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 lines of the
hydrogen atom, the study of which he took up at the suggestion of
Eduard Hagenbach also of Basel. Using
Ångström's measurements of the hydrogen lines, he arrived at a
formula for computing the wavelength as follows: :\lambda\ = h \, \frac{ n^2 }{ n^2 - m^2 } for
m = 2 and
n = 3, 4, 5, 6, and so forth;
h = 3.6456 · 10−7 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: \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 397
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 nm, 434.17 nm, 486.27 nm, and 656.47 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: : \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 the
Rydberg 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 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==