrum. In this way, fluorescent lamps of white light, warm white light, cold white light and daylight are produced.

The spectral composition of the radiation of fluorescent lamps is close to the scattered light of the northern part of the sky; a cold-white light lamp has a spectrum similar to that of direct solar radiation.

In this regard, fluorescent lamps are successfully used for "additional illumination" of agricultural crops grown on protected ground.

The distribution of energy in the emission spectrum of a fluorescent lamp is shown in fig. 367.

Fluorescent lamps are economical (their luminous efficiency is 10-20 times greater than that of incandescent lamps) and very durable (service life reaches 10,000 hours).

Another important application of luminescence is luminescence analysis, a method for determining the composition of a substance from its photoluminescence spectrum excited by ultraviolet rays. Being very sensitive, luminescent analysis makes it possible to detect the slightest changes in the chemical composition of a substance and thereby reveal the difference between objects that seem to be exactly the same. This method can, for example, reveal the very initial stages of decay food products(luminescent control of freshness of products), detect traces of oil in soil samples taken from boreholes (luminescent oil exploration), etc.

With the help of photoluminescence, it is possible to detect the finest cracks on the surface of machine parts and other products (luminescent flaw detection). To do this, the surface of the product under study is smeared with a liquid phosphor. After 15-20 minutes, the surface is washed and wiped. However, the phosphor remains in surface cracks. The glow of this phosphor (under ultraviolet irradiation of the product) will clearly outline the configuration of the cracks.

Finally, let us point out the use of photoluminescence for camouflage lighting and decorative purposes (the use of fluorescent and phosphorescent paints).

During photoluminescence, the atoms of a luminescent substance radiate completely inconsistently (randomly): their radiations are at different times, have different frequencies and phase differences, and propagate in all sorts of directions. Therefore, the brightness of photoluminescence turns out to be insignificant. However, in last years managed to find a way to artificially cause coherent identically directed radiation of many atoms, creating a narrow beam of monochromatic light, exceeding the brightness of ordinary luminescence millions of times. The device in which such radiation is carried out is called an optical quantum generator, or a laser.

The name "laser" is formed from the first letters of the English words: Light Amplification by Stimylated Emission of Radiation (light amplification by stimulated emission). Depending on the working substance used, crystal, gas and liquid lasers are distinguished.

In order for the laser to start operating, it is necessary to transfer a large number of atoms of its working substance into the same excited states, the so-called metastable states, in which the atom stays for a relatively long time.

time (significantly exceeding Sufficient electromagnetic energy from a special source (“pumping” method). Now, in the working substance of the laser (having the form of a thin long cylinder, one base of which is a mirror, the other is a partially transparent mirror), almost simultaneous forced transitions of all excited atoms to the normal state will begin. These transitions are accompanied by almost simultaneous emission of many light quanta (photons) having the same frequency and phase and moving in the same direction - along the laser axis. The stream of these photons forms a narrow, powerful beam of monochromatic light emerging from the laser.

The laser produces a light beam of very small divergence. Being, for example, directed at the Moon, such a beam creates on its surface a light spot with a diameter of only 1000000000000000000000000000 (the beam of an ordinary searchlight would create a light spot with a diameter of 1000 at the same distance. The energy density in the laser beam is exceptionally high - thousands and tens of thousands; moreover, calculations show that these are far from the limiting values of possible densities.With the help of a lens, you can focus the laser light so that it instantly melts and evaporates the illuminated area of any material.

All this makes the laser an exceptionally promising device, which is already widely used in many fields of science and technology. Welding of micro-objects, drilling and cutting of superhard materials, acceleration of chemical reactions, transmission of light signals over ultra-long distances (space communications), eye surgery (destruction of tumors on the retina) - this is not a complete list of laser applications.

Note that, along with optical quantum generators, quantum generators have been created in the range of short radio waves - masers

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luminescence in medicine, what is luminescence
Luminescence(from Latin lumen, genus case luminis - light and -escent - a suffix meaning weak action) - non-thermal luminescence of a substance that occurs after it absorbs excitation energy. Luminescence was first described in the 18th century.

Initially, the phenomenon of luminescence was used in the manufacture of luminous paints and light compositions based on the so-called phosphorus, for application to the scales of instruments intended for use in the dark. Luminescence did not attract much attention in the USSR until 1948, when the Soviet scientist S. I. Vavilov at the session Supreme Council proposed to start manufacturing economical fluorescent lamps and use luminescence in the analysis of chemicals. In everyday life, the phenomenon of luminescence is used most often in "daylight" fluorescent lamps and cathode-ray tubes of kinescopes. The phenomenon of light amplification, experimentally confirmed by the works of V. A. Fabrikant and underlying the scientific and technical direction of quantum electronics, is based on the use of the phenomenon of luminescence, specifically finding its application in light amplifiers and generators of stimulated radiation (lasers).

