Spectral analysis radiation emitted by atoms provides extensive information about their structure and properties. Usually observed emission of light from hot monatomic gases (or low-density vapors) or when electrical discharge in gases.

The emission spectrum of atoms consists of individual discrete lines, which are characterized by wavelength or frequency v = c/X. Along with emission spectra, there are absorption spectra, which are observed when radiation with a continuous spectrum (“white” light) is passed through cold vapors. Absorption lines are characterized by the same wavelength as emission lines. Therefore they say that the emission and absorption lines of atoms mutually invertible ( Kirchhoff, 1859).

In spectroscopy, it is more convenient to use not the radiation wavelength, but reciprocal v = l/X, which is called spectroscopic wave number, or simply wave number (Stoney, 1871). This value shows how many wavelengths fit per unit length.

Using experimental data, the Swiss physicist Ritz in 1908 found an empirical rule called combinational principle, according to which there is a system spectral terms, or simply terms, T p And T, the difference between which determines the spectroscopic wave number of a certain spectral line:

Therms are considered positive. Their value should decrease as the number increases P(and l,). Since the number of emission lines is infinite, the number of terms is also infinite. Let's fix an integer P. If we consider the number l to be a variable with the values ​​l+ 1, l + 2, l + 3,..., then, according to formula (1.8), a series of numbers arises to which the system corresponds spectral lines, called spectral series. A spectral series is a set of spectral lines located in a certain regular sequence, and the intensity of which also varies according to a certain law. At l,-o term T->0. Corresponding wave number v n = T p called border of this series. When approaching the boundary, the spectral lines become denser, i.e., the difference in wavelengths between them tends to zero. The intensity of the lines also decreases. The series boundary follows continuous spectrum. The totality of all spectral series forms the spectrum of the atom under consideration.

The combination principle (1.8) also has a different form. If yaya =T-T And y = T-T - wave numbers of two spectra

LL| P L| PP 2 P *

tral lines of the same series of some atom, then the difference of these wave numbers (for l, > l 2):

represents the wave number of a spectral line of some other series of the same atom. At the same time, not every possible combination line is actually observed in experiment.

The combination principle was completely incomprehensible at one time and was considered a fun game numbers. Only Niels Bohr in 1913 saw in this “game” a manifestation of deep internal patterns atom. For most atoms analytical expressions unknown for terms. Approximate formulas were selected by analyzing experimental data. For the hydrogen atom, such formulas turned out to be accurate. In 1885, Balmer showed that the wavelengths of the four visible lines observed in the spectrum of the hydrogen atom are

H Q, Нр, Н у, H ft (Fig. 1.6), which were first measured by Angstrom (1868), with to a large extent accuracy can be calculated using the formula

where number l = 3,4, 5, 6,.... Constant B= 3645.6-10 8 cm was determined empirically. For the wave number, the formula follows from (1.10)

Where R- empirical Rydberg constant (1890), R = 4/B. For the hydrogen atom the Rydberg constant is equal to

From formula (1.11) it is clear that the term for the hydrogen atom has a simple expression:

Consequently, for the wave numbers of the spectral series of the hydrogen atom, generalized Balter formula:

This formula correctly describes the spectral series of the hydrogen atom discovered in the experiment:

Balter series(l = 2, l, = 3, 4, 5, ...) - in the visible and near ultraviolet parts of the spectrum X = (6562...3646)* 10" 8 cm:

Lyman series(1914) (l = 1, l, = 2, 3, 4, ...) - in the ultraviolet part of the spectrum A = (1216...913)-10“ 8 cm:

Paschen series(1908) (l = 3, l, =4, 5, 6,...) - in the infrared part of the spectrum X = 1.88...0.82 microns:

series Brackett(1922) (l = 4, l, = 5, 6, 7, ...) - in the far infrared part of the spectrum X. = 4.05 ... 1.46 microns:

Pfund series(1924) (l = 5, l, =6, 7, 8,...) - in the far infrared part of the spectrum X = 7.5...2.28 microns:

Humphrey series(1952) (l = 6, l, = 7, 8,...) - in the far infrared part of the spectrum X = 12.5...3.3 µm:

The boundary of each series is determined by l, the head line of this series.

1. Find the limiting wavelengths of the spectral series of the hydrogen atom.

Answer. X t = n 1 /R. f/

2. Determine the head lines of the spectral series.

Answer. X^ =l 2 (l + 1) 2 /i (2l + 1).

