Scientist of the Day - Johann Jakob Balmer

The four Balmer lines of the hydrogen spectrum, modern photograph.  Hα is at the right, Hδ at left (Wikimedia commons)

Johann Jakob Balmer, a Swiss mathematician, died on May 1, 1898, at age 72. Balmer is remembered today for a single paper that he published in a journal in 1885, a paper on physics, which was not at all his field of study. He essentially solved a puzzle in spectroscopy.

Portrait of Johann Jakob Balmer as a young man, photograph, 1865, Basel University Library (Wikimedia commons)

It had been discovered in 1859 by Gustav Kirchhoff and Robert Bunsen that the dark lines in the spectrum of the Sun (called Fraunhofer lines, after their discoverer) could be used to identify the chemical elements that make up the Sun. Kirchhoff and Bunsen identified lines from sodium, calcium, oxygen, and other elements, but especially hydrogen. The latter were particularly prominent, and there were four of them in the visible spectrum – one red, one green, one blue, and one violet. They came to be called Hα, Hβ, Hγ, and Hδ (H alpha, H beta, H gamma, and H delta). You can see a modem photograph of these four lines in our first image.

First paragraph, "Notiz über die Spectrallinien des Wasserstoffs" [Note on the spectral lines of hydrogen], by Johann Jakob Balmer, Annalen der Physik, ser. 3, vol. 25, p. 80, 1885 (Linda Hall Library).

As spectral analysis improved, it became possible to measure the wavelengths of those four lines with better and better precision. They turned out to have wavelengths of 6562, 4861, 4340, and 4101 angstroms, a unit equal to one tenth of a nanometer, and designated by the symbol Å. I give you the exact numbers only so that you will recognize them in Balmer’s tables (fourth and fifth images).

Balmer devised a formula that would predict the wavelengths of all four hydrogen lines. It looked like this:

H (we would use λ or lambda for wavelength) = m² / (m²- 2²) x h (we would use B for Balmer)

Where m is 3, 4, 5, or 6, and h (B) is a constant = 3645 Å

Plug in 3, 4, 5, or 6 for m, and the formula will spit out the wavelengths of Hα, Hβ, Hγ, and Hδ.  Balmer had no idea why the formula worked, or where the constant 3645 Å came from. But the formula did work.

The Balmer formula or Balmer equation did not bring immediate fame to Balmer – it was just a trick.  But then, 28 years later, in 1913, Niels Bohr proposed his quantum theory of the hydrogen atom. Bohr suggested that the hydrogen atom has quantized orbits for its one electron; when the electron absorbs a quantum of light, it moves to a higher orbit; if it emits the right quantum of light, it will drop down to a lower orbit.  Bohr calculated the wavelengths of light that a hydrogen atom would emit if its electron moved from the 3rd to the 2nd orbit, 4th to 2nd, 5th to 2nd, and 6th to 2nd, and he found it yielded the four known hydrogen wavelengths. Moreover, his equation looked just like Balmer’s formula. The difference was that Balmer’s formula was empirical, trying to explain the known hydrogen lines. Bohr’s equation, however, was predictive, invoking Planck’s constant to predict the energy levels and determine the wavelengths of the light quanta from first principles.  Bohr, among other things, explained why Balmer’s formula worked. And Balmer’s name gained enhanced stature in this reflected light.

Detail of fourth image, showing Balmer’s formula (Formel) for predicting the wavelengths of the four prominent hydrogen spectral lines, Annalen der Physik, ser. 3, vol. 25, p. 83, 1885 (Linda Hall Library).

We have the papers of both Bohr and Balmer in our serials collection.  You can see the first page of Bohr’s paper in our post on Bohr, and here we show the first paragraph of Balmer’s paper, as it appeared in the Annalen der Physik for 1885 (third image). We also show the chart (fourth image) where Balmer gives the values of the wavelengths of the four hydrogen lines, according to various authorities, and below (and in a detail, fifth image), you can see his Formel (formula), and what it predicts for the four lines.

Balmer died in 1898 and so he did not learn how Bohr made sense of his formula and its predictions, and gave it physical meaning. Balmer would probably have been pleased that the mathematicians came first, and the physicists arrived late, to clean up.

We should probably mention that hydrogen emits many more spectral lines than the four Balmer lines, mostly in the infrared and ultraviolet, and after Balmer showed the way, other physicists came up with Balmer-like formulas to predict these other series. Bohr explained them all as transitions to the first electron orbit, or the third, or the fourth, whereas Balmer's lines were a result of transition to the second orbit. Since this is a post about Balmer and Bohr, we tried not to complicate the story.

William B. Ashworth, Jr., Consultant for the History of Science, Linda Hall Library and Associate Professor emeritus, Department of History, University of Missouri-Kansas City. Comments or corrections are welcome; please direct to ashworthw@umkc.edu.