# Rydberg, Johannes (Robert)

### atomic structure spectra formula

[rüd berg] (1854–1919) Swedish spectroscopist: early theorist on atomic number.

Educated at Lund, Rydberg stayed there for his entire career, as professor of physics from 1901. He was fascinated by periodic table of the elements and he had the brilliant and valuable intuition that the periodicity was related to atomic spectra and atomic structure. Working on atomic emission spectra in 1890, he found a simple general formula for the frequency of some of the spectral lines. He introduced the useful idea of wave numbers (1/?, where ? is the wavelength); and showed that equation giving the frequencies of many lines in the hydrogen spectrum could be generalized in the form 1/? =R(1/ *m* 2 –1/ *n* 2 ). Within 30 years successive spectral series were found fitting this formula, with simple integral values for *n* and *m* ; the Balmer series is that having *m* =2 and *n* = 3,4,5 etc. The constant R is known as the Rydberg constant. Rydberg himself never reached his goal of relating spectra to atomic structure, but his view that a relation between structure and spectra must exist was valuable and reached fruition with work on atomic structure in 1913, from which Rydberg’s formula emerges with a value of R calculated in excellent agreement with experiment.

Rydberg’s study of the periodic table led him in 1897 to see the importance of atomic number (rather than atomic weight), a view confirmed by in 1913; and in 1906 he stated for the first time that 2, 8 and 18 (ie 2 *n* 2 where *n* = 1, 2, 3) are the numbers of elements in the early periods. He also corrected the number of lanthanides to 32.

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