3. Determine the limiting wavelengths between which the spectral lines of the Balmer series are located.

ANSWER: Xf = 3647-10" 8 cm, X^ = 6565-10' 8 cm.

4. Determine the classical spectrum of the hydrogen atom.

Solution. An electron together with a nucleus can be considered as electric dipole, whose radius vector changes periodically. Projections of the radius vector of the electron onto the Cartesian axes are also periodic functions, which, in general, can be represented as series

Fourier: *(/)= ^2 , y(t)= I^e^ , where A s, B s- constants;

co is the frequency of electron revolution around the nucleus, determined by Kepler's third law. Average over the period 7'=2l/o) dipole radiation intensity

is determined by the formula: I =----(x 2 +y 2 where x 2 = - G dtx2. From here barely

6L? 0 C 3 V >T.J.

blows: / = ---((/I 2 + 5 2)w 4 + (l 2 + B)(2В)(3ш) 4 +...) Evil 0 s 3

Thus, the spectrum contains the frequency o and its harmonics 2o), 30,... and represents a series equally spaced lines. This contradicts experiment.

Atomic spectra, optical spectra resulting from the emission or absorption of light ( electromagnetic waves) free or weak bonded atoms; Monatomic gases and vapors, in particular, have such spectra. Atomic spectra arise during transitions between energy levels of the outer electrons of an atom and are observed in the visible, ultraviolet and near-infrared regions. Atomic spectra are observed in the form of bright colored lines when gases or vapors glow in electric arc or discharge (emission spectra) and in the form of dark lines (absorption spectra).

The Rydberg constant is a quantity introduced by Rydberg that is included in the equation for energy levels and spectral lines. The Rydberg constant is denoted as R. R = 13.606 eV. In the SI system, that is, R = 2.067 × 1016 s−1.

End of work -

This topic belongs to the section:

Fundamentals of atomic, quantum and nuclear physics

De Broglie's hypothesis and its connection with Bohr's postulates, the Schrödinger equation, physical meaning.. thermonuclear reactions.. thermonuclear reactions nuclear reactions between light atomic nuclei occurring at very high temperatures ..

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Models of atomic structure. Rutherford model
Atom - the smallest chemical indivisible part chemical element, which is the carrier of its properties. An atom is made up of atomic nucleus and the surrounding electron cloud. The nucleus of an atom consists of

Bohr's postulates. Elementary theory of the structure of the hydrogen atom and hydrogen-like ions (according to Bohr)
Bohr's postulates are the basic assumptions formulated by Niels Bohr in 1913 to explain the pattern line spectrum hydrogen atom and hydrogen-like ions and the quantum nature of the

Schrödinger equation. Physical meaning of the Schrödinger equation
The Schrödinger equation is an equation that describes the change in space and time of the pure state, given by the wave function, in Hamiltonian quantum systems. In quantum physics

Heisenberg uncertainty relation. Description of motion in quantum mechanics
The Heisenberg uncertainty principle is a fundamental inequality (uncertainty relation) that sets the limit on the accuracy of the simultaneous determination of a pair of characteristics of a quantum system

Properties of the wave function. Quantization
Wave function(state function, psi function) - a complex-valued function used in quantum mechanics to describe the pure state of a quantum mechanical system. Is the coefficient

Quantum numbers. Spin
Quantum number - numerical value any quantized variable of a microscopic object (elementary particle, nucleus, atom, etc.) characterizing the state of the particle. Specifying Quantum Hours

Characteristics of the atomic nucleus
Atomic nucleus - central part atom in which the bulk of its mass is concentrated, and the structure of which determines chemical element, to which the atom belongs. Nuclear physical nature

Radioactivity
Radioactivity is the property of atomic nuclei to spontaneously change their composition (charge Z, mass number A) by emitting elementary particles or nuclear fragments. Corresponding phenomenon

Nuclear chain reactions
Nuclear chain reaction - a sequence of single nuclear reactions, each of which is caused by a particle that appeared as a reaction product at the previous step in the sequence. An example of a chain

Elementary particles and their properties. Systematics of elementary particles
Elementary particle is a collective term referring to micro-objects on a subnuclear scale that cannot be broken down into their component parts. Properties: 1.All E. h-objects of claim

Fundamental interactions and their characteristics
Fundamental Interactions- qualitatively different types of interaction between elementary particles and bodies composed of them. Today, the existence of four fundamentals is reliably known

Regularities in atomic spectra

Material bodies are sources electromagnetic radiation, having a different nature. In the second half of the 19th century. Numerous studies have been carried out on the emission spectra of molecules and atoms. It turned out that the emission spectra of molecules consist of widely diffuse bands without sharp boundaries. Such spectra were called striped. The emission spectrum of atoms consists of individual spectral lines or groups of closely spaced lines. Therefore, the spectra of atoms were called line spectra. For each element there is a completely definite line spectrum emitted by it, the type of which does not depend on the method of excitation of the atom.