1 General characteristics
2 Types of luminescence
3 Luminescence spectra
- 3.1 Franck-Condon principle
- 3.2 Stokes-Lommel rule
- 3.3 Kashi's rule
- 3.4 Levshin's rule of mirror symmetry
4 Luminescence output
5 Luminescence quenching
6 See also
7 Literature
8 Links
9 Notes

general characteristics

"We will call luminescence the excess over the temperature radiation of the body in the event that this excess radiation has a finite duration of approximately 10−10 seconds or more." This is the canonical definition of luminescence given by the Russian scientist S. I. Vavilov in 1948. This means that the brightness of a luminescent object in the spectral range of its radiation waves is significantly greater than the brightness of an absolutely black body in the same spectral range, which has the same temperature as the luminescent body.

The first part of the definition makes it possible to distinguish luminescence from thermal radiation, which is especially important at high temperatures, when thermal radiation becomes more intense. An important feature of luminescence is that it can manifest itself at much lower temperatures, since it does not use the thermal energy of the radiating system. For this, luminescence is often called "cold glow". The duration criterion introduced by Vavilov makes it possible to separate luminescence from other types of nonthermal radiation: scattering and reflection of light, Raman scattering, and Cherenkov radiation. Their duration is less than the period of oscillation of the light wave (that is,<10−10 c).

The physical nature of luminescence consists in the radiative transitions of electrons of atoms or molecules from an excited state to the ground state. In this case, various factors can serve as the cause of their initial excitation: external radiation, temperature, chemical reactions, etc.

Substances with delocalized electrons (conjugated systems) have the strongest luminescence. Anthracene, naphthalene, proteins containing aromatic amino acids and some prosthetic groups, many plant pigments, and in particular chlorophyll, as well as a number of drugs, have a pronounced ability to luminesce. Organic substances capable of forming luminescent complexes with weakly luminescent inorganic compounds are often used in luminescence analysis. For example, fluorescein is often used in fluorescent titrimetry.

Initially, the concept of luminescence referred only to visible light. it currently applies to radiation in the infrared, visible, ultraviolet and x-ray ranges (see electromagnetic wave scale).

Many forms of natural luminescence have been known to people for a very long time. For example, the glow of insects (fireflies), the glow of marine fish and plankton, auroras, the glow of minerals, rotting wood and other decaying organic matter. At present, many artificial methods of excitation of luminescence have been added to natural forms. Solid and liquid substances capable of luminescence are called luminophores (from Latin lumen - light and other Greek phoros - carrier).

For a substance to be able to luminesce, its spectra must be discrete, that is, its energy levels must be separated by bands of forbidden energies. Therefore, metals in the solid and liquid state, which have a continuous energy spectrum, do not give luminescence. Excitation energy in metals continuously transforms into heat. And only in the short-wavelength range can metals experience X-ray fluorescence, that is, under the action of X-rays, emit secondary X-rays.

Types of luminescence

Photoluminescence of minerals under ultraviolet light

The luminescent glow of bodies is usually divided into the following types:

Photoluminescence - glow under the action of light (visible and UV range). It, in turn, is divided into
- fluorescence (lifetime 10–9–10–6 s);
- phosphorescence (10−3−10 s);
Chemiluminescence - a glow that uses the energy of chemical reactions;
Cathodoluminescence - caused by irradiation with fast electrons (cathode rays);
Sonoluminescence - luminescence caused by high frequency sound;
Radioluminescence - when a substance is excited by ionizing radiation;
Triboluminescence - luminescence that occurs when rubbing, crushing or splitting phosphors. Triboluminescence is caused by electrical discharges occurring between the formed electrified parts - the discharge light causes photoluminescence of the phosphor.
Bioluminescence is the ability of living organisms to glow, achieved independently or with the help of symbionts.
Electroluminescence - occurs when an electric current is passed through certain types of phosphors.
Candoluminescence - incandescent glow.
Thermoluminescence is a luminescent glow that occurs when a substance is heated. scientific literature often uses the term Thermally stimulated luminescence, abbreviated as TSL, which is the same thing.

At present, photoluminescence is the most studied.

There are three types of luminescence in solids:

monomolecular luminescence - acts of excitation and emission of light occur within a single atom or molecule;
metastable luminescence - acts of excitation and emission of light occur within a single atom or molecule, but with the participation of a metastable state;
recombination luminescence - acts of excitation and emission of light occur in different places.

Luminescence spectra

The luminescence spectrum is the dependence of the intensity of luminescent radiation on the wavelength of the emitted light. The simplest are atomic spectra, in which the dependence indicated above is determined only by the electronic structure of the atom. The spectra of molecules are much more complex due to the fact that various deformation and stretching vibrations are realized in the molecule. When cooled to ultralow temperatures, continuous luminescence spectra of organic compounds dissolved in a certain solvent turn into quasi-linear ones. This phenomenon is called the Shpolsky effect. This leads to a decrease in the detection limit and an increase in the selectivity of determinations, an expansion in the number of elements that can be determined by the luminescent method of analysis.

Franck-Condon principle

Part of the electronic energy during the absorption and emission of light must be spent on increasing the oscillations of the structure, and converted into heat. The phenomenon is observed as a result of a sharp change in the gradient of electron energy around nuclei during excitation and relaxation.

