Big encyclopedia of oil and gas. Absorption (absorption) of light by a substance
In physics for grade 11 (Kasyanov V.A., 2002),
task №87
to chapter " Quantum theory of electromagnetic radiation. MAIN PROVISIONS».
thermal radiation
Completely black body
thermal radiation- electromagnetic radiation emitted by heated bodies due to its internal energy.
Completely black body- a body that absorbs all the energy of radiation incident on it of any frequency at an arbitrary temperature.
Spectral density of energy luminosity is the energy of electromagnetic radiation emitted per unit of time per unit area of the body surface in a unit frequency interval. Unit of spectral density of energy luminosity J/m 2 . The energy of a radiation quantum is directly proportional to the frequency v of the radiation:
where h = 6.6 10 -34 J s is Planck's constant.
Photon- microparticle, quantum of electromagnetic radiation.
Laws of Thermal Radiation: Wien's Displacement Law
where λm is the wavelength at which the maximum spectral density of the blackbody energy luminosity falls, T is the temperature of the blackbody, b ≈ 3000 µm K is Wien's constant.
Stefan-Boltzmann law: The integral luminosity of a black body is proportional to the fourth power of its absolute temperature:
where σ =
5.67 10 -8 W / (m 2 K 4) - Stefan-Boltzmann constant.
photoelectric effect the phenomenon of ejection of electrons from solid and liquid substances under the action of light.
Laws of the photoelectric effect
1. The saturation photocurrent is directly proportional to the intensity of the light incident on the cathode.
2. The maximum kinetic energy of photoelectrons is directly proportional to the frequency of light and does not depend on its intensity.
3. For each substance there is a minimum frequency of light, called the red limit of the photoelectric effect, below which the photoelectric effect is impossible.
Einstein's equation for the photoelectric effect:
The energy of the photon is used to perform the work function and to communicate the kinetic energy to the emitted photoelectron. The work function is the minimum work that must be done to remove an electron from a metal.
red border photo effect
Corpuscular-wave dualism - manifestation in the behavior of the same object of both corpuscular and wave properties. Corpuscular-wave dualism is a universal property of any material objects.
wave theory correctly describes the properties of light at high intensities, i.e. when the number of photons is large.
Quantum theory is used to describe the properties of light at low intensities, i.e. when the number of photons is small.
Any particle with momentum p Answer the de Broglie wavelength is:
The state of the micro-object changes during the measurement process. Simultaneous precise determination of the position and momentum of a particle is impossible.
Heisenberg uncertainty relations:
1. The product of the uncertainty of the particle's coordinate and the uncertainty of its momentum is not less than Planck's constant:
2. The product of the uncertainty of the energy of a particle and the uncertainty of the time of its measurement is not less than Planck's constant:
Bohr's postulates:
1. In a stable atom, an electron can only move along special, stationary orbits, without radiating electromagnetic energy
2. The emission of light by an atom occurs during the transition of an atom from a stationary state with a higher energy E k to a stationary state with a lower energy Е n . The energy of the emitted photon is equal to the difference between the energies of the stationary states:
Bohr's orbit quantization rule:
On the circumference of each stationary orbit fits an integer n of de Broglie wavelengths, with Answer corresponding to the motion of an electron
Ground state of the atom is the state of minimum energy.
Luminescence- non-equilibrium radiation of matter.
Spectral analysis- a method for determining the chemical composition and other characteristics of a substance by its spectrum.
Basic radiative processes of atoms: absorption of light, spontaneous and stimulated emission.
light absorption is accompanied by the transition of the atom from the ground state to the excited state.
Spontaneous emission- radiation emitted during the spontaneous transition of an atom from one state to another.
stimulated emission- radiation of an atom that occurs when it passes to a lower energy level under the influence of external electromagnetic radiation.
Laser- source of radiation amplified as a result of induced radiation.
Inverse population of energy levels- non-equilibrium state of the medium, in which the concentration of atoms in the excited state is greater than the concentration of atoms in the ground state.
