Many theories were developed describing the wave-particle duality of radiation, and Balmer was able to fit the lines of the hydrogen spectrum mathematically, but no one was able to theoretically explain the line spectra of a hydrogen atom. That was until Niels Bohr proposed his model of the hydrogen atom.
6.3 Line Spectra and the Bohr Model Part 1
6.3 Line Spectra and the Bohr Model Part 2