Stokes-Lommel rule

The luminescence spectrum, as a rule, is shifted relative to the absorption spectrum towards long wavelengths. This rule is usually explained by the loss of some part of the absorbed energy for the thermal motion of molecules. There is, however, an anti-Stokes phosphor that emits shorter wavelength radiation than the incident one. As a rule, the same substance is capable of emitting radiation in both the Stokes and anti-Stokes regions of the spectrum relative to the frequency of the radiation that excites luminescence.

Kashi's rule

Main article: Kashi's rule

Regardless of the method of excitation and the wavelength of the exciting light, the luminescence spectrum remains unchanged at a given temperature. Since the emission of luminescence quanta always occurs from the lowest electronically excited level of the molecule, the luminescence spectrum will always be the same, regardless of which energy level the electron fell to as a result of the absorption of a photon. This rule is valid only in the case of using the same excited medium, the system for detecting luminescence radiation. The set of allowed energy levels in an atom/molecule, as well as the set of wavelengths of luminescence excitation sources, makes it possible for the medium used to obtain a set of luminescence spectra in different regions of the spectrum that do not repeat each other.

Levshin's mirror symmetry rule

The spectral lines of emission and absorption in frequency coordinates are mutual mirror reflections. The position of the axis of symmetry shows the energy of a purely electronic transition. This property is mainly possessed by liquid phosphors; Recent studies have shown that it can also be valid for media in other states of aggregation.

Luminescence output

Yield is one of the most important characteristics of luminescence. Allocate quantum yield and energy yield. Under the quantum yield understand the value showing the ratio of the average number of emitted photons to the number of absorbed:

- the number of emitted quanta,
is the number of absorbed quanta.

Vavilov showed that the quantum yield in solutions does not depend on the wavelength of the exciting light. This is due to the enormous rate of vibrational relaxation, during which the excited molecule transfers excess energy to solvent molecules.

Energy yield - the ratio of the energy of emitted photons to the energy of absorbed ones:

where is the radiation frequency. As the wavelength of the exciting light increases, the energy yield first grows in proportion to the wavelength of the light that excites it, then remains constant, and after a certain limiting wavelength drops sharply downwards (Vavilov's law).

Luminescence quenching

The difference in the luminescence yield from unity is due to the so-called. quenching processes. There are concentration, internal, temperature, external static and dynamic quenching.

Internal extinguishing due to nonradiative transitions of internal conversion and vibrational relaxation. It manifests itself most clearly in symmetrical structures with a large number of conjugated bonds, conformationally non-rigid structures.

Temperature quenching is a kind of internal. Under the influence of temperature, the ability of a molecule to deform increases, and, as a result, the probability of nonradiative transitions increases.

External static extinguishing is based on the interaction of a luminescent compound with another molecule and the formation of a non-radiating product.

dynamic quenching observed when an excited phosphor molecule enters into an extraneous reaction and loses its properties.

concentration quenching- the result of the absorption by the molecules of the substance of its own radiation.

Literature

Shpolsky E. V. Atomic physics (in 2 vols.). - M.: Nauka, 1984.
Landsberg G.S. Optics. - 6th ed., stereo. - M.: FIZMATLIT, 2003. - 647 p.
Lakovich J. Fundamentals of fluorescence spectroscopy. - M.: Mir, 1986. - 496 p.
Harvey D. Modern Analytical Chemistry. - Boston, 2000. - 798 p.
Stolyarov KP, Grigoriev NN Introduction to the luminescent analysis of inorganic substances. - L., 1967. - 364 p.
Zakharov IA, Timofeev VN Luminescent methods of analysis. - L., 1978. - 95 p.

Notes

Landsberg G.S. Optics. - 6th ed., stereo. - M.: FIZMATLIT, 2003. - 848 p.

luminescence, luminescence in medicine, what is luminescence, scheelite luminescence

Luminescence Information About

Luminescence. Spectra of luminescence. Types of luminescence. Stokes' law for photoluminescence. Chemiluminescence. Luminescence microscopy.

Luminescence is called excess over thermal radiation of the body, which has a duration significantly exceeding the period (~ 10 -15 s) of the emitted light waves.

The first part of the definition separates luminescence from equilibrium thermal radiation. Luminescence is usually observed in the visible or ultraviolet regions of the spectrum. Thermal radiation in this region occurs only at a temperature of several hundred or thousand degrees, while luminescence is observed at any temperature, so luminescence is often called cold glow.

The sign of duration in this definition was proposed by S. I. Vavilov in order to distinguish luminescence from some other phenomena of secondary luminescence, for example, reflection or scattering of light.

Electronically excited molecules (atoms) luminesce. Depending on the method of excitation, several types of luminescence are distinguished.

Luminescence caused by charged particles: ions - ionoluminescence, electrons - cathodoluminescence, nuclear radiation - radioluminescence. Luminescence under the influence of X-ray and Y (gamma) radiation is called X-ray luminescence, photons of visible light - photoluminescence. When rubbing, crushing or splitting some crystals, triboluminescence occurs. An electric field excites electroluminescence, a special case of which is the glow of a gas discharge. The luminescence that accompanies an exothermic chemical reaction is called chemiluminescence.