Metastable state- the excited state of the atom, in which it can be much longer than in other states.
2.7.Elementary quantum theory of emission of electromagnetic radiation by atoms [email protected]
If an atom is given additional energy, then it can go into an excited state (for example, for hydrogen, transitions from a state with n = 1 to states with n = 2, 3, 4, ... see Fig. 15). The excitation of atoms can be initiated in various ways: due to collisions with elementary particles - shock excitation, in collisions with atoms - thermal excitation, and, finally, when atoms absorb electromagnetic radiation. For the transition from the ground state to an excited atom with the main quantum number n, it is necessary to transfer energy equal to the difference between the energies of the E n and E 1 states. If energy is transmitted by electromagnetic radiation with a continuous spectrum of frequencies, then quanta with energies will be absorbed from this radiation by an atom. If we use expression (2.3) for possible energies, then we obtain a formula for a series of absorption frequencies of the hydrogen atom, which fully corresponds to the experimental data
.
(2.9)
If the energy transferred to the electron is large enough, then the electron can overcome the force of attraction to the nucleus and break away from the atom. This process is called the ionization of an atom. Figure 15 shows that the minimum energy required for the ionization of a hydrogen atom (transition n = 1n =), is equal to 13.6 eV. This value agrees well with the experimental data for the ionization energy of the hydrogen atom.
An atom cannot stay in an excited state for a long time. Like any physical system, the atom tends to occupy the state with the lowest energy. Therefore, after a time of about 10 -8 s, the excited atom spontaneously (spontaneously) passes into a state with a lower energy, emitting a quantum of radiation energy during the transition. This process continues until the atom is in the ground state (Fig. 16). The totality of all possible frequencies or wavelengths of the radiation of an atom is called the emission spectrum (when analyzing radiation with a spectroscope, they correspond to a set of spectral lines). If the structure of the energy levels of an atom is determined, then the spectra of possible radiations of a given atom can also be calculated. For example, using (2.12) for the hydrogen atom and Planck's formula 
, one can obtain a general formula describing all experimental series of hydrogen emission (1.1)-(1.3) ,
Fig.16. Possible transitions for the hydrogen atom.
If an atom passes from one quantum state to another with the emission or absorption of a photon, then only such transitions are possible for which the orbital quantum number changes by unit l =1. This rule is called the selection rule. The presence of such a selection rule is due to the fact that electromagnetic radiation (photon) carries away or introduces not only a quantum of energy, but also a quite definite angular momentum, which changes the orbital quantum number for an electron by one. Due to these features, each atom has its own individual radiation spectrum and absorption spectrum, which fully identify it (Fig.16).
Science, 1976. - 664 p.
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§ 5.
The elementary theory of radiation based on quantum concepts was created by Einstein. It has to some extent a phenomenological character. However, it allows
d) Einstein's assumptions are fully substantiated in modern quantum electrodynamics (see, for example, A. I. Akhiezer, V. B. Berestetsky, Quantum Electrodynamics, " Science, 1969).
ELEMENTARY QUANTUM THEORY OF RADIATION
31
based on modern quantum mechanics, to solve the problem of the intensities of radiation and absorption of light.
From a quantum point of view, the intensity of emission or absorption of electromagnetic radiation is determined by the probability of the transition of an atom from one state to another. The solution of the problem of intensities is reduced to the calculation of these probabilities.
Consider two states of some system, for example, an atom. One will be denoted by the letter /i, and the other by the letter p. Let the energy of the first state be Et, and the second En. For definiteness, let us assume that Em > Enu, so that the state m belongs to a higher quantum level Etu than the state n, which belongs to the quantum level En.
