The atomic structure[3]:the Bohr model

Spectral emission lines of atoms resulted to be formed by electromagnetic waves varying in a discrete way. The easier spectrum to  be calculated is Hydrogen, because its atom is composed by one only electron. The formula required to calculate the frequency of those lines was proposed by Rydberg in 1888.

The problem related to the interpretation of those experimental results was solved by Niels Bohr in 1913, that modified Rutherford's model, according to Quantum Mechanics. The main ideas are:

1. Electrons move around the nucleus in circular orbits (or elliptical, according to Sommerfeld) under the action of coulombian force;
2. Electrons cannot orbit in every orbit, but only in the ones with a certain angular momentum;
3. If electrons orbit in one of the allowed orbits, it doesn't radiate energy;
4. The atom emits energy and radiations only when electrons pass from an higher energy stationary state, to a lower one.

Bohr succeeded in calculating the value of atomic radius for Hydrogen, introducing quantization of energy in the relation between coulombian and centripetal force.

There are therefore infinite allowed stationary state, because n is a natural number. This infinity is a discrete one, and not a continue one, like in classical mechanics. This result is a direct consequence of the quantization of angular momentum, that involves also the quantization of the energy of the electron.

This atomic model can be however applied only for the Hydrogen atom. For more complex atoms it is necessary to introduce another quantum number. Spectral lines of those atoms presented multiplets, that imply the presence of further energy levels, closer to each other. 

It was explained by Sommerfeld, introducing elliptical orbits. Those theories were still based on a classical idea of atom, that is far from being correct, even thought the secondary quantum number is used also on wave quantum mechanics, and represents the shape of the orbital.