Luminescence Spectra

Photoluminescence is the radiation of electromagnetic energy excited in a substance under the action of optical radiation in the ultraviolet or visible ranges, which is excessive compared to thermal radiation, provided that such excess radiation has a duration exceeding the period of electromagnetic oscillations (luminescence) and the time of relaxation processes. If a substance (phosphor) in any state of aggregation is irradiated with ultraviolet or visible electromagnetic radiation, then the appearance of luminescent radiation delayed by at least 10-12 - 10-10 s is possible. The maximum of the spectrum of this radiation is shifted relative to the maximum of the spectrum of the exciting radiation towards lower frequencies (the Stokes-Lommel law).

Chemiluminescence- luminescence (glow) of bodies caused by chemical exposure or during the course of a chemical reaction. Chemiluminescence is associated with exothermic chemical processes.

Chemiluminescence is used to assess the composition of complex gas mixtures, in particular, the presence of impurities in the atmosphere. The advantage of this method is the ease of measurement automation and high selectivity. The disadvantage is the limited list of analyzed substances.

Luminescence microscopy is a microscopy method that allows one to observe the primary or secondary luminescence of microorganisms, cells, tissues or individual structures that make up them.

Luminescence color, i.e. the wavelength of the emitted light depends on the chemical structure and on the physicochemical state of the microscopic object, which makes it possible to use LM. for the purposes of microbiological and cytological diagnostics, for differentiation of individual cell components.

The luminescent microscope is equipped with a powerful source of illumination with a high surface brightness, the radiation maximum of which is in the short-wavelength region of the visible spectrum, a system of light filters, and an interference beam-splitting plate used when luminescence is excited by incident light.

Light sources for a fluorescent microscope are more often mercury-quartz lamps of ultrahigh pressure, as well as incandescent lamps: xenon and quartz-halogen.

To excite luminescence in luminescent microscopy, the long-wave ultraviolet, blue-violet, and sometimes green region of the spectrum is usually used; in a luminescent microscope, glass optics and ordinary glass slides and cover glasses are usually used, which transmit radiation in this part of the spectrum and do not possess their own luminescence. Immersion and encapsulation media must also meet these requirements.

The main advantages of fluorescence microscopy are high sensitivity (more sensitive than conventional cyto- and histochemical methods by at least 1000 times), ease of quantitative measurement of the content of various chemical compounds. components of tissue and cells, the availability of equipment. For L. the m of bodies and fabrics use primary and secondary luminescence.

Spectrophotometry. Spectrofluorimetry.

Spectrophotometry- physicochemical method for studying solutions and solids, based on the study of absorption spectra in the ultraviolet (200-400 nm), visible (400-760 nm) and infrared (> 760 nm) regions of the spectrum. The main dependence studied in spectrophotometry is the dependence of the absorption intensity of incident light on the wavelength. Spectrophotometry is used in the study of the structure and composition of various compounds, for the qualitative and quantitative determination of substances (determination of trace elements in metals, alloys, technical objects). Spectrophotometric instruments - spectrophotometers.

Spectrofluorimetry. The principle is the emission of light whose wavelength is greater than the wavelength of the absorbed light. . Application - quantitative analysis, kinetics, qualitative analysis.

Laser. Boltzmann distribution. The concepts of inverse population, stimulated emission. The working substance of the laser. Types of energy pumping sources. The main components of the laser design. Features of laser radiation.

Laser is a quantum generator of the visible range of radiation.

Types of laser working substance: gas, liquid, semiconductor and solid state.

Types of energy pumping sources: excitation with very intense light - "optical pumping", electric gas discharge, in semiconductor lasers - by electric current.

Boltzmann distribution

The distribution of particles over potential energies in force fields- gravitational, electrical, etc. - called the Boltzmann distribution.

As applied to the gravitational field, this distribution can be written as a dependence of the concentration n of molecules on the height h above the Earth level or on the potential energy of the molecule m 0 gh:

This expression is valid for ideal gas particles.

The main components of the laser system design are the laser active medium, the laser pump energy, the high reflector, the coupler, and the laser beam. The laser active medium is located in a reflective optical cavity, where the pump energy is directed. The laser active medium is a material that has certain properties that make it possible to amplify light by stimulated emission. In its simplest form, this active medium cavity consists of two mirrors (one of which is transparent) arranged so that the light hops back and forth as it passes through the active medium each time.

Light, passing through the active medium, is repeatedly amplified, leaving the beam of rays from the side of the transparent mirror. The pump energy of a laser is usually supplied as an electric current or as light in various wavelengths. Such light may be provided by a lamp or other laser. Most practical lasers contain additional elements that are responsible for properties such as the wavelength of the emitted light or the shape of the beam.

Laser radiation is unique due to three properties inherent only to it.

1) Coherence. In physics, there are 2 types of coherence - spatial and temporal. Spatial coherence is expressed in the uniformity of the wave front, i.e., the peaks and decays of the waves are parallel when the light exits the laser. This ensures phase synchronization and focusing on very small areas.

