Johann Jakob Balmer


May 01, 1825 in Lausen (Baselland)
March 12, 1898 in Basel

Johann Jakob Balmer was a Swiss mathematician and physicist.

The artistically and musically gifted was interested in Kabbalistic and numerology, so he calculated the number of steps of pyramids or the floor plan of biblical temples.

As a philosopher, Balmer worked in a quiet scholarly room and as an architect, he designed simple buildings and churches, something that was very close to his heart as a person who was faithful to the Bible.

In 1884 Balmer discovered a simple formula that made it possible to determine the wavelength for a series of spectral lines of the element hydrogen. This series of spectral lines is called the Balmer series today. However, the evidence that Balmer's formula provides the exact wavelengths was not provided until the beginning of our century with the development of quantum theory.

Atomic energy exchange

Johann Jakob BALMER was born on May 1st, 1825 in Lausen in Baselland and died on March 12th, 1898 in Basel. He studied mathematics and architecture in Karlsruhe and Berlin. The artistically and musically gifted, he contented himself with working as a writing and arithmetic teacher at the T & oumlchterschule in Basel. In addition, he taught descriptive geometry as a private lecturer at the University of Basel from 1865 to 1890.

He was a philosopher in a quiet scholarly room and thus worked as an architect. He held various public & office positions, including Basel Grand Council, school inspector, poor carer, church council. For the humble and deeply religious Balmer, the divine origin of nature showed itself in its inexhaustible richness and its harmonious simplicity. He was fascinated by the numerical relationships not only in buildings (Temple of Solomon in Jerusalem, Barfuunderkirche in Basel), but also in the spacing of lines in the spectrum of the hydrogen atom. He designed simple buildings as well as churches, which was very important to him as a person who was faithful to the Bible. In 1884, with the same withdrawal, he discovered the formula for the spectral lines of hydrogen. & Aringngstr & oumlm had determined the wavelengths of the first four hydrogen lines in 1866, which come closer to the violet side in closer succession. In 1884 Balmer found the famous Balmer formula for the wavelength λ = h [m 2 / (m 2 - n 2)] with h = 3645.6 & Aring and n = 2, m = 3, 4, 5. for the lines H&alpha, H&beta, H&gamma etc.), which later proved to be an essential confirmation of quantum theory and one of the foundations of Bohr's atomic theory. (Niels Bohr based the formula on two simple postulates in 1913.) Shortly before his death, Balmer was able to expand his approach to the spectra of other elements.

Balmer believed that similar laws could be found for other elements, with h assuming a different value that is characteristic of the element. Independently of Balmer, Rydberg examined the meanwhile more extensive data on the wavelengths of the hydrogen spectrum a little later and developed a relationship that can be considered the precursor of today's general series formula.

Balmer ascribes great importance to hydrogen for research into the structure of atoms. He writes: & quotHydrogen, the atomic weight of which is by far the smallest of the atomic weights of all substances known up to now and characterizes it as the simplest chemical element, the substance whose light, broken down by refraction in the solar spectrum, visibly tells us about the tremendous movements and forces which the surface of our central body seems more than any other body called to open new paths for research into the essence of matter and its properties.& quot

In part from: Armin Hermann & # 39Lexikon - History of Physics A-Z & # 39, Aulis-Verlag Deubner and G. Berg in Praxis 4/38.

Balmer, Johann Jakob

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Citation style

Balmer, Johann Jakob, index entry: German biography, [07/01/2021].



B. studied in Basel, Karlsruhe and Berlin (where he also heard the philosopher Schelling and the pedagogue Diesterweg). He earned his doctorate in 1849 with a dissertation on cycloids. In 1865 he qualified as a professor at the University of Basel for descriptive geometry. He resigned from his position as a university lecturer in 1890, while he continued teaching at the daughter's school in Basel into old age.

