Why does the sp3 hybrid of nitrogen exist, it has the exact same electronic configuration as the un-hybridised atom.

The sp3 hybridization of nitrogen occurs to maximize the electron density around the central atom and reduce electron repulsion. While nitrogen does indeed have the same electronic configuration in both hybridized and un-hybridized forms, the hybridization process allows for a more efficient arrangement of its valence electrons.

To understand why hybridization occurs, we need to consider the molecular geometry of the molecule. Nitrogen typically forms covalent bonds with three other atoms in a trigonal pyramidal arrangement. Each bond is formed by sharing a pair of electrons between nitrogen and the other atoms.

In its un-hybridized state, nitrogen has three electron pairs (one lone pair and two bonding pairs) distributed around the central atom. These electron pairs repel each other, leading to a distorted shape and increased potential energy due to electron-electron repulsion. This electron pair arrangement is known as "sp2 hybridization," as it is based on the mixing of one 2s orbital and two 2p orbitals.

To minimize electron repulsion and achieve a more stable arrangement, nitrogen undergoes sp3 hybridization. During hybridization, the 2s orbital and all three 2p orbitals of nitrogen combine to form four new hybrid orbitals known as sp3 orbitals. These orbitals are arranged in a tetrahedral geometry, with one hybrid orbital containing a lone pair and the other three forming covalent bonds with other atoms.

The sp3 hybridization allows nitrogen to achieve a more symmetrical structure and distribute electrons as far apart as possible. This results in a decrease in electron-electron repulsion and a more energetically favorable arrangement. Although the electronic configuration remains the same, the reorganization of orbitals through hybridization optimizes the structure of the nitrogen compound.