# Johann Jakob Balmer

SWISS MATHEMATICIAN

1825–1898

The name of Johann Jakob Balmer is immortalized in the Balmer series of
**
spectral lines
**
emitted from the hydrogen atom. Atoms that are excited to higher energies
return to lower energies by emitting electromagnetic radiation at specific
frequencies. Gustav Kirchhoff had shown in 1859 that each element has its
own unique spectrum, but attempts to predict the frequencies of these
spectral lines were unsuccessful until Balmer.

After receiving a doctorate in mathematics from the University of Basel in Switzerland in 1849, Balmer taught at a girls' secondary school in Basel for the rest of his life; he was also a part-time university lecturer for many years. In 1885 he proposed an empirical formula for the wavelengths (l) of four hydrogen spectral lines in the visible region. The modern form of this equation is

where
*
R
*
is a constant. With the values
*
n
*
= 2, and
*
m
*
= 3, 4, 5, 6, the equation predicts the wavelengths of the four lines
with considerable accuracy.

Aware of only these four lines, Balmer calculated l for a fifth line (
*
m
*
= 7). A line with a wavelength very close to the predicted value was
observed experimentally. Balmer suggested that his formula might also
predict wavelengths of other series of spectral lines by using integer
values for
*
n
*
other than 2 and
*
m
*
^{
3
}
*
n
*
+ 1. Other series of hydrogen lines were not known then, but were
subsequently discovered (the Lyman, Paschen, Brackett, and Pfund series of
lines).

There was no obvious reason why Balmer's formula should be so successful. Not until Niels Bohr proposed his atomic model in 1915 could line spectra be explained in terms of electrons moving from higher-energy orbits to lower-energy ones.

**
SEE ALSO
**
Bohr, Niels
.

*
Richard E. Rice
*

## Bibliography

### Internet Resources

Balmer, J. J.
*
Note on the Spectral Lines of Hydrogen.
*
Available from
http://webserver.lemoyne.edu/faculty/giunta/balmer.html
.

O'Connor, J. J., and Robertson, E. F.
*
Johann Jakob Balmer.
*
Available from
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Balmer.html
.

## Comment about this article, ask questions, or add new information about this topic: