# Johann Jakob Balmer

Johann Jakob Balmer born on May 1st 1825 with Lausen and dead the March 12th 1898 with Basle was a Physicien and Mathématicien Suisse.

In 1885, Ångström identified four lines in the visible spectrum of the Hydrogène, located at wavelengths of 656,3 Nm, 486,1 Nm, 434,0 Nm and 410,2 Nm. Balmer establishes empirically that these four wavelengths $\ lambda$ (which constitute the Série of Balmer), could be expressed by a formula, known as formula of Balmer:

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

where N is an entirety strictly higher than 2 and RH ≡ 4G = 109677,6 cm-1 (Constante of Rydberg). This formula was then generalized by Ritz and was checked in experiments by the discovery of new lines envisaged by the formula of Ritz :

$\ frac \left\{1\right\} \left\{\ lambda\right\} =R_ \left\{H\right\} \ left \left(\ frac \left\{1\right\} \left\{p^ \left\{2\right\}\right\} - \ frac \left\{1\right\} \left\{n^2\right\} \ right\right)$, (2),
p is an entirety (index of the series) and n>p (index of the line).

It is also said that any number of wave $\ sigma \ equiv \ frac \left\{1\right\} \left\{\ lambda\right\}$ of a line of the spectrum of the hydrogen atom puts in the form of a difference of two spectral terms $T_ \left\{K\right\} \ equiv \ frac \left\{R_ \left\{H\right\}\right\} \left\{k^2\right\}$, since one can rewrite (2) in the form $\ sigma=T_ \left\{p\right\} - T_ \left\{N\right\} \,$ ( principle of combination of Ritz ).

The series of Balmer corresponds to N = 2 . Other series were then highlighted: Series of Lyman in 1916 ( N = 1 ), of Paschen in 1908 ( N = 3 ), of Brackett ( N = 4 ), of Pfund ( N = 5 ).

One obtains formulas analog for the ions known as hydrogénoïdes , i.e. with only one electron, like He+ , with a value different from the constant of Rydberg.
Il is the same in a certain measurement for the spectrum of the alkaline (which have only one electron on their external layer), on the condition of modifying the second term in $T_ \left\{K\right\} \ equiv \ frac \left\{R_ \left\{H\right\}\right\} \left\{\left(k+p\right) ^2\right\}$ with p<1 (" correction of Rydberg").

The empirical description of regularities in the spectra of emission line (or absorption) of the atoms was a great discovery, the beginning of an new approach of the Spectroscopie, but especially one of the premises of the Quantum physics.

## References

Herzberg, Atomic will spectra and atomic structure , Dover, 1944 (republished since).
Atkins, Physical chemistry , 5th edition, Freeman, and Co., New York, 1994, chap. 13.

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