Moscow State University of Economics, Statistics, Informatics

Discipline abstract: KSE

on the topic :

"Planetary model of the atom"

Vikonav:

3rd year student

Groupi DNF-301

Ruziev Temur

Vikladach:

Mosolov D.M.

Moscow 2008

In Dalton's first atomic theory, it was said that light is made up of a single number of atoms - elementary zelins - with characteristic powers, eternal and invariable.
The number of manifestations changed dramatically after the appearance of the electron. All atoms are guilty of electronics. And how is the electronics they have sold out? Physicists could no longer philosophize, walking out of their knowledge from the gallery of classical physics, and step by step, all points of view were based on one model, proponed by J.J. Thomson. According to the model, the atom is made up of positively charged speech, interspersed with electrons in the middle (the stench can be found in intensive Russia), so that the atom is guessing a pudding with rodzinkami. Thomson's model of the atom could not be distorted, but all analogies witnessed the cruelty.
The German physicist Philip Lenard in 1903 propagated the model of an "empty" atom, in the middle of which "fly" as if no neutral particles were revealed, folded from mutually equal positive and negative charges. Lenard gave a name for his inconstant parts - dynamids. The only thing, the right to grounds that had to be suvorim, let's just say, beautiful consequences, was Rutherford's model.

The majestic scope of Rutherford's scientific work in Montreal - he was published as a special, and at the same time with others 66 articles, including the book "Radioactivity", - brought Rutherford the glory of a first-class contributor. We accept the request to take the chair from Manchester. On May 24, 1907, Rutherford turned to Europe. A new period of yoga life has begun.

The first attempt to create a model of the atom on the basis of the accumulated experimental data belongs to J. Thomson (1903). Vіn vvazhav, that the atom is an electrically neutral system of bell shape with a radius of approximately equal to 10-10 m. To explain the linear spectra of the variation of atoms, Thomson tried to calculate the spreading of electrons in atoms and the spreading of the frequencies of their splitting by the position of the equation. However, try not small success. Through the years of history, the great English physicist E. Rutherford found out that Thomson's model was wrong.

English physicist Ege. Rutherford did slіdzhuvav nature tsgogo vpromіnyuvannya. It turned out that a beam of radioactive vibration in a strong magnetic field was divided into three parts: a-, b- and y-viprominence. b-change is the flow of electrons, a-change is the nucleus of the atom to helium, y-change is a short-wave electromagnetic vibration. The phenomenon of natural radioactivity is evidence of the complexity of the life of the atom.
In Rutherford's experiments on the internal structure of the gold atom, the foil was treated with a-particles, which passed through slots in lead screens with a velocity of 107 m/s. a-parts, which are emitted by the radioactive dzherel, are the nuclei of the helium atom. After interaction with the atoms of the foil, the a-particles were placed on a screen covered with a ball of sulfur-free zinc. For the number of spalahs, the number of particles, scattered with foil on the song of the kuti, was indicated. Pidrahunok showing that most os-particles pass through the foil without crossing. However, some a-parts (one out of 20,000) were sharply exhaled directly in the cob.
Rutherford admitting that the fermentation of a-particles is conditioned by positively charged particles, which can be washed, equal to the mass of a-particles. On the basis of the results of similar studies, Rutherford propagated the model of the atom: at the center of the atom, a positively charged atomic nucleus is placed, just like the one (like the planets that wrap around the Sun) are wrapped around under the electric forces of gravity, the negatively charged electrons. The atom is electrically neutral: the charge of the nucleus is equal to the total charge of the electrons. The linear size of the nucleus is assumed to be 10,000 times smaller than the size of the atom. Such is the planetary model of the atom for Rutherford. How can we stop an electron from falling on a massive core? Zvichayno, shvidke wrapping dovkol new. But in the process of wrapping around the acceleration of the field of the nucleus, the electron is guilty of a part of its energy to vibrate on all sides and, step by step, hummingly, still fall on the nucleus. This thought did not give peace to the authors of the planetary model of the atom. Chergov's transition to the path of a new physical model, it seemed, was not enough to destroy the whole picture of the atomic structure with such a practice, and brought it to clear conclusions.
Rutherford was sure that there was a solution, but he could not admit that it would happen so soon. The defect of the planetary model of the atom is corrected by the Danish physicist Niels Bohr. Boron has dramatically expanded the Rutherford model and jokingly reconverted an explanation of what is evident in nature in spite of all the doubts: electrons, not falling on the nucleus and not seeing it, constantly wrap around their own nucleus .

In 1913, Niels Bohr, having published the results of trivial thoughts and investigations, the most important of which began to be called Bohr's postulates: in the atom, there is a large number of stable and strictly singing orbits, such that the electron can chat indefinitely for a long time, more than all forces, what to work on new , Viyavlyayutsya vrіvnovazhenimi; An electron can pass into atoms only from one stable orbit to another one, so the very same. Since, with such a transition, the electron moves away from the nucleus, it is necessary to call the number of energy, which will improve the difference in the energy reserve of the electron in the upper and lower orbits. As soon as the electron approaches the nucleus, then the charge of energy is thrown off at the sight of vibrance.
Imovirno, Bohr's postulates would have served a modest place in the midst of low civic explanations of new physical facts, brought by Rutherford, but there is more than one important setting. Bor for help knowing him spіvvіdnenі zumіv razrahuvati radii "permissible" orbits for the electron in the atom water. Boron admitting, what are the values, what characterize the microlight, guilty quantize , then. stench can take on less than a single discrete value.
Law the microworld - quantum laws! Tsi law on the cob 20 centuries have been established by science. Bohr formulated these three postulates. supplement (and "reply") Rutherford's atom.

