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{{Short description|Swiss mathematician (1825–1898)}}
{{Infobox scientist
|name              = Johann Jakob Balmer
|image             = Balmer.jpeg
|image_size        = 220px
|caption           =
|birth_date        = 1 May 1825
|birth_place       = [[Lausen]], [[Switzerland]]
|death_date        = {{death date and age|1898|3|12|1825|5|1|df=y}}
|death_place       = [[Basel]], Switzerland
|residence         =
|citizenship       =
|nationality       = Swiss
|ethnicity         =
|field             = [[Mathematics]]
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|alma_mater        = [[University of Basel]]
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}}

'''Johann Jakob Balmer''' (1 May 1825 – 12 March 1898) was a [[Switzerland|Swiss]] [[mathematician]] best known for his work in [[physics]], the [[Balmer series]] of [[hydrogen]] atom.

==Biography ==
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 [[PhD]] 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 spectral series. His major contribution (made at the age of sixty, in 1885) was an [[empirical]] formula for the visible [[spectral line]]s of the [[hydrogen]] atom, the study of which he took up at the suggestion of [[Eduard Hagenbach-Bischoff|Eduard Hagenbach]] also of Basel.<ref>{{cite journal |last1=Balmer |first1=J. J. |title=Notiz über die Spectrallinien des Wasserstoffs |journal=Annalen der Physik und Chemie |date=1885 |volume=25 |pages=80–87 |url=https://babel.hathitrust.org/cgi/pt?id=wu.89048352553;view=1up;seq=96 |series=3rd series |trans-title=Note on the spectral lines of hydrogen |language=German}}</ref><ref>{{cite book|last=Magie|first=William Francis|title=A Source Book in Physics|publisher=[[Harvard University Press]]|location=Cambridge, Massachusetts|date=1969}} p. 360</ref> Using [[Anders Jonas Ångström|Ångström]]'s measurements of the hydrogen lines, he arrived at a [[Balmer's formula|formula]] for computing the wavelength as follows:

:<math>\lambda\ = h \, \frac{ n^2 }{ n^2 - m^2 }</math>

for ''m'' = 2 and ''n'' = 3, 4, 5, 6, and so forth; ''h'' = 3.6456 · 10<sup>−7</sup> m = 364.56 nm.

In his 1885 notice, he referred to ''h'' as the "fundamental number of hydrogen." Today, ''h'' is known as the ''Balmer constant.'' Balmer used his formula to predict the wavelength for ''n'' = 7:

<math>\lambda\ = (364.56 \, {\rm nm}) \cdot \, \frac{ 7^2 }{ \, 7^2 - 2^2 \, } \simeq 397.0 \, {\rm nm}</math>

Hagenbach informed Balmer that Ångström had observed a line with wavelength 397&nbsp;[[Nanometer|nm]]. This portion of the Hydrogen emission spectrum, from transitions in electron energy levels with ''n'' ≥ 3 to ''n'' = 2, became known as the [[Balmer series]]. 

The Balmer lines refer to the emission lines that occur within the visible region of the Hydrogen emission spectrum at 410.29&nbsp;nm, 434.17&nbsp;nm, 486.27&nbsp;nm, and 656.47&nbsp;nm. These lines are caused by electrons in an [[excited state]] emitting a photon and returning to the first excited state of the hydrogen atom (''n'' = 2).

Two of Balmer's colleagues, [[Hermann Wilhelm Vogel]] and [[William Huggins]], were able to confirm the existence of other lines of the Balmer 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:

: <math>\frac{1}{\lambda}\ = \frac{4}{h} \left( \frac{1}{m^2} - \frac{1}{n^2} \right)= R_H \left( \frac{1}{m^2} - \frac{1}{n^2} \right)</math>

with <math>R_H</math> being the [[Rydberg constant#Rydberg constant for hydrogen|Rydberg constant for hydrogen]], <math>m=2</math> for Balmer's formula, and <math>n>m</math>.

A full explanation of why these formulas worked, however, had to wait until 18 years after Balmer's death with the presentation of the [[Bohr model of the atom]] by [[Niels Bohr]] in 1913.

Johann Balmer died in Basel, aged 72.

==Honors==
*Balmer formula and Balmer constant ''h'' are named after him, as well as [[Balmer line]]s and [[Balmer series]].
*The [[Balmer jump]] is useful in [[Astronomy]] for [[stellar classification]].
*The crater [[Balmer (crater)|Balmer]] on the [[Moon]] is named after him.
*[[Minor planet]] [[12755 Balmer]] is named after him.<ref>{{cite web|url=http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=12755|title=12755 Balmer|publisher=[[JPL]]}}</ref>

==References==
 <references/>

==External links==
* {{MacTutor Biography|id=Balmer}}
{{Scientists whose names are used in physical constants}}

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{{Use dmy dates|date=May 2018}}

{{DEFAULTSORT:Balmer, Johann}}
[[Category:1825 births]]
[[Category:1898 deaths]]
[[Category:19th-century Swiss physicists]]
[[Category:19th-century Swiss mathematicians]]
[[Category:Scientists from Basel-Stadt]]
[[Category:Spectroscopists]]
[[Category:People from Basel-Landschaft]]