Experience shows that a system can by itself pass from a higher state m to a lower state n, emitting a quantum of light
E ~E
\u003d Et - En with frequency co \u003d
having, in addition, a certain polarization and propagating inside the solid angle dQ (Fig. 6). Any polarization for a given direction of light propagation can be represented as the sum of two independent polarizations 1A and 12, perpendicular to each other. In the transition Em -+¦ En, a light quantum can be emitted either with a polarization of 1b or with a polarization of 12. We will mark the polarization with the index a (a = 1.2). Transition probability n
? __g
in 1 sec, with the emission of a quantum of frequency co = - inside the body
angle dQ with polarization a, we denote by
dW"r = anmadQ. (5.1)
This probability is called the probability of "spontaneous" (spontaneous) transition. The possibility of such a transition in the classical theory corresponds to the radiation of an excited oscillator.
If there is radiation surrounding an atom, then it affects the atom in two ways. Firstly, this radiation can be absorbed, and the atom will pass from the lowest state n to the highest m. The probability of such a transition in 1 sec will be denoted by dWa. Secondly, if the atom is in an excited state m, then external radiation can facilitate the transition of the atom to the lowest state n so that the probability of radiation increases by some value dW "r. We will call this additional probability the probability of the induced
O
Rice. 6. Characteristics of radiation.
li and 12 are two independent polarization directions.
32
FOUNDATIONS OF QUANTUM THEORY
[CH. I
(or forced) transition. Both types of transitions have an analogy in the classical theory: an oscillator under the influence of external radiation can both absorb and radiate energy, depending on the ratio of the phase of its oscillations and the phase of the light wave.
According to what has been said, the total probability of radiation is equal to
dWr = dW"r + dW"r.
The probability of absorption dWa and the probability of stimulated emission dWr, according to Einstein's assumption, are proportional to the number of light quanta of just the sort of absorption and emission of which we are talking. Let's define this number.
Radiation can be, generally speaking, not monochromatic, have different directions of propagation and different polarizations. To determine the nature of the radiation, we introduce the quantity pa (co, Q) dco dQ, which gives the energy density of radiation having a direction of propagation within the solid angle dQ, a polarization a, and a frequency lying within co, co + dco. Since the energy of a quantum is equal to Jco, the number of light quanta with a frequency within the limits co, co + dco, which propagate in a solid angle dQ and have a polarization a, is equal to (per 1 cm3)
pa(a), Q) d(d dQ fid)
Based on the remark about the proportionality between the number of quanta and the probabilities of absorption and stimulated emission, we can put
d№e = Cpa(<0, Q)dQ, (5.2)
dw; = bnm*Pa (co, Q) dQ. (5.3)
The quantities anma, b "nla, bnma are called Einstein's differential coefficients. They depend only on the kind of systems that emit and absorb light, and can be calculated by the methods of quantum mechanics (see § 88). However, some general conclusions can be made about the properties of these coefficients without their calculations.
Let us consider the conditions under which the equilibrium between emission and absorption takes place. Let the number of atoms in the excited state m be n, and the number of atoms in
living in the lowest state, - paragraphs. Then the number of light quanta emitted in 1 sec during the transitions w-> n will be equal to
nm(dW"r + dW;),
and the number of quanta absorbed in 1 sec during transitions n-> m, will be equal to
pp dWa.
ELEMENTARY QUANTUM THEORY OF RADIATION
33
Under equilibrium conditions, the number of absorption events should be equal to the number of emission events, i.e.
nadw * \u003d nm (dW "r + dW;).
Substituting here dW"r from (5.1) and d\V„, dW"r from (5.2) and (5.3), we find after reduction by dQ:
Absorption (absorption) of light by a substance. Booger's law. Elementary quantum theory of emission and absorption of light. Spontaneous and forced transitions. Einstein coefficients. Light amplification condition
Elementary quantum theory of emission and absorption of light. The condition of amplification of light Under the action of the electromagnetic field of a light wave passing through the substance, oscillations of the electrons of the medium arise, which is the reason for the decrease in the radiation energy spent on excitation of the oscillations of the electrons. Partially, this energy is replenished as a result of the emission of secondary waves by electrons; in part, it can be converted into other types of energy. Indeed, it was experimentally established and then theoretically proved by Bouguer that the intensity ...
