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 n as a variable with the values n+ 1, n + 2, n + 3,..., then, according to formula (1.8), a series of numbers arises, which correspond to a system of 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. Beyond 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 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 μm:
Pfund series(1924) (l = 5, l, =6, 7, 8,...) - in the far infrared part of the spectrum X = 7.5...2.28 μm:
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.
The study of radiation spectra played a major role in understanding the structure of atoms. First of all, this concerns spectra caused by the emission of atoms that do not interact with each other. These spectra consist of individual narrow spectral lines and are called line spectra.
The presence of many spectral lines indicates complexity internal structure atom. Studying atomic spectra served as the key to knowledge internal structure atoms. First of all, it was noticed that the spectral lines are not randomly located, but form a series of lines. Studying line spectrum atomic hydrogen, Balmer (1885) established a certain pattern. For some lines, the corresponding frequencies can be represented in modern notation as follows:
Where w- cyclic frequency corresponding to each spectral line ( w = 2πc/l), R- a constant called Rydberg constant :
R=2.07×10 16 s -1. (2.2)
Formula (2.1) is called the formula Balmera, and the corresponding series of spectral lines - Fig. 2.1 - the Balmer series (Fig. 2.1). The main lines of this series are in the visible part of the spectrum.
Further studies of the spectrum of atomic hydrogen showed that there are several more series.
In the ultraviolet part of the spectrum - Lyman series:
(2.3)
and in the infrared part of the spectrum - Paschen series:
(2.4)
All these series can be represented in the form generalized Balmer formula:
(2.5)
where is a constant number for each series: . For the series Lyman, n 0 = 1, for series Balmera etc. For a given n 0 number n accepts all integer values starting from n 0 + 1.
Maximum length waves series Lyman(3.12.3) answers n= 2, this is l max = 2 πс/w min = 8 With/3R= 121.6 nm. Corresponding spectral line called the hydrogen resonance line.
With growth n the frequency of lines in each series tends to a limiting value, which is called the series boundary (Fig. 2.1). Beyond the series boundary, the spectrum does not end, but becomes continuous. This is inherent not only in all series of hydrogen, but also in atoms of other elements.
Thus, the Balmer series of interest to us lies in the spectral range from 365 nm to 656 nm, i.e., indeed, all its main lines are located in the visible region of the spectrum.
Rutherford's experiments. Nuclear model atom.
Radiation electromagnetic waves possible with accelerated movement of charges. The atom as a whole is electrically neutral. On the other hand, it is known that the atom contains negatively charged electrons. Therefore, it must also contain positively charged particles.
The currently accepted model of the atom was proposed by Rutherford, based on the results of his experiments on particle scattering.
In these experiments, very thin gold foil was irradiated with a beam of − particles with quite great energy. -particles are one of the types of particles emitted by certain substances when radioactive decay. At that time, the mass of the particle () and its positive charge, equal to double elementary charge(electron charge modulus). Passing through the foil, the particles were scattered by the atoms of the substance, i.e. deviated by some angle from the original direction. Registration of scattered particles was carried out by flashes of light that occurred when they hit a screen coated with zinc sulfide.
As a result of the experiments, it turned out that almost all of the particles passed through the foil, deviating by very little large angles. However there was a small amount of-particles that were deflected at very large angles (almost up to 180). After analyzing the experimental results, Rutherford came to the conclusion that such a strong deflection of − particles is possible when they interact with the positively charged part of the atom, in which its bulk is concentrated.
The dimensions of this part can be estimated if we assume that the − particle is thrown back in the opposite direction after an “elastic head-on collision” with a positively charged part of the atom. To do this we need to equate kinetic energy−particles to potential energy its interaction with this part of the atom at the moment the particle stops:
, (2.6)
Where V- particle speed, 2e – her charge, Ze – the charge of the positive part of the atom is the minimum distance at which a particle can approach the positive part of the atom (in atomic physics It is customary to use the Gaussian system of units). Putting in this equality Z= 79 (gold), V=10 , =4 1.66 10 g = 6.6 10 g, we get
Let us recall that when studying the properties of gases using methods kinetic theory, the sizes of atoms can be determined. The sizes found in this way for all atoms are on the order of 10 cm. Thus, the size of the positive part of the atom turned out to be several orders of magnitude smaller size atom.
Based on these estimates, Rutherford proposed nuclear (or planetary) model of the atom. All the positive charge and almost all the mass of the atom are concentrated in its core, whose size is ≈ 10 cm, is negligible compared to the size of an atom. Electrons move around the nucleus, occupying a huge area compared to the nucleus with a linear size of the order of 10 cm.