First postulate:
Atoms can create a number of stationary stations that give the same energy values: E 1, E 2 ... E n. Perebuvayuchi at the stationary station, the atom of energy does not change, does not care about the power of electrons.

Another postulate:
At the stationary station of the atom, electrons are collapsing in stationary orbits, for which quantum cohesion is victorious:
m V r=n h/2 p (1)
de m · V · r = L - momentum, n = 1,2,3 ..., Planck's h-constant.

Third postulate:
Viprominyuvannya or poglanannya energy atom vіdbuvaєtsya during the transition from one stationary camp to another. When you change it, or else a portion of energy is fading ( quantum ), which is more expensive for the energy of stationary stations, between which the transition is expected: e \u003d h u \u003d E m -E n (2)

1. from the main stationary camp at the wake-up call,

2. from the awakened stationary camp to the main one.

Bohr's postulates supersede the laws of classical physics. They point out the characteristic feature of the microcosm - the quantum nature of the manifestations that appear there. Wisnovki, which are based on Bohr's postulates, are well suited to experiment. For example, to explain the regularities in the spectrum of the atom, the similarity of the characteristic spectra of x-ray changes is just that. On fig. 3 shows a part of the energy diagrams of stationary stations of the atom in water.

The arrows show the transitions of the atom, which lead to the conversion of energy. It can be seen that the spectral lines will merge in the series, which are added to it, on which line of the lower (higher) atom transitions are taken.

Knowing the difference between the energies of the electron in these orbits, it was possible to induce a curve that would describe the spectrum of the development of water in various energizing countries and signify that the life of an atom is to blame especially for the desire to release an atom of water, lead to a new superfluous energy, for example, for the help of a bright light of mercury . lampi. Tsya theoretical curve svіvnіstyu svіvpala zі spectrum vypromіvannya zbudzhenih atomі ​​v vodnіmіryanym Swiss scientists J. Balmersche in 1885 roci!

Vikoristovuvana literature:

1. A. K. Shevelyov “The structure of nuclei, particles, vacuum (2003)
2. A. V. Blagov "Atoms and nuclei" (2004)
3. http://e-science.ru/ - portal of natural sciences

planetary model of the atom

19. The planetary model of the atom accepts that the number

1) electrons in orbits more protons in the nucleus

2) protons are equal to the number of neutrons in the nucleus

3) electrons in orbits more than the sum of the numbers of protons and neutrons in the nucleus

4) neutrons in the nucleus are more than the sum of the numbers of electrons in orbits and protons in the nucleus

21. The planetary model of the atom is primed with doslids z

1) differentiation and melting of solid bodies 2) gas ionization

3) chemical character of new speeches 4) development of α-parts

24. Planetary atom model primed

1) roses of heavenly bodies 2) traces of electrification

3) results of the analysis of α-parts 4) photographs of atoms in a microscope

44. At Rutherford's reports - parts are scattered

1) electrostatic field of the atomic nucleus 2) electron shell of atoms in the target

3) the gravitational field of the nucleus of an atom 4) the surface of the target

48. According to Rutherford, most of the α-particles can easily pass through the foil, practically not moving in rectilinear trajectories, more

1) the nucleus of an atom has a positive charge

2) electronics can generate a negative charge

3) the nucleus of an atom is small (paired with an atom) expanded

4) α-particles can be large (equally equal to the nuclei of atoms) mass

154. How do the firmnesses support the planetary model of the atom?

1) The nucleus is at the center of the atom, the charge of the nucleus is positive, electrons are in orbits near the nucleus.

2) The nucleus is at the center of the atom, the charge of the nucleus is negative, electrons are in orbits near the nucleus.

3) Electrons - at the center of the atom, the nucleus wraps around electrons, the charge of the nucleus is positive.

4) Electrons - at the center of the atom, the nucleus wraps around electrons, the charge of the nucleus is negative.

225. E. Rutherford's investigations of the separation of α-particles showed that

A. mayzhe, the entire mass of the atom is sequestered at the nucleus. B. The nucleus has a positive charge.

Which one is correct?

1) only A 2) only B 3) both A, i B 4) neither A, nor B

259. How is the statement about the existence of the atom consistent with Rutherford's model of the atom?

1) The nucleus is at the center of the atom, the electrons are in orbits near the nucleus, the charge of the electrons is positive.

2) The nucleus is at the center of the atom, electrons are in orbits near the nucleus, the charge of electrons is negative.

3) The positive charge is evenly distributed over the atom, the electrons in the atoms repair the colivanya.

4) The positive charge is evenly distributed over the atom, and the electrons collapse into atoms in different orbits.

266. How can we believe about the existence of the atom? The greater mass of the atom is segregated

1) in the nucleus, the electron charge is positive 2) in the nucleus, the charge of the nucleus is negative

3) in electrons, the charge of electrons is negative 4) in the nucleus, the charge of electrons is negative

254. How is the statement about the existence of the atom consistent with Rutherford's model of the atom?

1) The nucleus is at the center of the atom, the charge of the nucleus is positive, the greater mass of the atom is seized by electrons.

2) The nucleus is at the center of the atom, the charge of the nucleus is negative, the greater mass of the atom is in the middle of the electron shell.

3) The nucleus is at the center of the atom, the charge of the nucleus is positive, the greater mass of the atom is located in the nucleus.