59. Absorption (absorption) light substance. Booger's law. Elementary quantum theory of emission and absorption of light. Spontaneous and forced transitions. Einstein coefficients. Light amplification condition
Under the action of the electromagnetic field of a light wave passing through a substance, oscillations of the electrons of the medium arise, which is the reason for the decrease in the radiation energy spent on the excitation of electron oscillations. This energy is partly replenished as a result of the emission of secondary waves by electrons, and partly it can be converted into other types of energy. If a parallel beam of light (a plane wave) is incident on the surface of a substance with an intensity I , then these processes cause a decrease in the intensity I as the wave penetrates the material. Indeed, it was experimentally established, and then theoretically proved by Bouguerre, that the radiation intensity decreases in accordance with the law(Bouguerre's law):
, (1)
where is the intensity of the radiation entering the substance, d is the layer thickness, is the absorption coefficient depending on the type of substance and the wavelength. We express the absorption coefficient from the Bouguer law:
. (2)
The numerical value of this coefficient corresponds to the thickness of the layer, after passing through which the intensity of the plane wave decreases in e = 2.72 times. By measuring experimentally the intensity values I 1 and I 2 , corresponding to the passage of light beams of the same initial intensity through layers of matter with a thickness and, accordingly, it is possible to determine the value of the absorption coefficient from the relation
. (3)
The dependence of the absorption coefficient on the wavelength is usually presented in the form of tables or graphs (a set of passports for color filters). An example is in Figure 1.
They have a particularly intricate lookabsorption spectra of metal vapors at low pressure, when the atoms can practically be considered as not interacting with each other. The absorption coefficient of such vapors is very small (close to zero) and only in very narrow spectral intervals (several thousandths of a nanometer wide) are sharp maxima found in the absorption spectra (Figure 2).
The noted regions of sharp absorption of atoms correspond to the frequencies of natural vibrations of electrons inside atoms. If we are talking about the absorption spectra of molecules, then absorption bands corresponding to the frequencies of natural vibrations of atoms in the molecule are also recorded. Since the masses of atoms are much greater than the mass of an electron, these absorption bands are shifted to the infrared region of the spectrum.
The absorption spectra of solids and liquids, as a rule, are characterized by broad absorption bands. In the absorption spectra of polyatomic gases, broad absorption bands are recorded, while the spectra of monatomic gases are characterized by sharp absorption lines. Such a difference in the spectra of monatomic and polyatomic gases indicates that the reason for the expansion of the spectral bands is the interaction between atoms.
Bouguer's law is fulfilledin a wide range of light intensities (as established by S.I. Vavilov, with a change in intensity of 10 20 times), in which the absorption index does not depend on either the intensity or the layer thickness.
For substances with a long lifetime of the excited state at a sufficiently high light intensity, the absorption coefficient decreases, since a significant part of the molecules is in an excited state. Under such conditionsBouguer's law is not fulfilled.
Considering the question of the absorption of light by a medium whose density is not everywhere the same, Bouguer argued that "light can undergo equal changes only when it encounters an equal number of particles capable of delaying rays or scattering them", and that, therefore, "not thicknesses" matter for absorption. , but the masses of the substance contained in these thicknesses. This second Bouguer's law is of great practical importance in studying the absorption of light by solutions of substances in transparent (virtually non-absorbing) solvents. The absorption coefficient for such solutions is proportional to the number of absorbing molecules per unit length of the light wave path, that is, the concentration of the solution with :
where A is a proportionality coefficient that depends on the type of substance and does not depend on concentration. After taking this ratio into account, Bouguer's law takes the form:
Coefficient Independence Assertion BUT from the concentration of a substance and its constancy is often called Beer's (or Beer's) law. The physical meaning of this statement is that the ability of molecules to absorb radiation does not depend on the surrounding molecules. However, there are numerous exceptions to this law, which is therefore a rule rather than a law. The value of the quantity BUT varies for closely spaced molecules; It also depends on the type of solvent. If there are no deviations from the generalized Bouguer's law, then it is convenient to use it to determine the concentration of solutions.
