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| {{Infobox scientist
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| |name = Johann Jakob Balmer
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| |image = Balmer.jpeg
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| |image_size = 220px
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| |caption =
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| |birth_date = May 1, 1825
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| |birth_place = [[Lausen]], [[Switzerland]]
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| |death_date = {{dda|1898|3|12|1825|5|1}}
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| |death_place = [[Basel]], [[Switzerland]]
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| |residence =
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| |citizenship =
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| |nationality = [[Switzerland]]
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| |ethnicity =
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| |field = [[Mathematics]]
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| |alma_mater = [[University of Basel]]
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| '''Johann Jakob Balmer''' (May 1, 1825 – March 12, 1898) was a [[Switzerland|Swiss]] [[mathematician]] and [[mathematical physicist]].
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| ==Biography ==
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| 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.
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| 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 a total of six children.
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| Despite being a mathematician, he is not remembered for any work in that field; rather, 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 book|last=Magie|first=William Francis|title=A Source Book in Physics|publisher=Harvard University Press|location=Cambridge, Mass|year=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:
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| :<math>\lambda\ = \frac{ hm^2 }{ m^2 - n^2 }</math> | |
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| for ''n'' = 2, ''h'' = 3.6456×10<sup>−7</sup> m, and ''m'' = 3, 4, 5, 6, and so forth.
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| 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 [[Nanometer|nm]]. Two of his colleagues, [[Hermann Wilhelm Vogel]] and [[William Huggins]], were able to confirm the existence of other lines of the [[Balmer series|series]] in the spectrum of hydrogen in white stars.
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| Balmer's formula was later found to be a special case of the [[Rydberg formula]], devised by [[Johannes Rydberg]].
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| : <math>\frac{1}{\lambda}\ = \frac{4}{h} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)= R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)</math> | |
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| with <math>R_H</math> being the [[Rydberg constant#Rydberg constant for hydrogen|Rydberg constant for hydrogen]], <math>n_1 = 2</math> for Balmer's formula, and <math>n_2 > n_1</math>.
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| 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.
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| Johann Balmer died in Basel.
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| ==Honors==
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| *[[Balmer line]]s and [[Balmer series]] are named after him.
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| *The crater [[Balmer (crater)|Balmer]] on the [[Moon]] is named after him.
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| ==References==
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| <references/>
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| ==External links==
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| * {{MacTutor Biography|id=Balmer}}
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| {{Scientists whose names are used in physical constants}}
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| {{Authority control|VIAF=64941315}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Balmer, Johann
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Swiss mathematician and physicist
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| | DATE OF BIRTH = May 1, 1825
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| | PLACE OF BIRTH = [[Lausen]], [[Switzerland]]
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| | DATE OF DEATH = March 12, 1898
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| | PLACE OF DEATH = [[Basel]]
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| }}
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| {{DEFAULTSORT:Balmer, Johann}}
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| [[Category:1825 births]]
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| [[Category:1898 deaths]]
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| [[Category:19th-century physicists]]
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| [[Category:19th-century Swiss mathematicians]]
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| [[Category:Swiss physicists]]
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| [[Category:People from Basel-Stadt]]
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| [[Category:Spectroscopists]]
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