4) The nucleus is at the center of the atom, the charge of the nucleus is negative, the greater mass of the atom is located in the nucleus.

Bohr postulates

267. Scheme of lower energy levels of atoms of a rarefied atomic gas may look like a small image. At the beginning of the hour, the atoms are rebuying at the station with energy E

1) 0.3 eV, 0.5 eV and 1.5 eV 2) more than 0.3 eV 3) less than 1.5 eV 4) any range between 0 and 0.5 eV

273. A diagram of the lower energy levels of the atom is depicted on the little one. At the beginning of the hour, the atom perebuvaє at the station energy E (2) . According to Bohr's postulates, each atom can convert photons with energy.

1) 1 ∙ 10 -19 J 2) 3 ∙ 10 -19 J 3) 5 ∙ 10 -19 J 4) 6 ∙ 10 -19 J

279. What is the frequency of the photon, which is emitted by the atom, similar to the Bohr model of the atom?

1) the difference in energy of stationary stations 2) the frequency of the electron around the nucleus

3) de Broglie's long wind for the electron 4) the Bohr model does not allow

15. The atom is rebuying at the station with energy E 1< 0. Минимальная энергия, необходимая для отрыва электрона от атома, равна

1) 0 2) E 1 3) - E 1 4) - E 1 /2

16. How many photons of different frequencies can change the atoms of water, which are found in another wakeful camp?

1) 1 2) 2 3) 3 4) 4

25. It is acceptable that the energy of atoms in gas can take those values, as shown in the diagram. Atoms are rebuying at the station with energy e (3). What kind of photon energy can clay gas?

1) be-like in the range of 2 ∙ 10 -18 J to 8 ∙ 10 -18 J 2) be-like, ale smaller 2 ∙ 10 -18 J

3) only 2 ∙ 10 -18 J 4) be it, more or less 2 ∙ 10 -18 J

29. When a photon with an energy of 6 eV is vibrated, the charge of an atom

1) does not change 2) increases by 9.6 ∙ 10 -19 C

3) increase by 1.6 ∙ 10 -19 C 4) change by 9.6 ∙ 10 -19 C

30. Light with a frequency of 4 ∙ 10 15 Hz is combined with photons with equal electric charge

1) 1.6 ∙ 10 -19 C 2) 6.4 ∙ 10 -19 C 3) 0 C 4) 6.4 ∙ 10 -4 C

78. The electron of the outer shell of the atom on the back of the cob passes from the stationary station with energy E 1 to the stationary station with energy E 2, fading the photon with frequency v 1 . Potim vіn go over to the station E 2 stationary station with energy E s, fading the photon frequency v 2 > v 1 . What happens during the transition of an electron from a state of E 2 to a state of E 1.

1) viprominyuvannya light frequency v 2 – v 1 2) shading the light with frequency v 2 – v 1

3) viprominyuvannya light frequency v 2 + v 1 4) poglanannya svitla frequency v 2 – v 1

90. The energy of a photon, which is lost by an atom during the transition from the main station with energy E 0 to the start of the station with energy E 1 more expensive (h - constant Planck)

95. On a small image of the energy equalities of the atom and the length of the photons are shown, which are changed and faded during transitions from one equal to the next. What is the length of time for photons, which are changed during the transition from the E 4 level to the E 1 level, such as λ 13 = 400 nm, λ 24 = 500 nm, λ 32 = 600 nm? Vіdpovіd vyslovіt y nm, і rounded up to tsіlih.

96. On a small scale there is a shard of energy lines of the electron shell of the atom and the frequencies of photons are indicated, which change and fade during transitions between these lines. Yaka minimal longevity of photons vibrating the atom at whatever

possible transitions between equals E 1, E 2, e z and E 4, yakscho v 13 \u003d 7 ∙ 10 14 Hz, v 24 = 5 ∙ 10 14 Hz, v 32 = 3 ∙ 10 14 Hz? Vіdpovіd vyslovіt nоmu i roundіt to tsіlih.

120. A diagram of the energy equalities of the atom is shown on the little one. Which of the transitions between the energy lines, designated by the arrows, is accompanied by the minimum frequency quantum?

1) from equal 1 to equal 5 2) from equal 1 to equal 2

124. On a small image of the energy level of the atom and the long-term photons are shown, which are changed and faded during transitions from one level to another. It has been experimentally established that the minimum duration of wear for photons, which is changed during transitions between equals, is 0 = 250 nm. What is the value of λ 13, how λ 32 \u003d 545 nm, λ 24 \u003d 400 nm?

145. A diagram of the possible values ​​of the energy of atoms in a rarefied gas is shown on the little one. At the cob hour, the atoms are rebuying at the station with energy E (3). It is possible to use gas photons with energy

1) only 2 ∙ 10 -18 J 2) only 3 ∙ 10 -18 and 6 ∙ 10 -18 J

3) only 2 ∙ 10 -18, 5 ∙ 10 -18 and 8 ∙ 10 -18 J 4) any kind 2 ∙ 10 -18 to 8 ∙ 10 -18 J

162. The equal energy of an electron in an atom is given by the formula E n = - 13.6/n 2 eV, de n = 1, 2, 3, ... . During the transition of the atom from the state E 2 to the state E 1, the atom releases a photon. Spent on the surface of the photocathode, the photon vibrates the photoelectron. Dovzhina whilі svіtla, scho vіdpovidає chervonіy interі і photoeffect for the material of the surface of the photocathode, λ cr = 300 nm. Why is the speed of the photoelectron maximally possible?