However, if we accept this model, it becomes unclear why electrons do not fall onto the nucleus. Between the electron and the nucleus there is only Coulomb force attraction. Therefore, the electron cannot be at rest. It should move around the core. But in this case, according to the laws classical physics, it must radiate, and at all frequencies, which contradicts experience. Losing energy, the electron must fall onto the nucleus (the atom will be emitted). Estimates have shown that all of its energy will be emitted in a time of about 10 s. This will be the “lifetime” of the atom.
Bohr's postulates.
Absolute instability planetary model Rutherford and at the same time the amazing regularity of atomic spectra, and in particular their discreteness, led the Danish physicist N. Bohr to the need to formulate (1913) two most important postulates quantum physics:
1. Atom can long time be only in certain, so-called stationary states, which are characterized discrete values energy E 1 , E 2 , E 3, ... In these states, contrary to classical electrodynamics, the atom does not radiate.
2. When an atom transitions from a stationary state with higher energy E 2 to a stationary state with lower energy E 1 a quantum of light (photon) with energy is emitted ћw:
(2.7)
The same relationship holds in the case of absorption, when an incident photon transfers an atom from a lower energy level E 1 to higher E 2, and he himself disappears.
Relationship (2.7) is called Bohr's frequency rule. Note that atomic transitions to higher energy levels can also be caused by collisions with other atoms.
Thus, the atom moves from one stationary state to another in jumps (they are called quantum). What happens to the atom during the transition process remains an open question in Bohr's theory.
Frank and Hertz experiments.
These experiments were carried out in 1913. given direct proof discreteness of atomic states. The idea of the experiments is as follows. During inelastic collisions of an electron with an atom, energy is transferred from the electron to the atom. If the internal energy of an atom changes continuously, then any portion of energy can be transferred to the atom. If the states of an atom are discrete, then its internal energy when colliding with an electron should also change
discretely - to values equal to the difference in the internal energy of the atom in stationary states.
Therefore, when inelastic collision An electron can transfer only certain portions of energy to an atom. By measuring them, it is possible to determine the values of internal energies stationary states atom.
This was to be tested experimentally using an installation, the diagram of which is shown in Fig. 2.2. In a cylinder with mercury vapor under pressure of about 1 mmHg. ("130 Pa) there were three electrodes: TO- cathode, WITH- mesh and A- anode.
Electrons emitted due to thermionic emission from the hot cathode were accelerated by the potential difference V between the cathode and the grid. Size V could be changed smoothly. A weak retarding field with a potential difference of about 0.5 V was created between the grid and the anode.
Thus, if some electron passes through the grid with an energy less than 0.5 eV, then it will not reach the anode. Only those electrons whose energy when passing through the grid is greater than 0.5 eV will reach the anode, forming an anode current I, available for measurement. Fig.2.3
In the experiments, the dependence of the anode current was studied I(measured by galvanometer G) from accelerating voltage V(measured with a voltmeter V). The results obtained are presented in the graph in Fig. 2.3. The maxima correspond to the energy values
E 1 = 4,9 eV, E 2 = 2E 1 , E 3 = 3E 1, etc.
This type of curve is explained by the fact that atoms can actually absorb only discrete portions of energy equal to 4.9 eV.
When the electron energy is less than 4.9 eV, their collisions with mercury atoms can only be elastic(without change internal energy atoms), and the electrons reach the grid with energy sufficient to overcome the braking potential difference between the grid and the anode. When does the accelerating voltage V becomes equal to 4.9 eV, electrons begin to experience near the grid inelastic collisions, giving all the energy to the mercury atoms, and will no longer be able to overcome the braking potential difference in the space behind the grid. So, to the anode A Only those electrons that have not experienced an inelastic collision can enter. Therefore, starting from an accelerating voltage of 4.9 IN anode current I will decrease.
At further growth accelerating voltage, a sufficient number of electrons after an inelastic collision manage to acquire the energy necessary to overcome the braking field behind the grid. A new increase in current begins I. When the accelerating voltage increases to 9.8 IN, electrons after one inelastic collision (approximately halfway through, when they manage to gain energy 4.9 eV) reach the grid with an energy of 4.9 eV, sufficient for the second inelastic collision. During the second inelastic collision, the electrons lose all their energy and do not reach the anode. Therefore, the anode current I begins to decrease again (second maximum on the graph). Subsequent maxima are explained similarly.