The absorption spectra of substances are used for spectral analysis, that is, to determine the composition of complex mixtures (qualitative and quantitative analysis).
The absorption of radiation by matter is explained on the basis of quantum concepts. Quantum transitions of an atomic system from one stationary state to another are due to the receipt or transfer of energy by this system to other objects or its radiation into the space surrounding the atom. Transitions in which an atomic system absorbs, emits, or scatterselectromagnetic radiation, are called radiative (or radiative). Each radiative transition between energy levels and in the spectrum corresponds to a spectral line characterized by the frequency and some energy characteristic of the radiation emitted (for emission spectra), absorbed (for absorption spectra) or scattered (for scattering spectra) by an atomic system.Transitions during which there is a direct exchange of energy of a given atomic system with other atomic systems (collisions, chemical reactions, etc.) are callednon-radiation(or non-radiative).
The main characteristics of the energy level are:
degree (multiplicity) of degeneracy, or statistical weightis the number of different stationary states (state functions) to which the energy corresponds;
– population is the number of particles of a given type per unit volume that have energy;
excited state lifetimeis the average duration of a particle in a state with energy.
The spectral position of the line (stripe), i.e. line frequency can be determined by applyingBohr frequency rule
. (4)
Quantum transitions are characterized by the Einstein coefficients, the physical meaning of which will be explained later.
On the example of the simplest - two-level - system, we analyze,what internal characteristics of the atomic system determine the intensity of the spectral line. Let and be two energy levels of an isolated atomic system (atom or molecule), the population of which will be respectively denoted N 1 and N 2 (Figure 3).
The number of particles per unit volume that make in time dt in the stationary mode of excitation, transitions accompanied by takeover energy of electromagnetic radiation, we define in accordance with the formula:
, (5)
where is the volume spectral energy density of the external (exciting) radiation, the frequency of which is .
In this case, particles transferred to an excited state with energy in a unit volume of matter,energy is absorbed
. (6)
It can be seen from expression (5 ) that
(7)
is probability of transition per unit time, accompanied by absorption, per particle. Thus, Einstein coefficienthas a probabilistic (statistical) meaning.
The process of emission of electromagnetic radiation can occur in accordance with two mechanisms: spontaneously (due to internal causes) and forced (when exposed to exciting radiation).
The total number of particles making per time dt spontaneous transitions, is directly proportional to the population of the level corresponding to the initial state of the system:
. (8 )
energy electromagnetic radiation, spontaneously emittedatoms (molecules) that arein a unit volume of a substance, during, can be represented as:
. (9 )
From formula (8 ) we express the value:
(10 )
Einstein coefficient meaningful the probability of a transition accompanied by spontaneous emission of electromagnetic radiation by one particle per unit of time.
Stimulated emission occurs under the action of external (forcing) radiation. in the considered system of levels directlyNumber of forced radiative transitions over time dt in proportion to the population N 2 level corresponding to the initial state of the system ( E 2 ) and the volume spectral energy density of the external (exciting) radiation u 12 :
. (11 )
The energy of stimulated radiation emitted in a unit volume of matter in a time dt , we write it in the form:
. (12)
From formula (11) it is easy to extract the quantity
(13)
the probability of a transition made by one particle per unit of time and accompanied by stimulated emission. Here - Einstein coefficient for stimulated radiative transitions.
H and on the basis of the above ideas,relations between the Einstein coefficients, for the considered transitions having the form:
, (14)
where and are the statistical weights of the energy levels and.
Thus, internal parameters of an atomic system that determine the energy of electromagnetic radiation absorbed or emitted by a substance, and, consequently, the intensity of spectral lines in the recorded spectrum, aretransition probabilities per unit time, that is, the Einstein coefficients.
At relatively low values of the volume density of the exciting radiation, the total emission probability is almost completely determined by the probability of spontaneous transitions with energy emission. At high irradiation power, the probability of stimulated emission can become much greater than the probability of spontaneous emission. Such a situation takes place in the active medium of a generating laser, as well as when a laser is used as a source of exciting radiation.
Thus , there is only one type of elementary processes that can be used to amplify optical radiation, namely: stimulated transitions with radiation. In accordance with expression (13), the probability of such transitions can be increased by increasing the spectral energy density of the "forcing" radiation. On the other side, c with a certain probability, the number of forced transitions per unit time, which determines the power of stimulated emission, also depends on the population of the upper energy level N2.
The balance of energy per unit volume of matter, emitted per unit time as a result of forced transitions and absorbed as a result of forced transitions with excitation of the atom, can be represented as:
(16)
Given that g 1 B 12 = g 2 B 21 , formula (16) can be rewritten as:
. (17)
Under natural conditions, in accordance with the Maxwell-Boltzmann distribution, always and∆W< 0, i.e. propagation of radiation in a medium is necessarily accompanied by a decrease in its intensity.
In order for the medium to amplify the radiation incident on it (∆W > 0), it is necessary that the conditionor (in the absence of degeneracy) N 2 > N 1 . In other words, the equilibrium distribution of populations must be broken in such a way that states with higher energy are more populated than states with lower energy.
A medium that is in a non-equilibrium state, in which the population distribution for at least two energy levels is inverted (inverted) with respect to the Maxwell-Boltzmann distribution, is called inverse. Such environments havenegative absorption coefficientα (see (1) - Bouguer's law), i.e. when radiation passes through them, its intensity increases.Such environments are called active . To amplify light in an active medium, the energy emitted per unit time must exceed the total energy losses due to the absorption of radiation in the medium and useful losses, that is, the removal of radiation from the medium in the direction of radiation propagation(for example, useful losses are the laser radiation energy).
Figure 2 - Fragment of the conditional
absorption spectrum
rarefied gas
EMBED Equation.3
Figure 1 - Sample spectral dependence of the coefficient
takeovers
Figure 3 - Varieties of radiative transitions of particles
in the simplest two-level system
hv ik
hv ik
hv ik
hv ik
E 2
E 1
AT 12
A 21
AT 21
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Under the action of the electromagnetic field of a light wave passing through a substance, oscillations of the electrons of the medium arise, which is the reason for the decrease in the radiation energy spent on the excitation of electron oscillations. This energy is partly replenished as a result of the emission of secondary waves by electrons, and partly it can be converted into other types of energy. If a parallel beam of light (a plane wave) is incident on the surface of a substance with an intensity I, then these processes cause a decrease in the intensity I as the wave penetrates the material. Indeed, it was experimentally established and then theoretically proved by Bouguer that the intensity of radiation decreases in accordance with the law (Bouguer's law):
where is the intensity of the radiation entering the substance, d is the layer thickness, is the absorption coefficient depending on the type of substance and the wavelength. We express the absorption coefficient from the Bouguer law:
The numerical value of this coefficient corresponds to the layer thickness , after passing through which the intensity of the plane wave decreases in e= 2.72 times. By measuring experimentally the intensity values I 1 and I 2, corresponding to the passage of light beams of the same initial intensity through layers of matter with a thickness and, accordingly, it is possible to determine the value of the absorption coefficient from the relation
The dependence of the absorption coefficient on the wavelength is usually presented in the form of tables or graphs (a set of passports for color filters). An example is in Figure 1.
The absorption spectra of metal vapors at low pressure have a particularly intricate form, when the atoms can practically be considered as not interacting with each other. The absorption coefficient of such vapors is very small (close to zero) and only in very narrow spectral intervals (several thousandths of a nanometer wide) are sharp maxima found in the absorption spectra (Figure 2).