B.'s lectures, publications, and educational work spanned an extraordinarily varied field. His interests were not only in higher mathematics - especially descriptive and projective geometry, stereoscopic images of crystal forms and others. -, but also of architecture, especially the old Near Eastern and Greek buildings, as early as the middle of the 19th century, the problems of social hygiene and social housing, and finally the common basic questions of science, philosophy and religion.

B.'s name is unforgotten in modern atomic theory. He received the suggestion from J. E. Hagenbach-Bischoff (1863–1906 professor of physics at the University of Basel) to look for regular relationships between the lines in the spectrum of hydrogen gas. J. Fraunhofer had already discovered such lines in 1815 with the spectral decomposition of sunlight. In 1866 the associated light wavelengths for the first four lines of a certain series of the visible and near ultraviolet range in the hydrogen spectrum, which is now called the B. series, were measured very precisely by the Swedish astronomer A. J. Angström. The numerical values ​​of these wavelengths are - in Angstrom units, i.e. H. the ten millionth part of a millimeter, expressed as follows: 6563 4861.4 4340.5 4101.7. - In order to track down the law on which this sequence of numbers is based, B. assumed a "basic number" 3646 and expressed the assumption, which was only confirmed experimentally much later, that the wavelengths of the light emitted or absorbed by hydrogen move towards the ultraviolet side approach this basic number in ever closer succession. By multiplying his base number 3646 by the fractions: 9/5 16/12 25/21 36/32 he was able to calculate exactly the wavelengths measured experimentally. B.'s mathematical intuition recognized the simple basic law of these relationships in the fact that the numerators of these fractions represent the squares of whole numbers, while the same square numbers, reduced by 2 2 = 4, appear in the denominators. Its whole numbers are identical to the “quantum numbers” postulated by the Danish physicist N. Bohr in 1913, which are characteristic of the discrete energy states of all atoms. The basic number determined by B. is represented in Bohr's atomic theory as a relationship between the basic atomic constants of electron mass and charge, Planck's quantum of action and the speed of light: through simple dimensional transformations, the basic number B. s gives the bond Energy of the electron in a hydrogen atom. - He assumed that there must also be lines in the ultraviolet and ultraviolet range in the hydrogen spectrum, which arise when the whole numbers in the B. formula take on all possible values. These series predicted by him were later found experimentally (Lyman, Paschen, Brackett and Pfund series). - In a work published 12 years later (1897), he expanded his theoretical approach to the spark spectra of other chemical elements, e.g. B. of lithium, in good agreement with the experimental measurements, especially by Kayser and Runge. - B.'s work is one of the foundations of today's atomic physics; above all, it has led to an elucidation of the legal relationships between atomic structure and spectral lines, which are associated with the names of N. Bohr and A. Sommerfeld.


i.a. Usually workers' apartments in and around Basel, 1853
Prophet Ezekiel's face from the temple, architecton. shown , 1858 (Habil. - Schr. Basel 1865): The natural research u. D. modern worldview, 1868
Business d. Baptists, v. J. M. Cramp, Baptist History), 1873

The apartment d. Worker, 1883

To project d. Circle, 1884

Note d. Spectral lines d. Hydrogen, in: Verhh. d. Naturforschenden Ges. Basel 7, 1884, 8, 1885. and in: Ann. d. Physics and Chemistry 25, 1885

The free perspective. 1887

Thoughts Substance, Spirit and God, 1891

A new formula for spectral waves, in: Verhh. d. Naturforschenden Ges. Basel 11, 1897, p. 448, and in: Ann. d. Physics and Chemistry 60, 1897, p. 380
see a. Total cat. d. Prussia. Bibl. X, 1937, col. 449.