From the experimental results it follows that the difference between the internal energies of the ground state of a mercury atom and the nearest excited state is 4.9 eV, which proves the discreteness of the internal energy of the atom.
Similar experiments were subsequently carried out with atoms of other gases. And characteristic potential differences were obtained for them; they are called resonance potentials or first excitation potentials. The resonance potential corresponds to the transition of an atom from the ground state (with minimum energy) to the nearest excited one. A more advanced technique was used to detect higher excited states, but the principle of the study remained the same.
So, all experiments of this kind lead to the conclusion that the states of atoms change only discretely. The experiments of Frank and Hertz also confirm Bohr's second postulate - the rule of frequencies. It turns out that when the accelerating voltage reaches 4.9 IN mercury vapor begins to emit ultraviolet radiation with wavelength 253.7 nm. This radiation is associated with the transition of mercury atoms from the first excited state to the ground state. Indeed, from condition (2.7) it follows that
This result agrees well with previous measurements.
Related information.
IN normal conditions atoms do not emit (as in a stationary state). To cause radiation of atoms, it is necessary to increase their internal energy. The spectra of isolated atoms are limited.
Moreover, the lines in the spectrum of an atom, including the hydrogen atom, are not randomly located, but are combined into groups, which are called spectral series. Formula, determine the value of the wavelength in each of the series: ν=1/λ=R(1/n 2 – 1/m 2). n=n+1, n+2,.. λ=1,2,3,… (serial file) R=1.092*10m -1 Rydberg post. IN general case write 1/λ=Rz 2 (1/n 2 – 1/m 2).
Energy of the previous photon from level n to m: hv=E m -E n =(hz 2 me 4 /(4πε 0) 2 2ħ 2)(1/n 2 -1/m 2).
Lymon series – ν=1/λ=R(1/1 – 1/n 2), n=2,3,4...,in the UV region.
Balmer series – ν=1/λ=R(1/2 2 – 1/n 2), n=3,4,5… visible region and near UV. Paschen series – ν=1/λ=R(1/3 2 – 1/n 2), n=4,5,6…, infrared region. Emitted in visible and near UV waves. All other series lie in the IR region of light.
Bohr's postulates. Bohr's atomic model.
The first attempt to formulate the laws governing the movement of electrons in an atom was made by Bohr, based on the idea that the atom is a stable system and that the energy that an atom can emit or absorb is quantum. 1) In order to eliminate the first drawback of the Resenford model, he assumed that of the entire variety of orbits that follow from equation (1), not all, but only some stable orbits, which he called stationary, are realized in nature, and, being on which the atom does not emit or absorb energy. Stationary orbits correspond to stable states of the atom, and the energies possessed by the atom in these states form discrete series values: E1, E2, E3…,En. Moving on stationary orbit the electron acquires an angular momentum that is a multiple of the reduced quantum constant
h (c); m (index e) * v (index e) r = n h (c) (1), h (c) = n/2π, n=1,2,3... That is when moving from orbit to orbit, it changes in portions that are multiples of h (c).
(1) – Bohr’s contigation rule or the rule for selecting stationary orbits.
2) To eliminate the 2nd contradiction of the Rusenford model, Bohr assumed that radiation or absorption of energy by an atom occurs when the atom transitions from one stationary state to another. With each such transition, a quantum of energy is emitted, equal to the difference energies of bodies of stationary states, between which a quantum jump of the electron occurs, hν=En – Em (2) (n>m, radiation, n 2 postulates: 1) An atom has stable or stationary states, and the energy of atoms in this state forms a discrete series of values (postulate of stationary values) E1, E2, E3…En. 2) Any radiation or absorption of energy must correspond to the transition of an atom from one stationary state to another. With each such transition, monochromatic radiation is emitted, the frequency of which is determined by ν=(En – Em)/h(в) (Bohr's frequency rule). Bohr's atomic model. 1913. Bohr accepted the new postulates of quantum mechanics, according to which, at the subatomic level, energy is emitted exclusively in portions, which are called “quanta.” Bohr took quantum theory a step further and applied it to the state of electrons in atomic orbits. Scientifically speaking, he proposed that the angular momentum of the electron is quantized. He further showed that in this case the electron cannot be at an arbitrary distance from the atomic nucleus, but can only be in a number of fixed orbits, called “allowed orbits.” Electrons in such orbits cannot emit electromagnetic waves of arbitrary intensity and frequency, otherwise they would most likely have to move to a lower, unresolved orbit. That's why they stay in their higher orbit, like an airplane at its departure airport when the destination airport is closed due to bad weather. However, electrons can move to another allowed orbit. Like most phenomena in the world of quantum mechanics, this process is not so easy to visualize. The electron simply disappears from one orbit and materializes in another, without crossing the space between them. This effect was called a “quantum leap” or “quantum leap.” In Bohr's picture of the atom, therefore, electrons move up and down the orbits in discrete jumps - from one allowed orbit to another, just as we go up and down the steps of a ladder. Each jump is necessarily accompanied by the emission or absorption of a quantum of energy of electromagnetic radiation, which we call a photon. The radiation of atoms that do not interact with each other consists of individual spectral lines. In accordance with this, the emission spectrum of atoms is called line. In Fig. Figure 12.1 shows the emission spectrum of mercury vapor. The spectra of other atoms have the same character. The study of atomic spectra served as the key to understanding the structure of atoms. First of all, it was noticed that the lines in the spectra of atoms are not randomly located, but are combined into groups or, as they are called, series of lines. This is most clearly revealed in the spectrum of the simplest atom - hydrogen. In Fig. Figure 12.2 shows part of the spectrum of atomic hydrogen in the visible and near ultraviolet region. The symbols indicate visible lines, indicating the boundary of the series (see below). It is obvious that the lines are arranged in a certain order. The distance between the lines naturally decreases as we move from longer waves to shorter ones. The Swiss physicist Balmer (1885) discovered that the wavelengths of this series of hydrogen lines could be accurately represented by the formula where is a constant, is an integer taking the values 3, 4, 5, etc. If we go from wavelength to frequency in (12.1), we get the formula where is a constant called the Rydberg constant after the Swedish spectroscopist. It is equal Formula (12.2) is called the Balmer formula, and the corresponding series of spectral lines of the hydrogen atom is called the Balmer series. Further studies showed that there are several more series in the spectrum of hydrogen. In the ultraviolet part of the spectrum is the Lyman series. The remaining series lie in the infrared region. The lines of these series can be presented in the form of formulas similar to (12.2): The frequencies of all lines in the spectrum of a hydrogen atom can be represented by one formula: where has the value 1 for the Lyman series, 2 for the Balmer series, etc. Given a number, the number takes on all integer values, starting with Expression (12.4) is called the generalized Balmer formula. As the frequency of the line in each series increases, it tends to a limiting value which is called the series boundary (in Fig. 12.2 the symbol marks the boundary of the Balmer series). Atomic spectra, optical spectra, resulting from the emission or absorption of light (electromagnetic waves) by free or weakly bound 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 an 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: De Broglie's hypothesis and its connection with Bohr's postulates Schrödinger equation physical meaning.. thermonuclear reactions.. thermonuclear reactions nuclear reactions between light atomic nuclei occurring at very high temperatures.. If you need additional material on this topic, or you did not find what you were looking for, we recommend using the search in our database of works: If this material was useful to you, you can save it to your page on social networks: Models of atomic structure. Rutherford model Bohr's postulates. Elementary theory of the structure of the hydrogen atom and hydrogen-like ions (according to Bohr) Schrödinger equation. Physical meaning of the Schrödinger equation In quantum physics 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 Wave function (state function, psi function) is a complex-valued function used in quantum mechanics to describe the pure state of a quantum mechanical system. Is the coefficient Quantum number is the numerical value of any quantized variable of a microscopic object (elementary particle, nucleus, atom, etc.), characterizing the state of the particle. Specifying Quantum Hours Nuclear physical nature 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 A nuclear chain reaction is 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 particle is a collective term referring to micro-objects on a subnuclear scale that cannot be broken down into their component parts. 
Fundamentals of atomic, quantum and nuclear physics
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An atom is the smallest chemically indivisible part of a chemical element, which is the carrier of its properties. An atom consists of an atomic nucleus and a surrounding electron cloud. The nucleus of an atom consists of
Bohr's postulates are the basic assumptions formulated by Niels Bohr in 1913 to explain the pattern of the line spectrum of the hydrogen atom and hydrogen-like ions and the quantum nature of the
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.
Heisenberg uncertainty relation. Description of motion in quantum mechanics
Properties of the wave function. Quantization
Quantum numbers. Spin
The atomic nucleus is the central part of an atom, in which the bulk of its mass is concentrated, and the structure of which determines the chemical element to which the atom belongs.
Radioactivity
Nuclear chain reactions
Elementary particles and their properties. Systematics of elementary particles
Properties: 1.All E. h-objects of claim
