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Elemental Hydrogen is a diatomic element. At STP (standard temperature and pressure) the stable form of the element is for two atoms to be bonded together.

In Hydrogen's case, each atom of Hydrogen brings one electron. These two electrons are shared, forming a covalent bond. This sharing of each of the atom's electrons is a more stable state than that of having only a single electron. Stable states are thermodynamically preferable.

Electrons travel around atoms in orbitals. Each orbital has two electrons.

For Hydrogen, having the 1s orbital filled with it's original electron and the electron shared from the other atom is more stable.

In atoms above Helium, the octet rule prevails.

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