Balmer series

A sequence of wavelengths of light emitted by atoms of hydrogen, and a mathematical formula that yields those wavelengths. One such wavelength lies in the red part of the spectrum, four others in the blue and violet regions, and the remainder in the ultraviolet region. Johann Jakob Balmer (1825-1898) a Swiss school and university teacher of mathematics, discovered that the first four wavelengths, λ, were yielded by the formula

λ = constant × m² / (m² − n²)

in which:

the constant is equal to 364.56 nanometres, m is an integer (whole number) from 3 to 6, and n is 2.

Balmer later learned from a colleague that a further five wavelengths, not previously known to him, closely matched the predictions of the formula.

An indefinitely large number of lines is predicted by this formula. Successive lines crowd together as larger values of m are considered, approaching but never quite equalling a wavelength of 364.56 nanometres.

Balmer also conjectured that other series of spectral lines would be found to correspond to the formula with other small integers replacing n in his formula. This was confirmed in the work of Johannes Rydberg (1854-1919), a Swedish physicist. He developed a more general formula from which the Balmer series can be derived, together with an unlimited number of series for, in principle, all atoms. The predictions derived are accurate for hydrogen and a few more ions (atoms stripped of most of their electrons), but not accurate for other atoms and ions, owing to the complexity of their structure.

The explanation for the forms of such series was provided by Niels Bohr's model of the atom, proposed in 1913. This explained electromagnetic radiation as being produced when an electron fell from one energy level in the atom to a lower one. Balmer's series represents the radiation given out by electrons falling to the second-lowest energy level (n = 2) from the third, fourth, fifth ... levels (m ≥ 3). Another series of lines, called the Lyman series, is produced by transitions to the lowest energy level (n = 1) from the second, third, fourth ... levels (m ≥ 2). These have high energies and all lie in the ultraviolet.