The simplest and most studied is the spectrum of the hydrogen atom. Analysis of empirical material has shown that individual lines in the spectrum can be combined into groups of lines, which are called series. In 1885, I. Balmer established that the frequencies of lines in the visible part of the spectrum of hydrogen can be represented in the form of a simple formula:

( 3, 4, 5, …), (7.42.1)

where 3.29∙10 15 s -1 is the Rydberg constant. Spectral lines that differ different meanings, form the Balmer series. Subsequently, several more series were discovered in the spectrum of the hydrogen atom:

Lyman series (located in the ultraviolet part of the spectrum):

( 2, 3, 4, …); (7.42.2)

Paschen series (lies in the infrared part of the spectrum):

( 4, 5, 6, …); (7.42.3)

Bracket series (lies in the infrared part of the spectrum):

( 5, 6, 7, …); (7.42.4)

Pfund series (lies in the infrared part of the spectrum):

( 6, 7, 8, …); (7.42.5)

Humphrey series (located in the infrared part of the spectrum):

( 7, 8, 9, …). (7.42.6)

The frequencies of all lines in the spectrum of the hydrogen atom can be described by one formula - the generalized Balmer formula:

, (7.42.7)

where 1, 2, 3, 4, etc. – defines a series (for example, for Balmer series 2), and defines a line in a series, taking integer values ​​starting from 1.

From formulas (7.42.1) – (7.42.7) it is clear that each of the frequencies in the spectrum of the hydrogen atom is the difference between two quantities of the form depending on an integer. Expressions of the form where 1, 2, 3, 4, etc. are called spectral terms. According to combinational principle Ritz, all emitted frequencies can be represented as combinations of two spectral terms:

(7.42.8)

and always >

Study of spectra more complex atoms showed that the frequencies of their emission lines can also be represented as the difference between two spectral terms, but their formulas are more complicated than for the hydrogen atom.

The experimentally established patterns of atomic radiation are in conflict with classical electrodynamics, according to which electromagnetic waves are emitted by an accelerating charge. Therefore, atoms contain electric charges, moving with acceleration in a limited volume of an atom. When radiating, the charge loses energy in the form of electromagnetic radiation. This means that the stationary existence of atoms is impossible. However, the established patterns indicated that spectral radiation atoms is the result of as yet unknown processes inside the atom.

The line spectrum of an atom is a collection large number lines scattered throughout the spectrum without any apparent order. However, a careful study of the spectra showed that the arrangement of the lines follows certain patterns. These patterns appear most clearly, of course, in relatively simple spectra, characteristic of simple atoms. For the first time, such a pattern was established for the spectrum of hydrogen shown in Fig. 326.

Rice. 326. Line spectrum of hydrogen (Balmer series, wavelengths in nanometers). and - designations of the first four lines of the series lying in the visible region of the spectrum

In 1885, Swiss physicist and mathematician Johann Jakob Balmer (1825-1898) established that the frequencies of individual hydrogen lines are expressed by a simple formula:

,

where denotes the frequency of light, i.e. the number of waves emitted per unit time, a value called the Rydberg constant, equal to and is an integer. If you set the values ​​to 3, 4, 5, etc., you get values ​​that match very well the frequencies of successive lines in the hydrogen spectrum. The collection of these lines constitutes the Balmer series.

Subsequently, it was discovered that the spectrum of hydrogen still contains numerous spectral lines, which also form series similar to the Balmer series.

The frequencies of these lines can be represented by the formulas

, where (Lyman series),

, where (Paschen series),

and it has the same thing numeric value, as in Balmer's formula. Thus, all hydrogen series can be combined with one formula:

where and are integers, .

The spectra of other atoms are much more complex, and the distribution of their lines in a series is not so simple. It turned out, however, that the spectral lines of all atoms can be distributed in a series. It is extremely important that serial patterns for all atoms can be presented in a form similar to Balmer's formula, with the constant having almost the same value for all atoms.