180. On the little one there is a sprat of the lowest atomic energy equals water. Can an atom, which is resting at the station E 1, die a photon with an energy of 3.4 eV?

1) so, when the atom passes from the camp E2

2) so, at which point the atom passes from the camp E3

3) so, when an atom ionizes, falling into a proton and an electron

4) nі, photon energy is not enough for the transition of an atom in the excitation of the camp

218. A simplified diagram of the energy equalities of the atom is depicted on a small scale. The numbered arrows indicate the number of possible transitions of the atom between these equals. To establish the difference between the processes of ignoring the light of the greatest life of the wind and the improvement of the light of the greatest life of the wind with arrows, which point to the energy transitions of the atom. To the skin position of the first column, take the appropriate position of the other one and write down the selected numbers in the table under the appropriate letters.

226. A fragment is shown on a small scale with diagrams of the energy equalities of the atom. Which of the transitions between energy equalities, designated by arrows, is accompanied by the evolution of a photon with maximum energy?

1) from equal 1 to equal 5 2) from equal 5 to equal 2

3) from equal 5 to equal 1 4) from equal 2 to equal 1

228. The figure shows some of the lower energy levels of an atom in water. What kind of transition does a photon with an energy of 12.1 eV depend on?

1) E 3 → E 1 2) E 1 → E 3 3) E 3 → E 2 4) E 1 → E 4

238. An electron, which has a momentum p = 2 ∙ 10 -24 kg ∙ m / s, sticks with a proton, which rests, making the atom water in the state with energy E n (n = 2). In the process of the atom's dissolution, a photon is promoted. Find frequency v that photon, the inexhaustible kinetic energy of the atom. The equal energy of an electron atom and water is given by the formula , de n =1,2, 3, ....

260. Scheme of the lower energy levels of the atom may look like a small image. At the beginning of the hour, the atom perebuvaє at the station energy E (2) . According to Bohr's postulates, the atom can change photons with energy.

1) only 0.5 eV 2) only 1.5 eV 3) whether or not, less than 0.5 eV 4) whether or not in between 0.5 to 2 eV

269. A diagram of the energy levels of the atom is depicted on the little one. Which number indicates the transition, which is the transition viprominuvannya photon with the lowest energy?

1) 1 2) 2 3) 3 4) 4

282. Prominence of a photon by an atom is recognized for

1) electron movement in a stationary orbit

2) the transition of the electron from the main state to the excited

3) the transition of the electron from the awakened state to the main

4) all resurfacing processes

13. Vibration of photons is taken into account during the transition from the wake-up stations with energies E 1 > E 2 > E 3 to the main station. For the frequencies of the second photons v 1 , v 2 , v 3

1) v 1 < v 2 < v 3 2) v 2 < v 1 < v 3 3) v 2 < v 3 < v 1 4) v 1 > v 2 > v 3

1) greater than zero 2) more than zero 3) less than zero

4) more or less than zero

98. An atom at rest glinting a photon with an energy of 1.2 ∙ 10 -17 J. At this moment, the momentum of the atom

1) not changing 2) becoming equal 1.2 ∙ 10 -17 kg ∙ m/s

3) becoming equal 4 ∙ 10 -26 kg ∙ m/s 4) becoming equal 3.6 ∙ 10 -9 kg ∙ m/s

110. It is acceptable that the scheme of energy equalities of atoms may look like a speech,

indications are small, and the atoms are rebuying at the station with energy E (1) . An electron collapsing with a kinetic energy of 1.5 eV, stuck with one of these atoms and jumped, adding additional energy to the deac. Appreciate the momentum of the electron after the stumbling, but the atom rests before the stumbling. Mozhlivistyu viprominyuvannya svetla atom at zіtknennі z elektronom znehtuvat.

111. It is acceptable that the scheme of energy equalities of atoms, as if speech could look like evidence for a little one, and the atoms will change at the station of energy E (1) . The electron, having snared from one of these atoms, jumped out, adding additional energy to the deak. The momentum of the electron after the atom, which is at rest, appears equal to 1.2 ∙ 10 -24 kg ∙ m / s. Change the kinetic energy of the electron to zero. Mozhlivistyu viprominyuvannya svetla atom at zіtknennі z elektronom znehtuvat.

136. A π°-meson with a mass of 2.4 ∙ 10 -28 kg splits into two γ-quanta. Find the momentum modulus of one of the dissolved γ-quanta in the system, in view of the fact that the first π°-meson is dormant.

144. Atomic water flows near the vessel. The water atom in the main station (E 1 = - 13.6 eV) dies a photon and ionizes. An electron that leaves the atom after ionization collapses far into the nucleus with speed v = 1000 km/s. What is the frequency of a clayed photon? The energy of the thermal rush of atoms in the water is suffocated.

197. The atom of water, which is resting, in the main station (E 1 = - 13.6 eV) dies in the vacuum, a photon with a long hair λ = 80 nm. With what kind of swiftness does the electron fall far into the nucleus, what does it mean for the atom to follow the ionization? The kinetic energy of the ion, which, having settled down, resent.

214. Vilniy pіvonіya (π°-meson) with the energy of calm 135 MeV collapses with the swidkіst v, as it is signifi- cantly less for the swidkіst of the light. As a result of this disintegration, two γ-quanta were created, and one of them expands straight ahead, and the other one expands straight ahead. The energy of one quantum is 10% higher, lower. Why is the freshness of pivony until it breaks down?

232. At the table, the energy value for the other and the fourth energy equals of the atom is indicated.

What is the energy of a photon, which is changed by an atom during the transition from the fourth level to another?

