The observation of discrete lines from hydrogen gas in an electric discharge provided further evidence that there are quantum energy levels. Not only are there discrete lines, but those lines follow a pattern. The pattern deduced by Rydberg sugested that the energy levels have a dependence E_n = -R/n², where R is the Rydberg constant. However, this observation is not very satisfying unless one can explain why the energy levels have the indicated dependnence. "

Implications for quantum theory

By 1900 scientists knew that there were numerous observations aside from hydrogen that required some kind of explanation based on discrete energy levels. Absorption by atoms in the sun gave rise to Fruenhofer lines in the solar spectrum. These are discrete absorption lines that follow various patterns. The complexity comes from the fact that the sun contains hydrogen, helium and other elements in small amounts. Observation of light from the sun also tells us that there are absorptions in the atmosphere. These too are speciifc although they are quite broad compared to the atomic absorption and emission lines. All of these observations tell us that the electrons in atoms and molecules must have quantized energy levels. The difficult problem remained to understand how such quantum levels arose. We now know that we can explain these using atomic and molecule orbitals. In order to get to that point scientists first had to solve the wave equation for the hydrogen atoms. This was done for the first time using a semi-classical theory by Niels Bohr in 1913. The wave equation for hydrogen was solved using a full quantum mechanical treatment by Schrodinger in 1926..