2) monochrome(temporal coherence). This means that light waves have the same length. Some lasers emit beams of different wavelengths. But this phenomenon is predictable, and lasers emit light only of the length that is provided for by the medium used in the laser.

3) Collimation. This means that all beams emitted by a laser are parallel and do not scatter with distance.

51. Types of radioactive radiation. Radioactivity. Law of radioactive decay. Radioactivity is the phenomenon of spontaneous transformation of some atomic nuclei into others, accompanied by emission various kinds ionizing radiation.

The main types of radioactive decay are:

BUT alpha decay consists in the spontaneous transformation of one nucleus into another with the emission of alpha particles.

An example of alpha decay for the isotope 238 U

Beta decay consists in the extranuclear mutual transformation of a neutron and a proton.

The law of radioactive decay: the number of radioactive nuclei that have not yet decayed decreases with time according to an exponential law:

52. Ionizing radiation any radiation is called, the interaction of which with a substance leads to the formation of ions of different signs.

Interaction with matter α-radiation

α-particles interact strongly with various substances, i.e., are easily absorbed by them. A thin sheet of paper or a layer of air a few centimeters thick is sufficient to completely absorb the alpha particles.

When passing through matter, a-particles almost completely give up their energy as a result of electrostatic interaction with the electrons of the shells of atoms.

The energy of α-particles goes to ionization and excitation of the atoms of the absorbing medium (ionization losses). This process can be considered as an elastic collision of an α-particle with electrons, in which the α-particle loses some of its energy.

Interaction with matter β-radiation

β-particles are electrons (or positrons) emitted by radonuclide nuclei during β-decay.

The probability of interaction of β-particles with matter is less than for α-particles, since β-particles have half the charge and approximately 7300 times less mass.

The interaction of electrons and positrons with matter is qualitatively the same and consists of three main processes:

elastic scattering on atomic nuclei;

scattering on orbital electrons;

inelastic collisions with an atomic nucleus.

When heavy materials are used, bremsstrahlung (secondary) radiation, which is X-ray and has a high penetrating power.

Statistics.

1. Random event is an event that, under given conditions, may or may not occur. The relative frequency of events is called probability and shows the ratio of the number of expected events to the number of possible ones. Statistical definition probability implies the probability as the limit to which the relative frequency tends. With the classical definition of rel. frequency and probability are the same. In this case, the total number of possible events and the number of expected events (tails, dice, etc.) must be known. Joint Events can occur in parallel to each other; incompatible events exclude the appearance of each other in the course of the experiment. addicted An event is called an event whose probability is influenced by the outcome of some other event. Independents are the opposite.

2. Theorem addition of probabilities: the probability of occurrence of any event from several incompatible ones is equal to the sum of their probabilities (either one or the other) Probability multiplication theorem: The probability of joint occurrence of independent events is equal to the product of their probabilities (both). Conditional Probability- the probability of one event, provided that another event has already happened (experiment with balls in a bag that are pulled out and not returned)

3. Discrete. The relationship between the possible values of a random variable and their probabilities is called the distribution law of a discrete random variable (whose possible values form a finite or infinite sequence of numbers). The distribution law can be specified analytically, in the form of a table or graphically. Expected value Dispersion

4. Continuous random variables always have a probability equal to zero, since the number of its possible numerical values is infinitely large. Expected value has the meaning of the mean value of a random variable. For discrete cases. quantities, it is defined as the sum of products of cases. magnitude on the probability of its occurrence. Dispersion describes the spread of cases. values relative to the mathematical expectation. Dispersion of discrete cases. values is defined as the sum of the squares of the difference sluch. values and mathematical expectation on the corresponding probabilities of occurrence of these random variables. Standard deviation- this is Square root from the arithmetic mean of all squared differences between the given quantities and their arithmetic mean.

5. A random variable is called discrete random variable if it takes at most a countable number of values. Examples:

1) Bernoulli discrete random variable (Bernoulli distribution law). The distribution law of a discrete random variable Bernoulli has the following form: 0

This distribution corresponds to the tossing of a coin, on one side of which - 0, and on the other - 1.

2) discrete binomial random variable (binomial distribution). The distribution law of this discrete random variable will be written as follows:

The number of successes in n trials of the Bernoulli scheme has a binomial distribution.

3) Poisson discrete random variable (Poisson distribution with a parameter). The Poisson distribution law for a discrete random variable is given as follows:

Where is a parameter.

The Poisson random variable distribution law is called the law of rare events, for example, the number of calls received at the telephone exchange, the number of decayed unstable particles, etc.

4) discrete geometric random variable (geometric distribution). The distribution law of a geometric discrete random variable has the form

Let independent trials be made, and in each trial two outcomes are possible - "success" with probability p or "failure" with probability 1 - p, 0< p < 1 . Обозначим через число испытаний до первого появления "успеха", тогда будет дискретной геометрической случайной величиной.

The distribution of a random variable is called continuous, and the random variable itself - a continuous random variable, if for any

where is a Lebesgue integrable function. The function is called the distribution density of the random variable.