1) 5.45 ∙ 10 -19 J 2) 1.36 ∙ 10 -19 J 3) 6.81 ∙ 10 -19 J 4) 4.09 ∙ 10 -19 J

248. An atom, which is resting, changes a photon with an energy of 16.32 ∙ 10 -19 J as a result of the transition of an electron from an excited state to the main one. The atom at the result of the operation begins to collapse step by step at the protile directly with kinetic energy of 8.81 ∙ 10 -27 J. Find the mass of the atom. The density of the atom should be taken into account with a small amount of light.

252. A vessel has atomic water discharges. The water atom in the main station (E 1 \u003d -13.6 eV) dies a photon and ionizes. The electron, which leaves the atom after ionization, crashes far into the nucleus at a speed of 1000 km/s. Yak dovzhina hvili clay photon? The energy of the thermal rush of atoms in the water is suffocated.

1) 46 nm 2) 64 nm 3) 75 nm 4) 91 nm

257. A vessel has atomic water discharges. The water atom in the main station (E 1 \u003d -13.6 eV) dies a photon and ionizes. An electron that leaves the atom after ionization collapses far into the nucleus with speed v = 1000 km/s. What is the energy of a clayed photon? The energy of the thermal rush of atoms in the water is suffocated.

1) 13.6 eV 2) 16.4 eV 3) 19.3 eV 4) 27.2 eV

The stability of any system on an atomic scale is evident from Heisenberg's principle of insignificance (the fourth division of the seventh division). Therefore, the last step in the power of the atom is only possible within the framework of quantum theory. Tim is not less, but the results, which may have important practical significance, can be taken into account within the framework of classical mechanics, praising the additional rules for quantizing orbits.

At whom we have divided the camp of energy equals of the atom of water and water ions. A planetary model is put into the basis of the rozrahunkіv, zgіdno with some kind of electrons wrap around the nucleus under the influence of the forces of Coulomb's gravity. Please note that electrons are collapsing in circular orbits.

13.1. The principle of integrity

The quantization of the apex moment is stagnant in the model of the atom, proponated by Bohr in 1913. Boron was talking about the fact that the results of quantum theory of inter-small energy quanta seem to be consistent with classical mechanics. Vіn formulating three postulates.

The atom can spend more than a 30 minutes at the singing camps with discrete energy levels E i . The electrons, wrapping themselves behind the most discrete discrete orbits, are collapsing quickly, but the stench does not vanish. (At the classical electrodynamics, the vipprominyues whether it is accelerated by the roar of a part, as if there is a charge of zero).

Viprominyuvannya to go out or swear by quanta at the hour of the transition between energy equalities:

Three postulates of the rule of quantization of the moment of wrapping the electron

,

de n you can add to any natural number:

Parameter n called basic quantum number. For the implementation of formulas (1.1), we can depend on the energy of the equal through the moment of wrapping. Astronomical variables require knowledge of dozhin hvil іz to achieve great accuracy: six upper digits for optical lines and up to eight - for radio bands. Therefore, when the atom is wounded, the waters about the infinitely large mass of the nucleus appear too rude, so as to bring to pardon in the fourth significant figure. It is necessary to shake the cores. For yoga, the appearance is introduced understand pointed masi.

13.2. Masa

Electron collapses near the nucleus under the influence of electrostatic force

,

de r- Vector, the cob of which zbіgaєtsya from the positions of the nucleus, and the ending points to the electron. Guess what Z is the atomic number of the nucleus, and the charge of the nucleus and the electron is equal Zeі
. Behind Newton's third law, on the core there is a force, equal - f(It is more modulo and straightened in proportion to the force that affects the electron). Let's write down the speed of the electron

.

We introduce new changes: the speed of the electron and the size of the nucleus

that speed to the center of mass

.

Clauses (2.2a) and (2.2b), taken

.

Thus, the center of the mass of a closed system collapses evenly and rectilinearly. Now let's go (2.2b) to m Z and we see yogo z (2.2a), divided by m e. As a result, the equalness of the viable density of the electron appears:

.

The value to enter before the new

called guided by the mass. In this rank, the question about the collapse of two particles - the electron and the nucleus - will be asked. To look at the surface of the nucleus of one particle, the place that zbіgaєtsya from the positions of the electron, that її mass of the old induced mass of the system.

13.3. A ring between energy and that moment of wrapping

The power of the Coulomb's interchange is straightened out by a direct charge, which goes down, and the module can only lie in the air r between them. Also, equalization (2.5) assigns a part to the centrally symmetrical field. An important power move on the field with central symmetry and energy conservation that wraps up the moment.

Let's write down the mind, that the momentum of the electron in a circular orbit is dependent on the Coulomb's gravity to the nucleus:

.

From the new you can see that the kinetic energy

good half of potential energy

,

taken with a return sign:

.

Povna energy E, obviously, dorivnyuє:

.

Vaughn looked negative, like I can buti for steel mills. Stan atoms and ions with negative energy are called pov'yazanimi. Multiplying equalization (3.4) by 2 r that replaced in the left part of Tver mVr at the time of the wrap M, vislovimo swidkіst V in a moment:

.

Substituting the value of fluidity (3.5), we take away the formula for the total energy:

.

It is a beast of respect that the energy is proportional to the steam stage to the moment of wrapping. Theoretically, this fact may have important implications.

13.4. Quantization of the moment

Another equal for the other Vі r we take away the rules of quantization of orbits, the visnovok of which we know, based on Bohr's postulates. Differentiating the formula (3.5), we take the relationship between small changes in the moment and energy:

.

