Elements of quantum physics of atoms and molecules
The theory of the hydrogen atom in Bohr's model
§1 Tthe atomic model of Thomson and Rutherford

The doctrine of the atomic structure of matter originated in ancient times. However, before the end of XIX century atom considered a fundamental principle of indivisible unit ("brick") of any substance.

In the middle of the XIX century, it was experimentally shown that the electron is one of the main components of any substance. (In 1749, Benjamin Franklin hypothesized that electricity is a kind of material substance. Central role of electrical matter, he assigned atomistic conception of the structure of the electric fluid. In Franklin's work first appeared terms: charge, discharge, positive charge, negative charge, a capacitor, a battery particles of electricity. Johann Ritter in 1801 suggested discrete grain structure of electricity.
Wilhelm Weber in the works since 1846 introduces the concept of an atom of electricity and the hypothesis that its motion around the nucleus of the material can be attributed to thermal and light phenomena.
Michael Faraday introduced the term "ion" for the carriers of electricity in the electrolyte, and suggested that the ion has the same charge. Helmholtz in 1881 showed that the concept of Faraday must be consistent with Maxwell's equations. George Stoney in 1881, first to calculate the charge of the monovalent ion in electrolysis, and in 1891, one of the theoretical works Stoney proposed the term "electron" to describe electric charge monovalent ion in electrolysis.).

In 1905, was proposed by JJ Thomson (Lord Kelvin), the first model of the atom, according to which the atom is continuously charged positively charged sphere of radius ~ 10-10 m, within which about their equilibrium positions fluctuate electrons. Net negative charge of the electrons is equal to the positive charge of the ball, so the atom as a whole is neutral (Thomson model of the atom is called "raisin bun" or "plum pudding").

Rutherford's model of the atom

Rutherford in 1909 conducted an experiment on the passage of α - particles through thin metal plates of gold and platinum. (α-particles are produced by radioactive transformations. charge α - particles equal to two charges of the electrons: qα = 2e = 2·1.6·10-19 Cl, the mass of the proton four masses: mα = 4 mp = 4·1.67·10 -27 kg). α - particles emitted by radium placed inside the cavity lead to the channel so that all particles except moving along the canal, absorbed lead. Narrow beam incident on a foil of gold, perpendicular to its surface. α - particles that have passed through the foil and scattered it in outbreaks (scintillations) on a fluorescent screen.

Experiments have shown that in most cases α - particles after passing through the foil, the previous direction or rejected at very small angles. However, some α - particles (about one in 20,000) were deflected at large angles, about 135 ÷ 150 °. Because electrons cannot significantly alter the movement α - particles (), Rutherford is suggested that all the positive charge of the atom is concentrated in its nucleus - an area which occupies a very small amount compared to the total volume of the atom.

The rest of the atom is a cloud of negatively charged electrons, the total charge is equal to the positive charge of the nucleus. This model of the atom was proposed by Rutherford in 1911 and was called the planetary model of the atom, as it resembles the solar system in the center of the system is the "sun" - the core, and around it are moving in orbits "planet" - electrons.
Flaws Rutherford:

a) The electrons in the atomic model can not be fixed, as the under the influence of the Coulomb force, they would be pulled (and "would fall") to the nucleus. In this model, there are infinitely many values ??of the radii of the orbits of the electron and the corresponding values ??of speed


This implies that the radius and velocity can change continuously. Consequently, it can emit any amount of energy, and therefore, the spectrum of the atom must be continuous. In fact, experience shows that atoms have a line spectrum.

b) When r ≈10-10 m v≈ 106 m/s and  and according to electrodynamics, electrons moving with acceleration should radiate and therefore continually lose energy. Then, the electron will spiral closer to the core, and after  τ ≈ 10-10 s to fall to him. On the other hand, the frequency of the radiation must continually change due to changes r, v, T. Therefore, the atom will produce a continuous spectrum.
Attempts to construct a model of the atom with the laws of classical mechanics, electricity and optics have led to a contradiction with the experimental data:
model - a) instability of the atom, and b) a continuous spectrum;
experiment - a) stable atom b) emits under certain conditions, c) the line spectrum.


§ 2 The line spectrum of the hydrogen atom.
The Balmer – Rydberg formula

Luminous gases produce a line emission spectra, consisting of individual spectral lines. When light passes through gases having absorption line spectra - each atom absorbs those spectral lines, which itself can emit.

Spectrum - a set of harmonic components or wavelengths. For example, if the wave can be represented as a superposition of two waves with frequencies ω1 and ω2, then we say that the spectrum has two components or two lines with λ1 and λ2. The spectra are:

a) ruled - from atoms and simple molecules discharged gases striped - complex molecules, solid - heated solids and liquids;

b) emission-in electric a gas discharge, heating of solids, etc., absorption - light passes through gases, liquids and solids, and thus each atom absorbs those spectral lines, which itself can emit;
c) dispersion (prismatic) - obtained by the decomposition of white light through a prism, diffraction - the decomposition of a diffraction grating;
d) nuclear - the spectrum obtained by the atoms (e.g. discharge in gases), molecular (band) - has a kind of bands formed by closely spaced spectral lines
1) vibrational -> FIR (far infrared λ = 0,1 ÷ 1 mm);
2) rotational -> IR λ = 1 ÷ 10 microns;
3) electron - vibrational (the visible and ultraviolet region of the spectrum λ = 0,3 μm and above);
d) etc.

First studied the spectrum of the simplest elements - hydrogen. Balmer in 1885 found that the wavelength known at the time the nine lines of the hydrogen spectrum can be calculated by the formula

J. Rydberg (Swedish scientist) offered some form of record

- Balmer - Rydberg formula.

R’ = 10973731 m-1 – the Rydberg constant (R’ = 1.1·107  m-1),

because, then we can write

where R =R’c = 3.29·1015 s-1 – the same as the Rydberg constant.

The Balmer – Rydberg formula first pointed to the special role of the integers in the spectral patterns.
Now we know a large number of spectral lines of hydrogen, whose wavelengths with high accuracy satisfy Balmer – Rydberg formula. Of Balmer - Rydberg  formula shows that the spectral lines are various values ??of n, form a group, or a series of lines, called the Balmer series. With increasing n the spectral lines of the series closer to each other.
Balmer series is in the visible spectrum, so the first was discovered.
At the beginning of XX century in the spectrum of the hydrogen atom was discovered a few series in the invisible part of the spectrum.
Thus, the following are known series of the hydrogen atom spectrum

Position number

name of series

Kind Balmer - Rydberg formula for a series

The value of n - levels with which the transition of the electron


year of discovery


Lyman series

n = 2, 3 ,4, …

UV (ultraviolet) portion of the spectrum



Balmer series

n = 3 ,4, 5, …

and near UV



Paschen series

n = 4, 5, 6, …





Brackett series

n = 5, 6, 7, …





series Pfunda

n = 6, 7, 8, …




Humphrey series

n = 7, 8, 9, …




All of the above series can be described by a single formula, called the generalized formula of Balmer

Series formulas indicate the existence of physical laws in the spectrum of the hydrogen atom, which are explained by classical physics is impossible.

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