LP Georg-August-Universität Göttingen

In this experiment Bohr's atomic model is to be used through the spectrum of the hydrogen atom. The measured wavelengths of the first three lines are compared with the formula of the Balmer series.
The experimental setup consists of a hydrogen lamp and an optical grating that is spaced apart by cm is placed. The grid has 570 lines per mm, so that is the grid constant mm. If you look through the grid in the direction of the hydrogen lamp, you can see the line spectrum of the hydrogen in the form of individual, different-colored lines. The experimental setup is shown schematically in Figures 1639 and 8072. The figure 8073 shows the brightly shining hydrogen lamp. The positions of the three lines are measured three times each in order to reduce systematic reading errors. The following pairs of values ​​are measured: From the distance cm from the grille to the lamp, the distances the spectral lines to the lamp and the lattice constants mm the wavelength of the lines can be calculated. The Rydberg formula specifies the wavelength of the light emitted by a hydrogen atom during the transition from the mth excited state to the nth, where is the Rydberg constant.

This formula is also known as the Balmer formula.
In the visible part of the spectrum lies the Balmer series with n = 2 and m = 3, 4, 5,. . The following table shows the summary of the measurements of the wavelengths and the theoretical calculation from the Balmer series:

The right column shows the Rydberg constant derived from our wavelength measurement by inserting the Balmer formula. The mean value of 1 / s agrees very well with the literature value of 1 / s match.

Depending on the energy level one assumes a distinction is made between different hydrogen series:

The Balmer series is the only one that can be observed for the most part (four lines) in the visible area. This can be checked very well with the above formula. The Lyman series, on the other hand, is in the ultraviolet range, all series with lie in the infrared range. The different series of hydrogen are shown schematically in Figure 5094.

Fig. 5094 Transitional series of hydrogen (SVG)

The four visible lines become when there is a transition from after descending according to the wavelength as follows:

  • Physics. Alonso, M. Finn, E.J. 3rd edition, 2000, Oldenbourg
  • Physics. Halliday, David 2nd ed., 2009, Wiley-VCH
  • The new basic physics internship. Eichler, H. J. Kronfeldt, H.-D. Sahm, J. 2nd edition, 2006, Springer Berlin Heidelberg New York
  • Physics. For scientists and engineers. Tipler, Paul A. Mosca, Gene 7th ed., 2015, Spektrum Verlag Munich
  • Experimental Physics 3 - Atoms, Molecules and Solids. Demtröder, Wolfgang 5th edition, 2016, Springer Berlin Heidelberg New York
  • Atomic and Quantum Physics. Hook, H. Wolf, H.C. 8th edition, 2004, Springer Berlin Heidelberg New York

Atomic spectra
Balmer series
Bohr's atomic model
Brackett series
Lyman series
Paschen series
Pound series


Balmer was born in Lausen, Switzerland , the son of a chief justice also named Johann Jakob Balmer. His mother was Elizabeth Rolle Balmer, and he was the oldest son. During his schooling he excelled in mathematics, and so decided to focus on that field when he attended university.

He studied at the University of Karlsruhe and the University of Berlin, then completed his Ph.D. from the University of Basel in 1849 with a dissertation on the cycloid. Johann then spent his entire life in Basel, where he taught at a school for girls. He also lectured at the University of Basel. In 1868 he married Christine Pauline Rinck at the age of 43. The couple had six children.

Despite being a mathematician, Balmer is best remembered for his work on the spectral series. His major contribution (made at the age of sixty, in 1885) was an empirical formula for the visible spectral lines of the hydrogen atom, the study of which he took up at the suggestion of Eduard Hagenbach also of Basel. & # 911 & # 93 & # 912 & # 93 Using Ångström's measurements of the hydrogen lines, he arrived at a formula for computing the wavelength as follows:

for n = 2 and m = 3, 4, 5, 6, and so forth H = 3.6456 × 10 −7 m.

In his 1885 notice, he referred to H (now known as the Balmer constant) as the "fundamental number of hydrogen." Balmer then used this formula to predict the wavelength for m = 7 and Hagenbach informed him that Ångström had observed a line with wavelength 397 & # 160nm. Two of his colleagues, Hermann Wilhelm Vogel and William Huggins, were able to confirm the existence of other lines of the series in the spectrum of hydrogen in white stars.