According to the third postulate, the frequency of the viprominated (otherwise it fades) photon is the same as the frequency of the electron in orbit:

.

3 formulas (3.4), (4.2) and link

between swidkistyu, the moment of wrapping and the radius of the wave is simple to change the moment of momentum for the hour of the transition of the electron between land orbits:

.

Integrating (4.3), we can take

Constants C Shukatimemo at the same time for a critical interval

.

Sustained inconsistency (4.5) do not pay annual additional demarcation: yakscho W go beyond the boundaries (4.5), її can be turned in the same interval, simply by renumbering the values ​​of the moment in the formula (4.4).

The laws of physics are the same for all systems. Let's move from the right-handed coordinate system to the left-handed one. Energy, as if it were a scalar value, with whom to lose a lot,

.

Otherwise, the axial vector of the wrapping moment can be translated. As you can see, the skin axial vector changes the sign when the operation is not assigned:

Між (4.6) and (4.7) there is no superficiality, that's why the energy, zgіdno (3.7), is wrapped in proportion to the square of the moment and becomes unchanged when the sign is changed M.

Later, when you collect negative values, you can repeat the collection of positive values. In other words, for skin positive value M n obov'yazkovo can be known equal to youmu for the module of negative value M – m :

Combining (4.4) - (4.8), we take linearly equal for W:

,

with decisions

.

It is easy to confuse that formula (4.9) gives two values ​​of the constant W that satisfies the inconsistencies (4.5):

.

Subtracting the result is an illustrative table, in which a series of moments is induced for three values ​​of C: 0, 1/2 and 1/4. It’s good to see what’s in the rest of the row ( n\u003d 1/4) the value of the moment wrapping for positive and negative values n vіdrіznyaєtsya for the absolute value.

Zbіg z eksperimentalnymi dannymi Boru far away otrimati, having put a constant C equal to zero. The same rule of quantization of the orbital moment is described by formulas (1). Ale so maє sens that meaning C older half. Vono describe internal moment electrona, or yoga spin- understand, as a report will be reviewed in other chapters. Often the planetary model of the atom is developed, starting from the formula (1), but historically it was created from the principle of viability.

13.5. Electron orbital parameters

Formulas (1.1) and (3.7) can be reduced to a discrete set of orbital radii and electron widths, which can be renumbered after an additional quantum number n:

Їm vіdpovidaє discrete energy spectrum. Povna electron energy E n can be calculated using formulas (3.5) and (5.1):

.

We took away a discrete set of energy states of the atom, water or water of the ion. Stan, which shows the meaning n, equally alone, called main, all else - zbudzhenimi, but yakscho n even greater, then - strongly agitated. Figure 13.5.1 illustrates the formula (5.2) of the water atom. dotted line
designated between ionization. It is good to see that the first awakening of the rіven is significantly closer to the inter-ionization, lower to the main

camp. Approaching the inter-ionization, the lines in Fig. 13.5.2 thicken step by step.
Infinitely richly equal may be less water-silicon atom. In the real middle, the differences in interactions with the sustant particles are brought to the point where the atom is filled with only the last number of the lower rivs. For example, for the minds of the dawning atmospheres, the atom may sound for 20-30 stations, but for a rarefied interzonal gas, hundreds of equals can be guarded, but not more than a thousand.

At the first one, we introduced Rydberg, who went out of the world of peace. Formula (5.2) reveals the physical curve of the constant as a manual unit of the atomic energy. In addition, she will show that Ry is deposited in the
:

.

Due to the great influence of the mass of the nucleus and the electron, the staleness is already weak, but in such situations it is impossible to overcome it. The numeral of the remaining formula has a constant

erg
ev,

kakoї pragne value of Ry with uncoated zbіlshennі masses of the nucleus. In this order, we specified the unit of the Ry vimir, I put it in the first division.

Momentum quantization rule (1.1) . Apparently, the formulas (3.6) - (3.7) may be more than just a few. Prote, as we reconsider below, the residual result (5.2) for the energy equalities is better than the solutions of the Schrödinger equalization. It can be corrected in all modes, as the relativistic corrections are insignificantly small.

Later, zgіdno z planetary model of the atom, in zv'yazanih mills wrapping speed, radius of orbit and energy of the electron take a discrete series of values ​​and are actually assigned by the magnitude of the head quantum number. I will call with positive energy free; the stench is not quantized, and all the parameters of the electron in them, the moment of wrapping, can take on any value, so as not to exceed the laws of conservation. The wrapping moment is quantified forever.

The formulas of the planetary model make it possible to calculate the ionization potential of an atom, water or water ion, as well as the duration of the transition between countries with different values n. You can also estimate the size of the atom, the linear and vertex speed of the electron in orbit.

Vivedenі formulas mayut two obezhennya. Firstly, they are not immune to relativistic effects, which give pardon to order ( V/c) 2 . The relativistic correction increases with the increase in the charge of the nucleus Z 4 and for the FeXXVI ion, it becomes even more frequent. For example, we can see the effect of this division, lingering at the boundaries of the planetary model. In another way, the cream of the quantum number n the energy of equals is determined by other parameters - the orbital and internal moments of the electron. That is why equals are split into sprats. The amount of splitting is also proportional Z 4 and become litter with important ions.

Mustache singularities of discrete equalities are protected by subsequent quantum theory. Tim is not less, Bohr's simple theory appears to be simple, easy to achieve with the exact method of investigating the structure of ions and atoms.