The existence of spectral patterns common to all atoms undoubtedly indicated a deep connection between these patterns and the basic features of the atomic structure. Indeed, the Danish physicist, creator quantum theory atom Niels Bohr (1885-1962) in 1913 found the key to understanding these laws, establishing at the same time the fundamentals modern theory atom (see Chapter XXII).

Question 3. Bohr's postulates and explanation of the origin of line spectra. Regularities in atomic spectra.

Experimental data on the hydrogen atom. It is natural to start studying the structure of atoms with the simplest atom - the hydrogen atom. By the time Bohr's theory about the hydrogen atom was created, the following experimental information was available. A hydrogen atom consists of a nucleus (proton) carrying positive charge, equal in magnitude to the charge of an electron, and one electron, which, according to planetary model Rutherford, moves around the nucleus in a circular or elliptical orbit. The dimensions of a hydrogen atom are determined by the diameter of the electron orbit and are slightly larger than 10 -10 m .

The most important information for creating the theory of atoms was obtained from the emission spectrum of hydrogen. The spectrum of hydrogen turned out to be the simplest in comparison with the spectra of other elements. In it, surprisingly simple and at the same time observed with very high accuracy patterns in the arrangement of spectral lines, the so-called spectral series (spectral series were also found in the spectra of other elements, but the formulas for their description turned out to be more complex, and the agreement of these formulas with experiment was much less accurate). It turned out that the frequencies of all lines that are observed in the emission spectrum of hydrogen are determined by the formula:

This is a generalized Balmer formula. Here ν is the frequency of the light wave, is the Rydberg constant ( =3.293 10 15 c -1 , n=1,2,3 …, m=2, 3, 4 …) .

Nuclear model atom combined with classical mechanics and electrodynamics turned out to be unable to explain either the stability of the atom or the character atomic spectrum. A way out of this impasse was found in 1913 by the Danish physicist Niels Bohr, although at the cost of introducing assumptions that contradict classical ideas. The assumptions made by Bohr are contained in two postulates he stated.

1.Bohr's first postulate (stationary state postulate) reads: from infinite number electron orbits possible from the point of view classical mechanics, only some discrete orbits that satisfy certain quantum conditions are actually realized. An electron located in one of these orbits, despite the fact that it is moving with acceleration, does not emit electromagnetic waves (light).

According to the first postulate, an atom is characterized by a system energy levels, each of which corresponds to a specific stationary state. Stationary states correspond to stationary orbits in which an electron can rotate around the nucleus indefinitely without emitting energy. The energy of an atom can change only when an electron jumps from one energy state to another.

2. Bohr's second postulate (frequency rule) formulated as follows: radiation is emitted or absorbed in the form light quantum energy during the transition of an electron from one stationary (stable) state to another (Fig. 19.4). The magnitude of the light quantum is equal to the difference in energies of those stationary states between which the quantum transition of the electron occurs:

. (19.3)

It follows that the change in atomic energy associated with radiation when a photon is absorbed is proportional to frequency ν:

photon absorption, proportional to frequency ν:

, (19.4)

those. the frequency of emitted light can be represented as the difference between two quantities characterizing the energy of the emitting system.

Bohr's second postulate also contradicts Maxwell's electrodynamics. According to Bohr, the frequency of radiation is determined only by the change in the energy of the atom and does not depend in any way on the nature of the electron’s motion. And according to Maxwell (i.e. from the point of view classical electrodynamics) the frequency of radiation depends on the nature of the electron’s motion.

Important role The empirical regularities obtained for the line spectrum of the hydrogen atom played a role in the development of the planetary model.

In 1858, the Swiss physicist I. Balmer established that the frequencies of nine lines in the visible region of the hydrogen spectrum satisfy the relation

, m=3, 4, 5, …, 11. (19.5)

The discovery of the Balmer hydrogen series (19.5) provided the impetus for the discovery of other series in the spectrum of the hydrogen atom in the early 20th century.

From formula (19.5) it is clear that as m the frequency of the spectrum lines increases, while the intervals between adjacent frequencies decrease, so that at frequency . The maximum frequency value in the Balmer series obtained at is called border Balmer series, beyond which there is a continuous spectrum.

In the ultraviolet region of the hydrogen spectrum is the Lyman series:

, m= 2,3,4… (19.6)

There are four more series in the infrared region:

Paschen series, , m = 4,5,6…

Bracket Series , m = 5,6,7… (19.7)

Pfund series , m = 6,7,8…

Humphrey series , m = 7,8,9…

As already noted, the frequencies of all lines in the spectrum of the hydrogen atom are represented by one formula (19.2).