The noted regions of sharp absorption of atoms correspond to the frequencies of natural vibrations of electrons inside atoms. If we are talking about the absorption spectra of molecules, then absorption bands corresponding to the frequencies of natural vibrations of atoms in the molecule are also recorded. Since the masses of atoms are much greater than the mass of an electron, these absorption bands are shifted to the infrared region of the spectrum.
The absorption spectra of solids and liquids, as a rule, are characterized by broad absorption bands. In the absorption spectra of polyatomic gases, broad absorption bands are recorded, while the spectra of monatomic gases are characterized by sharp absorption lines. Such a difference in the spectra of monatomic and polyatomic gases indicates that the reason for the expansion of the spectral bands is the interaction between atoms.
Bouguer's law is fulfilled in a wide range of light intensity values (as established by S.I. Vavilov, when the intensity changes by a factor of 1020), in which the absorption index does not depend on either the intensity or the layer thickness.
For substances with a long lifetime of the excited state at a sufficiently high light intensity, the absorption coefficient decreases, since a significant part of the molecules is in an excited state. Under such conditions, Bouguer's law is not fulfilled.
Considering the question of the absorption of light by a medium whose density is not everywhere the same, Bouguer argued that "light can undergo equal changes only when it encounters an equal number of particles capable of delaying rays or scattering them", and that, therefore, "not thicknesses" matter for absorption. , but the masses of the substance contained in these thicknesses. This second Bouguer's law is of great practical importance in studying the absorption of light by solutions of substances in transparent (virtually non-absorbing) solvents. The absorption coefficient for such solutions is proportional to the number of absorbing molecules per unit length of the light wave path, that is, the concentration of the solution with:
where BUT is a proportionality coefficient that depends on the type of substance and does not depend on concentration. After taking this ratio into account, Bouguer's law takes the form:
Coefficient Independence Assertion BUT from the concentration of a substance and its constancy is often called Beer's (or Beer's) law. The physical meaning of this statement is that the ability of molecules to absorb radiation does not depend on the surrounding molecules. However, there are numerous exceptions to this law, which is therefore a rule rather than a law. The value of the quantity BUT varies for closely spaced molecules; It also depends on the type of solvent. If there are no deviations from the generalized Bouguer's law, then it is convenient to use it to determine the concentration of solutions.
The absorption spectra of substances are used for spectral analysis, that is, to determine the composition of complex mixtures (qualitative and quantitative analysis).
The absorption of radiation by matter is explained on the basis of quantum concepts. Quantum transitions of an atomic system from one stationary state to another are due to the receipt or transfer of energy by this system to other objects or its radiation into the space surrounding the atom. Transitions in which an atomic system absorbs, emits, or scatters electromagnetic radiation, are called radiation(or radiant). Each radiative transition between energy levels and in the spectrum corresponds to a spectral line characterized by the frequency and some energy characteristic of the radiation emitted (for emission spectra), absorbed (for absorption spectra) or scattered (for scattering spectra) by an atomic system. Transitions during which there is a direct exchange of energy of a given atomic system with other atomic systems (collisions, chemical reactions, etc.) are called non-radiation(or non-radiative).
The main characteristics of the energy level are:
– the degree (multiplicity) of degeneracy, or statistical weight is the number of different stationary states (state functions) to which the energy corresponds;
– population is the number of particles of a given type per unit volume, having energy ;
– the lifetime of an excited state is the average duration of a particle in a state with energy .
The spectral position of the line (stripe), i.e. the line frequency can be determined by applying the Bohr frequency rule
Quantum transitions are characterized by the Einstein coefficients, the physical meaning of which will be explained later.
Using the simplest two-level system as an example, let us analyze what internal characteristics of the atomic system determine the intensity of the spectral line. Let and be two energy levels of an isolated atomic system (atom or molecule), the population of which will be respectively denoted N 1 and N 2(Figure 3).
