One of the great triumphs of 20th century science was the reduction of chemistry to physics via quantum mechanics. By 1927, Wolfgang Pauli was able to explain the structure of the periodic table of elements by means of his Pauli Exclusion Principle, which is a consequence of quantum theory. Now all of chemistry can in principle be reduced to physics.
In 1913, Neils Bohr developed a new model of the atom, which contains fixed orbitals to which the electrons are restricted. Electrons are allowed to jump from one orbital to another but at all times they must remain in a single orbital. By 1927, once quantum theory reached fruition, Pauli derived his exclusion principle, which states that no two electrons can occupy the same quantum mechanical state at the same time. This means that at most two electrons can occupy the same orbital, each having opposite spin in the case of two occupying the same orbital.
By applying the Pauli Exclusion Principle, one can build up the periodic table. A hydrogen atom contains just one electron, which goes to the ground state, labeled as 1s, the number 1 being the principal quantum number, indicating its energy, which in this case is the lowest possible energy, and the s indicating the angular momentum quantum number. Helium has two electrons in the 1s orbital, each with opposite spin. These two electrons fill up the first shell, whose principle quantum number is 1. In lithium, the third element, the third electron must occupy the second shell, so its configuration is 1s^2 2s^1. Like the 1s orbital, the 2s orbital can only occupy two electrons, taking us to atomic number 4 (beryllium). Beyond this, the 2p orbitals, of which there are three, begin to fill. By neon, these orbitals are filled, completing the second row of the periodic table. Each row of the table is completed similarly.
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