Balmer's formula was later found to be a special case of the Rydberg formula, devised by Johannes Rydberg in 1888.

with [math] displaystyle [/ math] being the Rydberg constant for hydrogen, [math] displaystyle [/ math] for Balmer's formula, and [math] displaystyle [/ math].

A full explanation of why these formulas worked, however, had to wait until the presentation of the Bohr model of the atom by Niels Bohr in 1913.


The discoverer Balmer investigated the light emanating from gas discharges in hydrogen because he suspected that there is a causal connection between the light emission and the structure of the atoms. The emitted light, spectrally broken down with a grating, shows the four discrete lines in the visible range (line spectrum). In 1884 Balmer found the Education Act (see above) with the constant A. = & # 1603645,6 & # 160 · & # 16010 −10 & # 160m.

He considered his discovery to be a special case of an as yet unknown, more general equation that could also be valid for other elements. This assumption is confirmed by later studies of spectra of atoms or ions with only one electron in the outermost shell. For Balmer, however, the physical meaning of remained unclear n.

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BALMER, Johann. "Note on the spectral lines of hydrogen" in Annals of physics and chemistry, 1885, 25 pp. 80-87, 1885). Volume in contemporary cloth and boards. Small sticker to spine. Interior clean & # 0160 and fresh and with no marks. Almost fine. $ 600

"In 1885. Balmer create (d) a simple mathematical formula to list the particular wavelengths at which a hydrogen atom radiates light and publishes it in [this paper]." Claire Parkinson, Breakthroughs p. 409

& quot In 1885, Johann Jakob Balmer (1825–1898), a Swiss mathematics teacher, published the “Balmer formula” for the spectral lines in the hydrogen spectrum without stating any underlying physical theory. He had noticed that every line in the hydrogen spectrum in the visible light region was related to a single number (364.56 nanometers), and from this concocted a formula that correctly predicted other spectral lines in the visible and infrared spectrum (the "Balmer series" ). & quot Wenner, History of Physics

& quotBalmer’s major article on the hydrogen spectrum is “Note about the spectral lines of the page hydrogen,” in Negotiations of the Natural Research Society in Basel, 7 (1885), 548-560, 750-752 so in Annals of Physics, 3rd ser., 25 (1885), 80-87. & Quot - DSB online

“The Balmer series, or Balmer lines in atomic physics, is one of a set of six named series describing the spectral line emissions of the hydrogen atom. The Balmer series is calculated using the Balmer formula, an empirical equation discovered by Johann Balmer in 1885. & quot - Wikipedia

"Although physicists were aware of atomic emissions before 1885, they lacked a tool to accurately predict where the spectral lines should appear. The Balmer equation predicts the four visible spectral lines of hydrogen with high accuracy. Balmer & # 39s equation inspired the & # 0160Rydberg equation & # 0160as a generalization of it, and this in turn led physicists to find the & # 0160Lyman, & # 0160Paschen, and & # 0160Brackett series, which predicted other spectral lines of hydrogen found outside the & # 0160visible spectrum ."--Tungsten

“In 1913 Bohr proposed his quantized & # 0160shell model & # 0160 of the atom (see & # 0160Bohr atomic model) to explain how electrons can have stable orbits around the nucleus. The & # 0160motion & # 0160of the electrons in the & # 0160Rutherford model & # 0160was unstable because, according to classical mechanics and electromagnetic theory, any charged particle moving on a curved path emits electromagnetic radiation thus, the electrons would lose & # 0160energy & # 0160and spiral into the nucleus . Bohr’s model accounts for the stability of atoms because the electron cannot lose more energy than it has in the smallest orbit, the one with & # 0160n & # 0160 = 1. The model also explains the & # 0160Balmer & # 0160formula for the spectral lines of hydrogen. The light energy is the difference in energies between the two orbits in the Bohr formula. Using Einstein’s formula to deduce the frequency of the light, Bohr not only explained the form of the Balmer formula but also accurately explained the value of the constant of proportionality & # 0160R. ”- Encyclopedia Britannica