The number of particles per unit volume that make in time dt in the stationary mode of excitation, the transitions , accompanied by the absorption of the energy of electromagnetic radiation, will be determined in accordance with the formula:
where is the volume spectral energy density of the external (exciting) radiation, the frequency of which is .
In this case, particles transferred to an excited state with energy in a unit volume of matter absorb energy
It can be seen from expression (5) that
is the probability of transition per unit time, accompanied by absorption, per particle. So the Einstein coefficient has a probabilistic (statistical) meaning.
The process of emission of electromagnetic radiation can occur in accordance with two mechanisms: spontaneously (due to internal causes) and forced (under the influence of exciting radiation).
The total number of particles making per time dt spontaneous transitions is directly proportional to the population of the level corresponding to the initial state of the system:
The energy of electromagnetic radiation spontaneously emitted by atoms (molecules) located in a unit volume of a substance over time can be represented as:
From formula (8) we express the value :
is the Einstein coefficient, which has the meaning of the probability of a transition accompanied by spontaneous emission of electromagnetic radiation by one particle per unit time.
Stimulated emission occurs under the action of external (forcing) radiation. in the considered system of levels directly The number of stimulated radiative transitions during the time dt in proportion to the population N 2 level corresponding to the initial state of the system ( E 2) and the volume spectral energy density of the external (exciting) radiation u 12:
The energy of stimulated radiation emitted in a unit volume of matter in a time dt, we write in the form:
From formula (11) it is easy to extract the quantity
is the probability of a transition made by one particle per unit of time and accompanied by stimulated emission. Here, is the Einstein coefficient for stimulated radiative transitions.
On the basis of the presented representations, the relations between the Einstein coefficients are established, for the transitions under consideration having the form:
where and are the statistical weights of the energy levels and .
Thus, the internal parameters of the atomic system, which determine the energy of electromagnetic radiation absorbed or emitted by a substance, and, consequently, the intensity of the spectral lines in the recorded spectrum, are transition probabilities per unit time, that is, the Einstein coefficients.
At relatively low values of the volume density of the exciting radiation, the total emission probability is almost completely determined by the probability of spontaneous transitions with energy emission. At high irradiation power, the probability of stimulated emission can become much greater than the probability of spontaneous emission. Such a situation takes place in the active medium of a generating laser, as well as when a laser is used as a source of exciting radiation.
Thus, there is only one type of elementary processes that can be used to amplify optical radiation, namely stimulated transitions with radiation. In accordance with expression (13), the probability of such transitions can be increased by increasing the spectral energy density of the "forcing" radiation . On the other hand, with a certain probability, the number of stimulated transitions per unit time, which determines the stimulated emission power, also depends on the population of the upper energy level N 2.
The balance of energy per unit volume of matter, emitted per unit time as a result of forced transitions and absorbed as a result of forced transitions with excitation of the atom, can be represented as:
Given that g 1 B 12 = g 2 B 21 , formula (16) can be rewritten as:
Under natural conditions, in accordance with the Maxwell-Boltzmann distribution, always and ∆W< 0, i.e. propagation of radiation in a medium is necessarily accompanied by a decrease in its intensity.
In order for the medium to amplify the radiation incident on it ( ∆W> 0), it is necessary that the condition or (in the absence of degeneracy) N 2 > N 1 In other words, the equilibrium distribution of populations must be violated in such a way that states with higher energy are more populated than states with lower energy.
A medium that is in a non-equilibrium state, in which the population distribution for at least two energy levels is inverted (inverted) with respect to the Maxwell-Boltzmann distribution, is called inverse. Such media have a negative absorption coefficient α (see (1) - Bouguer's law), i.e. when radiation passes through them, its intensity increases. Such environments are called active. To amplify light in an active medium, the energy emitted per unit time must exceed the total energy losses due to the absorption of radiation in the medium and useful losses, that is, the removal of radiation from the medium in the direction of radiation propagation (for example, useful losses are the laser radiation energy).
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