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The first to determine the general structure of the atom (a positive nucleus surrounded by a cloud of negative charge) was Rutherford, using his scattering experiment.

The theory was developed by Bohr to explain absorption and emission spectra. The Bohr model is also sufficient to explain some chemical reactions.

The modern theory is explained by the schodinger equation, which explains quantised energy levels the electrons exist at, and the Pauli exclusion principle, which states that no two fermions (the class of particles to which electrons belong) can exist in the same quantum state. This helps explain the number of electrons in each shell.

It might be useful to research Dirac, who's equation describes fermions.

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