Balmer series
As Balmer series describes a specific sequence of spectral lines in the electromagnetic spectrum of the hydrogen atom. It is emitted during the transition of an electron from a higher energy level to the second lowest.
The line series is named after the Swiss Johann Jakob Balmer, 1885 its mathematical regularity, the Balmer formula realized.
Discovery
In the visible region of the hydrogen spectrum, four lines can be observed, their distances from each other are smaller with decreasing wavelength. They are, beginning with the longest wavelength than Hα (H -alpha), Hβ, and Hδ hv respectively. Their wavelengths can be calculated using the Balmer formula:
A is an empirical constant (A = 364.5068 nm = 3645.068 × 10-10 m, so a wavelength in the ultraviolet ). N are the integers 3, 4, 5 and 6 be used ( n ≥ 2 1); n is the sequential number of the shell, the principal quantum number of the excited state in question.
In the non-visible to the naked eye ultraviolet part of the spectrum more lines have been discovered that are continually referred to Hε, Hζ etc. and let the wavelengths to calculate also very good for integer n 6 above:
Thus, the above series converges for increasing n from above against the wavelength A. The constant A is valid under the assumption that the proton has an infinitely heavy mass, so that it is not moved in the hydrogen atom.
Considering, however, the out-of- proton center common center of gravity of the electron and proton, the barycenter, A has a value of 364.705337 nm instead referred to in the above table are calculated values in order for the vacuum (all in nm):
Hα = 656.46961; Hβ = 486.27378; Hv = 434.17302; Hδ = 410.29350; Hε = 397.123589; Hζ = 388.019026; Hη = 383.651069.
The measured values listed in the table suggest that they were determined in air and allow for comparison with vacuum values, the refractive index of 1.00292 for surface air disregarded.
Generalization by Rydberg
The wave number can be explained by the relationship
In the wavelength or by
Convert into the corresponding photon energy; in the last equation, c is the speed of light in vacuum, h is the Planck's constant.
With the relationship between wavelength and wave number, and the equation can be found by Balmer also written in the form:
Is
Named after the Swedish physicist Johannes Rydberg Rydberg constant; n are integers greater than 2 to use.
As early as 1890 Johannes Rydberg generalized the equation of the Balmer Rydberg formula:
Up to this point in the hydrogen spectrum only lines were known for, that is, his equation was a prediction for not yet found lines. The discovery of a new series for by the U.S. physicist Theodore Lyman in 1906 confirmed Rydbergs extension.
Cal Ritz combination principle
The equation describes the Rydberg hydrogen spectrum quite accurately. However, in most other atoms it does not provide correct results. A progress in the description of atomic spectra yielded in 1908 the Swiss mathematician Walter Ritz. He discovered named after him Ritz combination principle: Simplified ". Using additive or subtractive combination, it was the series formulas themselves, whether the incoming into it constants, other series formulas can form " words, this means that by two well-known lines of a possible can be calculated third line. However, can not be observed all these calculated lines. Which lines actually occur, Ritz could not explain.
Interpretation by the Bohr model of the atom
The formulas up to this point purely empirically settled first understand the Bohr model. Thereafter, the spectral lines attributable to the transition of electrons to a different energy level. With the model of Bohr obtained as a general equation for these transitions:
The first term in the parenthesis, is the so -called primary term, the second is referred to as scrolling term. If you hold firmly in the ground term and varies in each case in the current term, the result is the series listed below, named after their discoverers. With the exception of Hα (red), Hβ ( blue-green), hv, Hδ, Hε and Hζ (all purple) they lie in the ultraviolet or infrared regions of the spectrum.
Is already in the Bohr model of the atom, in contrast to the Balmer formula, the constant is not a purely empirical quantity. Rather, the value can be directly attributed to incoming natural constants in the bill. The index indicates here that the movement of the nucleus and the electron taken into consideration about the common center of gravity. The restriction to integer values for and as well as the condition
Follow from this model. The variables and are then the principal quantum numbers for that reason or excited state, where the electron falls back, and the higher-energy, beyond excited state from which it decays, ie a transition between electrons is in general - such as possible between two excited states - in the Balmer series.
The figure shows the energy level diagram of the hydrogen atom and visualizes the above equations ( in the figure will take the title, and instead the term used ): on the left vertical axis is plotted. On the right vertical axis is the corresponding excitation energy, measured from the ground state, given in eV. The spacing of the energy levels is to scale. In the horizontal direction, the first transitions are exemplarily shown for each series. The corresponding principal quantum numbers of the state are given about it. The spacing of the lines to each other, i.e., in the horizontal direction is not to scale, but of the same size for the sake of clarity. The figure shows that all the lines of a series running on the same energy level. The Hα line of the Balmer series is thus a transition from = 3 after = 2
To the right, the series is dotted each series limit shown, that is,
The electron is no longer bound to the nucleus, the atom is ionized. For the Lyman series is obtained using the Bohr equation, an energy of 13.6 eV. This value agrees with the experimentally determined value for the ionization energy of the hydrogen atom in the ground state well.
The question of what to actually occur the lines that are possible according to the Ritz combination principle is clarified by the selection rules. These arise from quantum mechanical calculations.
History
The discoverer Balmer examined the gas discharges in hydrogen outgoing light because he suspected that there is a causal relationship between the light emission and the structure of atoms. The emitted light, spectrally analyzed with a grid indicates the four discrete lines in the visible region ( line spectrum). Balmer was 1884, the Education Act (see above) with the constant A = 3645.6 × 10-10 m.
He kept his discovery for a special case of a more general equation still unknown, which could be also valid for other elements. This assumption is confirmed by subsequent studies spectra of atoms or ions of only one electron in the outermost shell. Remained unclear for Balmer However, the physical meaning of n