Johann Jakob Balmer

& # 42 May 1st, 1825 in Lausen & # 8211 † March 12th, 1898 in Basel
Occupation: & # 160Teacher at the Basler Töchterschule, private lecturer at the University of Basel, researcher and discoverer in math. and phys. area
Office: & # 160Grossrat (BS)
Place of origin: & # 160Lausen and Basel (honorary citizen)
Full name: & # 160Johann Jakob Balmer
Denomination: Reformed

Son of Ballmer Johann Jakob, mayor, and Elisabeth Rolle. Marriage to Pauline Rinck von Grenzach.

High school in Basel, study of philology and mathematics in Basel, Dr.phil. 1849, Habilitation and PD 1865, studied architecture in Karlsruhe and Berlin. For forty years teacher at the daughter school in Basel and from 1869 PD for descriptive geometry at the university. In addition, private researchers with scientific publications ranging from mathematics and physics to architecture to philosophy and theology. His most important works are the "Note on the Spectral Lines of Hydrogen" (1885) and "A New Formula for Spectral Waves" (1897). The "Balmer formula" is still valid today and identifies its inventor as a pioneer in atomic physics. He put his knowledge of architecture to good use in his many years of activity as a Basel Grand Councilor and as a member of the poor relief and church synod. Successfully campaigned for the construction of the "crooked" Wettstein Bridge in the 1870s.

W .: among other things: Workers' apartments in and around Basel (with plans and cost calculations for a residential area built on the width), 1853. - The worker's apartment, Basel 1883. - Note on the spectrum lines of hydrogen, negotiations of the natural research society 7, 1885 - Thoughts on matter, spirit and God, Aphorisms, 1891. - A new formula for spectral waves, 1897.

Lit .: HBLS 1, 551. - Martin Ernst in: Lausen. Our village then and now. A local lore, 1963, 68-72. - Stohler Gerhard in: BasS 1985, 70-75.

This text is from: Birkhäuser, Kaspar: The personal dictionary of the canton of Basel-Landschaft. Liestal 1997.

Table of contents

The quantum mechanical calculation of the energy levels of the hydrogen atom is unsuitable for school because of its complexity and incomprehensibility, which is why one has to fall back on simplified models and approximations (see [4] milq). If you look at various textbooks, such as Physik Oberstufe (2009) & # 912 & # 93, Fokus Physik (2014) & # 913 & # 93 or Metzler Physik (2015) & # 914 & # 93, the hydrogen atom is often accessed using the Bohr's atomic model. This model has both merits and limitations.

The Bohr model of the atom gives good results for the spectrum of the hydrogen atom. It is also easy to understand and imagine for schoolchildren. If one takes the historical context into account, it becomes clear that Bohr was calling classical physics into question for the first time with this model. The problem with Bohr's model, however, is that it already fails for atoms with more than one electron in the shell. In addition, the assumptions of the model have not been derived "from a deeper theory" (cf. Müller & # 915 & # 93 (2003), pp. 64f.).

Various teaching concepts for quantum physics have been developed, which have been summarized in (see Burkard & # 916 & # 93 (2009), pp. 19ff.) Have been analyzed. In the following some concepts are mentioned which speak out against the application of Bohr's atomic model.

1. Bremen concept (see Niedderer & # 917 & # 93 (1992), p. 88) The Bremen concept focuses on the Schrödinger atomic model. Bohr's atomic model is only taken into account to the extent that it is introduced by the students themselves. 2. Munich concept (see Müller & # 915 & # 93 (2003), p. 109ff.) The Munich concept tries to counteract the idea of ​​the planetary model of the atom and places value on quantum mechanical concepts. 3. Berlin concept (see Fischler & # 918 & # 93 (1992), p. 244) In the Berlin concept one adheres to Bohr's atomic model, but the hydrogen atom is treated without using Bohr's atomic model.