The line frequency in each series tends to the maximum maximum value , which is called the series boundary. The Lyman and Balmer spectral series are separate, the remaining series partially overlap. For example, the boundaries (wavelengths) of the first three series (Lyman, Balmer, Paschen) are respectively equal

0,0912 µm; 0,3648 µm; 0, 8208 µm (λ min = c/ν max).

Bohr introduced orbit quantization rule which reads: in stationary state atom electron moving in a circular orbit

radius r, must have discrete, i.e. quantized, angular momentum values ​​satisfying the condition:

n= 1, 2, 3…, (19.8)

Where n– the main quantum number, – also Planck’s constant.

Discreteness of orbital radii and energies of stationary states. Consider an electron (Fig. 19.5) moving at a speed V in the field of an atomic nucleus with a charge Ze. A quantum system consisting of a nucleus and only one electron is called a hydrogen-like atom. Thus, the term "hydrogen-like atom" is applicable in addition to the hydrogen atom, which Z= 1, to a singly ionized helium atom Not+ , to the doubly ionized lithium atom Li+2, etc.

An electron moving in a circular stationary orbit is affected by an electric force, i.e. Coulomb force attraction from the core,

, (19.9)

which is compensated centrifugal force:

. (19.10)

Substituting the expression for speed from (19.8) into formula (19.10) and solving the resulting equation for r n, we get a set discrete values radii of electron orbits in hydrogen-like atoms:

, (19.11)

Where n = 1,2,3… .

Using formula (19.11), the radii of allowed stationary orbits in the Bohr semi-quantum model of the atom. Number n= 1 corresponds to the orbit closest to the nucleus, therefore for the hydrogen atom ( Z=1) radius of the first orbit

m, (19.12)

and the electron speed corresponding to this orbit is

km/s.

Smallest radius of the orbit is called the first Bohr radius (). From expression (19.11) it is clear that the radii of orbits more distant from the nucleus for hydrogen-like atoms increase in proportion to the square of the number n(Fig. 19.6)

(19.13)

Now we calculate for each of the allowed orbits full energy electron, which consists of its kinetic and potential energies:

. (19.14)

Recall that the potential energy of an electron in the field of a positively charged nucleus is a negative quantity. Substituting the speed value into expression (19.14) V from (19.8), and then, using formula (19.13) for r, we obtain (taking into account the fact that ):

, n = 1, 2, 3 … (19.15)

Negative sign in expression (19.15) for the atomic energy is due to the fact that for the zero value potential energy electron is considered to be the value that corresponds to the electron moving to infinity from the nucleus.

The orbit with the smallest radius corresponds to lowest value energy and is called TO- orbit, followed by L- orbit, M– orbit, etc. When electrons move along these orbits, the atom is in a stable state. The diagram of energy levels for the spectral series of the hydrogen atom, determined by equation (19.15), is shown in Fig. 19.7. Horizontal lines correspond to the energies of stationary states.

The distances between energy levels are proportional to the energy quanta emitted by the atom during the corresponding electron transitions (depicted by arrows). When an atom absorbs energy quanta, the directions of the arrows should be reversed.

From expression (19.14) it is clear that in Bohr’s planetary model, the energy states of the hydrogen atom are characterized by an infinite sequence of energy levels E n. Values E n inversely proportional to the square of the number n which is called main quantum number . Energy state of an atom c n=1 is called main or normal, i.e. unexcited state, which corresponds to minimum value energy. If n> 1, the state of the atom is excited ().

Energy E 1 ground state of the hydrogen atom from (19.15) is equal to

– 13,53 eV.

Ionization energy hydrogen atom, i.e. E i = │ E 1 - E∞│= 13,53 eV, equal to the work done when moving an electron from the ground state ( n= 1) to infinity without imparting kinetic energy to it.

Spectral patterns. In accordance with Bohr's second postulate, during the transition of an electron of a hydrogen atom from an excited state to a state corresponding to the level n(n<m) a hydrogen atom emits a quantum of electromagnetic radiation with a frequency

whence = =3.29·10 15 s -1 . (19.17)

From frequency you can go to wavelength:

, (19.18)

where is the value

, (19.19)

which is also called the Rydberg constant. To transfer an electron in a hydrogen atom from n th energy level ( n-th orbit) on m th energy level ( m-th orbit) at n the atom must be given an energy equal to the difference between the energies of the atom in the final and initial states.