The first quantitative description of the hydrogen spectrum was given by johann balmer, a swiss school teacher, in 1885. by trial and error, he found that the correct wavelength λ of each line observed in the hydrogen spectrum was given by 1λ=r(122−1n2), where r is a constant, later called the rydberg constant, and n may have the integer values 3, 4, 5, if λ is in meters, the numerical value of the rydberg constant (determined from measurements of wavelengths) is r = 1.097×107 m−1 . balmer knew only the four lines in the visible spectrum of hydrogen. thus, the original formula was written for a limited set of values of n. however, as more techniques to detect other regions of the spectrum were developed, it became clear that balmer's formula was valid for all values of n. the entire series of spectral lines predicted by balmer's formula is now referred to as the balmer series.