Lichtfeldt and Fischler carried out a study of pupils' ideas about quantum physics as part of the Berlin teaching concept. At this point only the questions about the atomic concept will be investigated. To do this, the students were asked to draw a picture of the hydrogen atom. In addition, they should answer the question why the atomic nucleus and electrons do not "stick together" (cf. Müller & # 915 & # 93 (2003), p. 27).

Pictures of the hydrogen atom before the quantum physics class:

Pictures of the hydrogen atom after the quantum physics class:

Both before and after class, the pupils increasingly take the view of Bohr's model of the atom, as they largely drew the image of the electrons moving on orbits around the nucleus. Other students drew a smeared cloud around the atomic nucleus. The last group drew chemical structural formulas of molecules, which is why the term "dumbbell" was assigned to this group. It is also interesting that after the lesson there was a fourth group of students who did not draw any picture of the hydrogen atom. (see Müller & # 915 & # 93 (2003), p. 27 and p. 30)

Stability of atoms before quantum physics class:

Stability of the atoms after the quantum physics class:

When asked about the stability of the atoms, the idea of ​​electrons, which move on fixed circular paths around the nucleus, also dominates. The group "charge" explains the stability due to charge repulsion. The idea of ​​a solid shell (shell) on which the electrons sit or move is represented by fewer students after class. Here, too, the addition of a new group after the lesson is noticeable, which is based on explanations of Heisenberg's uncertainty relation. (see Müller & # 915 & # 93 (2003), p. 27 and p. 30)

Based on these and other studies and investigations (cf. Müller & # 915 & # 93 (2003), pp. 17ff.), The Munich concept derives the following pupils' ideas on the subject of the atom. "The planetary model of the atom is a very dominant and stable misconception from the field of atomic physics. The electrons in the atom are viewed as localized objects that circle around the atomic nucleus on well-defined orbits" (Müller & # 915 & # 93 (2003), p. 111).

With regard to this concept of the atom, the Munich concept aims to take up Bohr's atomic model due to its familiarity and familiarity with the students, but nevertheless to address the reasons why it cannot be reconciled with quantum mechanics (Müller & # 915 & # 93 ( 2003), p. 111).

The Munich concept, which is made up of a qualitative basic course and a quantitative advanced course, was evaluated with questionnaires and interviews on pupils' ideas. After implementing the concept, the students represented a quantum mechanical concept of the atom and largely rejected Bohr's model of the atom. Many students used Bohr's atomic model as a starting point and spoke out against it. "These results can be seen as a confirmation of the approach not to avoid Bohr's atomic model in the classroom, but to go into detail on the background of the results from the basic course (double-slit experiment / location property, uncertainty relation) as to why Bohr's atomic model does not provide an adequate quantum mechanical description of atoms "(Müller & # 915 & # 93 (2003), p. 164).

The image of the circling electrons on the orbits is often impressed on the students. From a quantum mechanical point of view, this consideration is problematic, as it can lead to misconceptions on the part of the students (cf. [5] milq). The Munich Internet project for teacher training in quantum mechanics (short: milq) of the University of Munich has basically no objections to the calculation of the basic state of the hydrogen atom "by minimizing the total energy depending on the atomic radius" (Wiesner and Müller & # 919 & # 93 (1996) , P. 2). For this approach, however, it should be made clear that this is an estimate and not a strict derivation (cf. Wiesner and Müller & # 919 & # 93 (1996), p. 2).

The project also proposes a further method of calculation by "replacing the Coulomb potential of the core with a suitably adapted box potential" (see [6] milq). The detailed calculation can be read here.

The relevant literature should be consulted for detailed information on the individual concepts. Mr. Drobniewski also dealt with these and other concepts in the didactic part of his Wiki article (see [7]).

Video: Johann Jakob Balmer und die Farben (January 2022).