Johann Jakob Balmer

Johann Jakob Balmer
Born	1 May 1825 Lausen,Switzerland
Died	12 March 1898(1898-03-12)(aged 72) Basel,Switzerland
Nationality	Swiss
Alma mater	University of Basel
Scientific career
Fields	Mathematics

Johann Jakob Balmer(1 May 1825 – 12 March 1898) was aSwissmathematicianbest known for his work inphysics,theBalmer seriesofhydrogenatom.

Biography

Balmer was born inLausen,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 theUniversity of Karlsruheand theUniversity of Berlin,then completed hisPhDfrom theUniversity of Baselin 1849 with adissertationon thecycloid.Johann then spent his entire life in Basel, where he taught at a school for girls. He also lectured at theUniversity 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 anempiricalformula for the visiblespectral linesof thehydrogenatom, the study of which he took up at the suggestion ofEduard Hagenbachalso of Basel.UsingÅngström's measurements of the hydrogen lines, he arrived at aformulafor computing the wavelength as follows:

$\lambda \ =h\,{\frac {n^{2}}{n^{2}-m^{2}}}$

form= 2 andn= 3, 4, 5, 6, and so forth;h= 3.6456 · 10⁻⁷m = 364.56 nm.

In his 1885 notice, he referred tohas the "fundamental number of hydrogen." Today,his known as theBalmer constant.Balmer used his formula to predict the wavelength forn= 7:

$\lambda \ =(364.56\,{\rm {nm}})\cdot \,{\frac {7^{2}}{\,7^{2}-2^{2}\,}}\simeq 397.0\,{\rm {nm}}$

Hagenbach informed Balmer that Ångström had observed a line with wavelength 397nm.This portion of the Hydrogen emission spectrum, from transitions in electron energy levels withn≥ 3 ton= 2, became known as theBalmer series.

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

Two of Balmer's colleagues,Hermann Wilhelm VogelandWilliam 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 theRydberg formula,devised byJohannes Rydbergin 1888:

${\frac {1}{\lambda }}\ ={\frac {4}{h}}\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right)=R_{H}\left({\frac {1}{m^{2}}}-{\frac {1}{n^{2}}}\right)$

with$R_{H}$being theRydberg constant for hydrogen,$m=2$for Balmer's formula, and$n>m$.

A full explanation of why these formulas worked, however, had to wait until after Balmer's death with the presentation of theBohr model of the atombyNiels Bohrin 1913.

Johann Balmer died in Basel, aged 72.

Honors

• Balmer formula and Balmer constanthare named after him, as well asBalmer linesandBalmer series.
• TheBalmer jumpis useful inAstronomyforstellar classification.
• The craterBalmeron theMoonis named after him.
• Minor planet12755 Balmeris named after him.

External links

• O'Connor, John J.;Robertson, Edmund F.,"Johann Jakob Balmer",MacTutor History of Mathematics Archive,University of St Andrews