13.6. Rydberg's post

In the optical range of the spectrum, it is not the energy of the quantum that vibrates E, and dozhina hvili  transition between equals. Therefore, for vimiryuvannya energy equals often vikoristovuetsya hvilovaya number E/hc, which wins at the back centimeters. Khvil'ov number that you see
, signified :

cm .

The index  guesses that the mass of the nucleus in which one is appointed is considered infinitely great. Z urakhuvannyam kіntsevoj masi kernel postіyna Rіdberga dorivnyuє

.

In important nuclei, there is more, less in the lungs. Change of mass of a proton and an electron is more

Substituting the value (2.2), we take the numerical value of the constant Rydberg for the water atom:

The nucleus of an important isotope of water - deuterium - is composed of a proton and a neutron, and is approximately twice as important as the nucleus of an atom of water - a proton. Therefore, zgіdno (6.2), postіyna Rіdberg at deuterіu R D more, lower at water R H:

Even more so is the unstable isotope of water - tritium, the nucleus of which is made up of a proton and two neutrons.

In the elements in the middle of the Mendelian table, the effect of the isotopic effect competes with the effect associated with the terminal dimensions of the nucleus. Tsі efekti mayut protilezhny sign and compensate one for one for elements close to calcium.

13.7. Isoelectronic sequence of water

Zgіdno z vznachennyam, let's give at the fourth division of the som division, and they, which are formed from the nucleus of that one electron, are called water. In other words, the stench can be seen to the isoelectronic consistency of the water. Their structure is like a good guess at the atom, and the camp of energetic equals of ions, the charge of the nucleus of which is already great ( Z Z\u003e 20) are caused by a number of differences associated with relativistic effects: electron density due to mobility and spin-orbital interaction.

We look at the naytsіkavіshi in astrophysics ion to helium, sour that bay. In spectroscopy, the charge of an ion is given for help spectroscopic symbol, which is written in Roman numerals right-handed in the chemical symbol of the element. The number, which is represented by a Roman numeral, outweighs the number of atoms of electrons by one. For example, a water atom is designated as HI, and water ions are designated as helium, sour and cold, obviously, HeII, OVIII and FeXXVI. For rich electron ions, the spectroscopic symbol is associated with the effective charge, which is the valence electron.

Rozrahuemo ruh electron in a circular orbit with the improvement of the relativistic fallow yogo species swidkost. Equal (3.1) and (1.1) in the relativistic direction look like an offensive rank:

Masa m assigned by formula (2.6). Guess so, scho

.

Let's multiply the first equal by and do yoga on a friend. As a result, we take

The constant fine structure  is introduced at the formula (2.2.1) of the first division. Knowing the speed, we calculate the radius of the orbit:

.

In the special theory of the kinetic energy of the kinetic energy of the body, the total energy of the body and the energy of calmness for the presence of the external force field:

.

Potential energy U as a function r determined by formula (3.3). Submitting to Virazi for T і U take the value  that r, We take away the same energy of the electron:

For an electron that wraps in the first orbit of a water-borne ion, the value of 2 is equal to 0.04. The lighter elements won, obviously, even less. At
fair layout

.

First of all, as it is easy to overconvert, with accuracy up to a significant value of energy (5.2) in the non-relativistic theory of Bohr, and in the other, with a foolish relativistic correction. Significantly the first dodanok yak E B todi

We write explicitly for the relativistic correction:

Also, we can see the magnitude of the relativistic correction є proportional to the creation  2 Z 4 . Rahuvannya zalezhnostі masi elektron vіd shvidkostі to produce to zbіlshennya dlini rivnіv. It is possible to comprehend the approaching rank: the absolute value of energy grows together with the mass of a particle, and the electron, which is collapsing, is important for its unruliness. Attenuation of the effect of the growth of the quantum number nє naslіd povіlnіshho ruhu elektronu v zbudzhenomu stanі. Strong fallow Z є naslidkom high mobility of the electron in the field of the nucleus with a great charge. Nadalі we calculate the value according to the rules of quantum mechanics and take away the new result - the reduction of the revival behind the orbital moment.

13.8. High energy standards

The camp of an atom or an ion of any chemical element, in which one of the electrons is located on a high energy level, is called high-energy, or rydbergivsky. The stench may be important to power: the position of the excited electron can be described with high accuracy within the framework of the Bohr model. On the right, in that the electron has a large quantum number n, zgіdno (5.1), is already far from the nucleus of those other electrons. In spectroscopy, such an electron is usually called "optical", or "valence", otherwise an electron from the nucleus - "atomic excess". Schematically, the structure of an atom with one strongly excited electron is shown in Fig. 13.8.1. Zliva below placed atomic

surplus: the core of that electronics in the main station. The dotted arrow points to the valence electron. Vіdstan mіzh usіma electrons in the middle of the atomic excess is richly less, lower vіdstan vіd any of them to the optical electron. Therefore, the total charge can be put into practical use by placing it near the center. Also, you can consider that the optical electron collapses under the influence of the Coulomb force directed to the nucleus, and in this way the equal energy is calculated according to Bohr's formula (5.2). The electrons of the atomic surplus screen the core, but on the surface. For the appearance of a private screening, a concept has been introduced effective charge atomic surplus Z eff. For this drop of a strongly distant electron, the value Z eff The difference between the atomic number of a chemical element Z that number of electrons in atomic excess. Here we are surrounded by the abundance of neutral atoms, for which Z ff = 1.