Examples

1) a normal continuous random variable, or a continuous Gaussian random variable (normal distribution). The important role of this distribution is explained by the fact that it usually occurs in phenomena subject to the action of a large number of small random variables. Thus, the mathematical theory of the sampling method in statistics makes extensive use of the normal distribution to calculate certain indicators.

2) exponential (exponential) continuous random variable (exponential distribution). Exponential distribution is subject to the decay time of the nuclei of atoms of various elements. It has an important property - the absence of consequences. It is easy to verify that the probability of the decay of the nucleus in time, provided that before that it has already lived through time, coincides with the unconditional probability of the decay of the same nucleus in time. It is this property that represents the absence of a consequence.

3) Uniform on a continuous random variable (uniform distribution on a segment). Uniform distribution implements the principle of geometric probability when throwing a point on a segment.

Bernoulli's law: number of expected events that appear in trials with n independent trials, in which the expected events have the same probability p or:

Expected value

Let be a random variable defined on some probability space. Then where the symbol M denotes the mathematical expectation.

6. see ticket 5

Poisson distribution law: satisfies the probability of occurrence of a given number of rarely occurring random events observed in a series of a large number of independent repeated experiments. The probability is much less than 1.

Where m is the number of expected events, a is the distribution parameter coinciding with the mathematical expectation, e is the base of the natural logarithm. The Poisson distribution is satisfied by the number of rare events that occur in a certain period of time.

7. Continuous and discrete random variables. Probability Density. Normal distribution law. Mathematical expectation and dispersion. Graphical representation. Examples.

Discrete random variables are variables that can take on a countable number of values, finite or infinite.
example: the number of passengers in a vehicle.

Continuous random variables are quantities. Which take on an infinite number of possible values in a finite, or in an infinite range of changes
example: time, mass, volume, body temperature.

The probability density f(x) of a continuous random variable X is the derivative of the distribution function F(X) of this variable: f(x)=F’(X)

Basic density properties:
one). The probability density is a non-negative function: f(x)>0
2) the probability that as a result of the test is continuous. Case. The value will take any value from the interval (a, b), equal to a certain integral (in the range from a to b) of the probability density of this random variable.

3). The definite integral in the range from minus infinity to plus infinity from the probability plane of a continuous random variable is equal to one ..

4) a definite integral ranging from "-" infinity to x from the probability density of a continuous random variable is equal to the distribution function of this variable.

where parameter μ σ ² - dispersion.

8. Standard normal distribution. standard intervals. Concepts of Confidence Interval and Confidence Probability.

A confidence interval is an interval constructed using a random sample from a distribution with an unknown parameter such that it contains the given parameter with a given probability.

Let be a sample from some distribution with a density depending on a parameter that can vary in the interval . Let be some statistics and be the distribution function of the random variable when the sample has a distribution with a density . Suppose there is a decreasing function of the parameter . Denote the distribution quantile , then there is an increasing function of . Let us fix a positive number close to zero (for example, 0.05 or 0.01). Let . For every inequality

performed with a probability close to one. Let us rewrite inequalities (1) in another form:

(2)

Denote , and write (2) in the following form:

The interval is called confidence interval for the parameter, and the probability is confidence level.

The normal distribution, also called the Gaussian distribution, is a probability distribution that is given by a distribution density function:

where parameter μ - the average value (expectation) of a random variable and indicates the coordinate of the maximum distribution density curve, and σ ² - dispersion.

Graphs of normal distribution

9. The concept of the general population and sampling. Sample size, representativeness. Statistical distribution (variation series). Examples. Sample characteristics.

The general population is a set of any homogeneous elements that are to be studied by statistical methods; the set of all values of a random variable, and the variant is one of the values of the general population.

A sample is a certain part of the elements selected according to a certain rule from a gene. aggregates.

The sample size is the number of selected elements in the general population. The minimum statistically acceptable sample size is considered to be three items.

The sample is made in order to describe the general population. If this description is complete and correct, then the sample is representative. The results of repeated measurements of any physical quantity x, carried out under the same conditions, are often called a sample from an infinite general population, since it is believed that in the experiment it is theoretically possible to make an arbitrarily large number of measurements under the same conditions, and the set of all possible measurement results forms this the general population. The mathematical expectation of such a general population is considered the true value of the measured quantity. Thus, in the course of several repeated measurements of a physical quantity, a set of results is obtained, which is a sample of volume n: x 1, x 2, ... .., x n, where n is the number of repeated measurements. Both discrete and continuous, random variables can be obtained as a result of experience - observation - that is, in the form of a variational series: 4.67; 5.49; 5351 and so on. However, this way of setting is uninformative - requiring additional processing, for any even superficial idea of a random variable.

Selected features include:

average value (X cf), as an estimate of the mathematical expectation

sample standard deviation (S x), as an estimate of the general value of the standard deviation (σ) sample variance (S x 2)

N - number of sample elements

№ 10 Point estimates of the parameters of the general population.

Let the sample volume n presented in the form of a variation series. Let's call sample mean value

The value is called relative frequency feature values x i. If the values of the attribute obtained from the sample are not grouped and presented as a variation series, then the formula must be used to calculate the sample mean.

Sample variance

Here is another example of a point estimate. Let each object of the general population be characterized by two quantitative features x and y. For example, a part can have two dimensions - length and width. It is possible to measure the concentration of harmful substances in the air in different areas and record the number of pulmonary diseases of the population per month. It is possible to compare the profitability of the shares of a given corporation at regular intervals with some index characterizing the average profitability of the entire stock market. In this case, the population is a two-dimensional random variable x,h . This random variable takes the values x,y on a set of objects of the general population. Without knowing the law of the joint distribution of random variables x and h, we cannot speak about the presence or depth of the correlation between them, however, some conclusions can be drawn using the sampling method.

Sampling volume n in this case, we present it in the form of a table, where
i-th selected object ( i= 1,2,...n) is represented by a pair of numbers x i, y i :

x 1	x 2	...	x n
y 1	y 2	...	y n

The sample correlation coefficient is calculated by the formula

, ,

The sample correlation coefficient can be considered as a point estimate of the correlation coefficient r x h characterizing the general population.

Sample parameters or any others depend on which objects of the general population were included in the sample and differ from sample to sample. Therefore, they themselves are random variables.

Let the sample parameter d be considered as a sample estimate of the parameter D of the general population and, at the same time, the equality

M d = D .

This sampling is called unbiased.

To prove the unbiasedness of some point estimates, we will consider a sample of size n as a system n independent random variables x 1 ,x 2 ,... x n, each of which has the same distribution law with the same parameters as the random variable x representing the population. With this approach, the equalities become obvious: Mx i = M x i=M x;
Dx i = D x i s n parameter D the general population is called wealthy, if it converges in probability to D . This means that for any positive numbers e and g there is such a number n e g, which for all numbers n satisfying the inequality n > n e g the condition . and are unbiased, consistent, and efficient estimates of the quantities Mx and Dx.

Interval estimates.

Point estimates of the parameters of the general population can be taken as indicative, initial results of processing sample data. Their disadvantage is that it is not known with what accuracy the parameter is estimated. If for large samples the accuracy is usually sufficient (under the condition of unbiasedness, efficiency and consistency of the estimates), then for small samples the question of the accuracy of the estimates becomes very important.

Let us introduce the concept of an interval estimate of an unknown parameter of the general population (or a random variable x defined on the set of objects of this general population). Let's denote this parameter by D. Based on the selection made, according to certain rules, we find the numbers D 1 and D 2 so that the condition is fulfilled:

P(D 1 <D<D 2) =P (DÎ( D 1 ; D 2)) = g

Numbers D 1 and D 2 are called trust boundaries, interval ( D 1 , D 2) - confidence interval for parameter D. The number g is called confidence level or reliability the assessment made.

Reliability is set first. Usually it is chosen equal to 0.95, 0.99 or 0.999. Then the probability that the parameter of interest to us fell into the interval ( D 1 , D 2) is quite high. Number ( D 1 + D 2) / 2 - the middle of the confidence interval - will give the value of the parameter D With precision (D 2 – D 1) / 2, which is half the length of the confidence interval.

Borders D 1 and D 2 are determined from sample data and are functions of random variables x 1 ,x 2 ,...,x n, and hence the random variables themselves. Hence, the confidence interval ( D 1 , D 2) is also random. It can cover the parameter D or not. It is in this sense that a random event should be understood, which consists in the fact that the confidence interval covers the number D.

11. Graphical characteristics of random variables. Bar chart. Position characteristics (mode, median, sample mean).

LUMINESCENCE(from Latin lumen, genus case luminis - light and -escent - a suffix meaning weak action), a glow in the islands that occurs after it absorbs the energy of excitation. Represents an excess over thermal radiation, emitted in-tion at a given t-re due to its internal (thermal) energy. Unlike other types of luminescence (eg, light scattering, bremsstrahlung), luminescence is characterized by a glow time that is much longer than the oscillation period of the light wave and ranges from 10 -12 s to several. days. The concept of luminescence is applicable only to such a substance (a collection of particles), the state of which does not differ too much from thermodynamic equilibrium, otherwise the distinction between luminescence and thermal radiation loses its meaning. The mechanism of luminescence is the formation under the action of energy from external. or int. source of excited states of atoms, molecules, crystals and last. their emission of light quanta (photons). According to the type of excitation, photoluminescence (the source of excitation energy is light), radioluminescence (radioactive radiation), X-ray luminescence (X-ray radiation), electroluminescence (electric field), cathodoluminescence (electron beam), triboluminescence (mechanical effect), chemiluminescence (chemical solutions), etc. There are molecular luminescence, in which molecules or atoms emit photons upon transition from excited state to the ground quantum state, and recombination luminescence, when charge carriers (electrons and holes in crystal phosphors) or ions and radicals (in gases, liquids, glasses) are formed under the action of excitation energy, the latter. recombination to-rykh is accompanied by the emission of photons. Radiate the transition from the excited state to the ground occurs spontaneously (spontaneous luminescence) or under the action of an external. electromagnetic radiation (induced luminescence). Light emission can occur not necessarily by the same molecules that are excited when energy is absorbed, but also by others, if it occurs without radiation. transfer of excitation energy (sensitized luminescence). Luminescence is characterized by an emission spectrum (photoluminescence is also an excitation spectrum), quantum yield, polarization, decay kinetics. This article discusses the pier. photoluminescence, which is widely used in technology and analyte. chemistry (see Luminophores, Luminescent analysis), photochemistry and chem. kinetics to study St. in excited states of particles and very fast chem. districts, in photobiology, biochemistry and medicine to study St. in biol. objects and mechanism biol. processes. For other types of luminescence, see Crystal phosphors, X-ray spectroscopy, Chemiluminescence.
Luminescence mechanism. Molecular photoluminescence is subdivided into fluorescence and phosphorescence. Fluorescence is characterized by a short duration (less than 10 -6 s) and is due to the emission of photons during the transition of the system from an excited state of the same multiplicity as the ground state. Phosphorescence - long glow (from fractions to several tens of seconds), a cut occurs during the transition to the main. a state from an excited state of a different multiplicity; such a transition occurs in violation of the spin selection rule (see ). For most org. molecules with an even number of electrons DOS. the state is singlet, and the lowest excited states have a multiplicity of 1 and 3, i.e., they can be singlet and triplet. For such molecules, fluorescence is radiant. transition to main state S 0 from the excited singlet state S 1 (transition 2 in Fig. 1).