Becoming strongly zbudzhenih ryvnіv go theoretically Bohr be-any atom. Sufficient in (2.6) replace per mass of atomic excess
, yak mensha for the mass of the atom
by the size of the mass of the electron. For the help of the possessed star of the sameness

we can use Rydberg's posture as a function of the atomic energy A chemical element that can be seen:

planetary modelsatom... + --- a -- = 0; (2.12) h² h ∂t 4πm ∂а Δβ + 2(grad agradβ) – ----- = 0. (2. 13 ) h ∂t For βh φ = -- (2.14) 2πm

What is it? Tse model of the atom by Rutherford. The won is named after the British physicist of the New Zealand expedition Ernest Rutherford, who in 1911 told about the discovery of the nucleus. In the course of their experiments with the separation of alpha particles on thin metal foil, they showed that most alpha particles directly passed through the cracked foil, but the deacons jumped. Rutherford admitted that in the area of ​​this small area, in spite of the stench they jumped, the nucleus was positively charged. Tse caution called for yoga to describe the structure of the atom, as amendments to quantum theory are accepted today. Just as the Earth wraps around the Sun, the electric charge of the atom is surrounded by the nucleus, how much the electrons of the opposite charge wrap around, and the electromagnetic field reduces the electrons in the orbit of the nucleus. Therefore, the model is called planetary.

Before Rutherford, another model of the atom was based on the model of Thompson's speech. It had a nucleus, it was positively charged with a “cupcake”, filled with “rodzinks” - electrons, which turned out to be free for him. Before the speech, Thompson herself spoke electronically. At modern schools, if they start to know, they will start from this model.

Models of the atom by Rutherford (left-handed) and Thompson (right-handed)

// wikimedia.org

The quantum model, as it is today describing the structure of the atom, is surprisingly different, as Rutherford invented it. In Russia there are no planets in the Sun, there is no quantum mechanics, and in Russia there are no electrons in the nucleus. The concept of the orbit of dosi has been theoretically deprived of the existence of the atom. Moreover, since it became known that the orbits are quantized, then between them an uninterrupted transition, as Rutherford thought, it became incorrect to call such a model a planetary one. Rutherford smashed the first crochet in the right direction, and the development of the theory of the atom would follow this path, which would be the inspiration.

Why is it good for science? Rutherford's experiment on the curve of the nucleus. But everything that we know about them, we recognized it after. This theory has been developed over a span of ten years, and in it there are signs of fundamental nourishment of everyday matter.

In Rutherford's model, paradoxes were suddenly revealed, and for themselves: as soon as an electron is charged, it wraps around the nucleus, it is guilty of expropriating energy. We know that the body, as if collapsing on a stake with a constant windfall, all the same, it will sooner, because the vector of windfall is constantly turning. And if a part is charged, it collapses with haste, it’s guilty of violating energy. Tse means that she can practically spend it all and fall into the core. Therefore, the classical model of the atom does not fit itself to the end.

So the physical theories began to appear, as if they were trying to fix the hem of the wipe. An important addition to the model of the existence of the atom was brought in by Niels Bohr. Vіn demonstrating that near the atom there is a small amount of quantum orbits, by which the electron moves. Letting it go, the electron is not vibrating energy for the whole hour, but rather moving from one orbit to another.

Boru model of the atom

// wikimedia.org

And behind Bohr's model of the atom, Heisenberg's non-insignificance principle appeared, which explained why it was impossible for an electron to fall on a nucleus. Heisenberg, having shown that an excited atom has an electron in distant orbits, and at the moment, if the photon vibrates, it falls into the main orbit, having spent its energy. The atom crosses over to a stable camp, under which the electron will wrap itself around the nucleus of the dot, until nothing is awakened. The whole stable camp, the distance of such an electron is not falling.

Zavdyaki to the fact that the main camp of the atom is a stable camp, matter is known, everything is known to us. Without quantum mechanics, stable matter would ignite in us. Whose senses have the main nourishment, how can you not put quantum mechanics, why don’t everyone fall into a rage? Why doesn't all speech come to a point? I quantum mechanics

Need to know? For the singing sensation, Rutherford's experiment was repeated anew at the hour of the discovery of quarks. Rutherford pointed out that positive charges - protons - are found in nuclei. And what about the protons in the middle? Now we know that there are quarks in the middle of protons. We recognized this by performing a similar experiment with a deep, springless scattering of electrons on protons in 1967 by the SLAC (National Accurate Laboratory, USA).

This experiment was carried out according to the same principle, like Rutherford's experiment. Then alpha particles fell, and then electrons fell on protons. As a result, the protons can be filled with protons, or they can be awakened through great energy, and even when the protons are scattered, other particles can be born, for example p-mesons. It was clear that this transition should be carried out in such a way that there are no protons in the middle and storage points. We know right away that these dotted warehouses are quarks. In the singing sensation, I saw Rutherford, and yet on the offensive level. Since 1967, the quark model has become impossible. But what will be given, we do not know. Now you need to grow up on quarks and marvel at what the stench is to fall apart. Ale tse advancing crock, until tse robiti go in.

In addition, in the name of Rutherford, the most important plot of the history of feudal science is connected. At the yoga laboratory, Petro Leonidovich Kapitsa. On the cob of the 1930s, youma was fenced off by people from the country and from the vineyards of anger in the Radyansk Union. Having found out about it, Rutherford sent Kapitsa all the accessories, like they were in the new in England, and in this way helped to create the Institute of Physical Problems in Moscow. Tobto, Zavdyaki Rutherford was given the source of a part of Radian physics.