j L = j i k E t i .

As a rule, for excited singlet states j i = 1, for triplet states j i [ 1. If j i does not depend on the frequency of the exciting light, Vavilov's law is fulfilled, according to Krom the quantum yield of luminescence is constant in the given range of frequencies of the exciting light. Deviations from the Vavilov law arise if, upon excitation to higher electronic states, new ways of deactivation of excited molecules appear that compete with the internal. conversion to lower excited state. The constant k E can be calculated from the quantum transition moment M 21 =< Y 2 | m | Y 1) between two electronic-vibrational (vibronic) states described by wave functions Y 2 and Y 1 (m is the dipole moment operator):

(c - speed of light, n - index of refraction in-va, n - transition frequency). Experimentally, the values of k E in the case of fluorescence are determined from the integral of the long-wavelength band of the absorption spectrum:

where N A - Avogadro's constant, - wave number (cm- one). e () - molar decimal coefficient. absorption (in dm 3. mole- one . cm - 1), <>- average value in the fluorescence spectrum:
where F() is the dependence of the number of emitted photons on wave number. For polyatomic molecules with a typical half-width of the absorption band of the order of several. thousand cm - 1 the approximate expression is valid:

k E ~ 10 4 e max

(e max - molar decimal factor. absorption at the maximum of the band).
Kinetics of luminescence. In simple systems they say. luminescence after short excitation (compared with t i) the light pulse usually decays exponentially. law: I(t) = I 0 exp(-t/ t i), where I 0 is the initial radiation intensity, t is the current time. Value, reciprocal t i , is equal to the sum of the rate constants k j of all emitted. and they don't radiate. (including chem. p-tion) processes of death of a given excited state: 1 / t i = S j k j . For many rigid molecules (aromatic hydrocarbons, heterocyclic compounds and some of their derivatives) t i is determined by Ch. arr. rate constant k ISC intercombination. conversion from the S 1 state to one of the triplet states with lower energy. The value of k ISC , in turn, depends on the symmetry of the electronic wave functions of both states. So, for a transition between states of the same nature [for example, 1 ( p, p *) and 3 (p, p *)] k ISC has a value of the order of 10 7 -10 8 s - 1 , and for states decomp. nature [e.g. 1 ( p, p *) and 3 (n, p *) or 1 (n, p *) and 3 (p, p *)] it is 10 10 -10 11 s - one . As a result, molecules , for which, for example, the state S 1 has 1 (n, p *) nature, and the state T 1 3 ( p,p *) is characterized by lower energy, practically does not fluoresce, but has a high quantum yield of the formation of excited triplet states and phosphoresces in the solid phase. In nonrigid molecules, the processes of ext. conversions resulting in relaxation of the electronic excitation energy and the absence of both fluorescence and phosphorescence. In solid solutions, the lifetime of a molecule in the triplet state is determined by Ch. arr. radiate rate constants. intercombination transition T 1: S 0 and are nonradiative. electronic oscillatory. energy transfer to relatively high-frequency vibrations of C-H, O-H bonds, etc. in the same molecule or in the p-solvent molecule. Therefore, the quantum yield of phosphorescence j I only in several times less than the quantum yield j I formation of triplet states: j P [ j I = k ISC t S , where t S is the lifetime of the state S 1 . In deuterated p-solvents, the energy transfer is greatly slowed down and j I approaches the reciprocal of the rate constant radiate. intercombination transition 1/k P (and can reach 10 2 s), and the quantum yield of phosphorescence increases. In liquid solutions, effective quenching of triplet excited states by impurities (including dissolved

Luminescence: types, methods, application. Thermally stimulated luminescence - what is it? Franck-Condon principle and laws of fluorescence. Luminescence of biologically important molecules. Mechanisms of energy migration The luminescence spectrum depends on

general characteristics

Types of luminescence