A. Carbon sp3 hybridization - Mathematical operation to create four ...

A. Carbon sp 3 hybridization - Mathematical operation to create four sp 3 hybrid orbitals
that are all equal in energy so that their orientation relative to one another is tetrahedral.
Below is a pictorial representation on the hybridization without calculus.
1. Carbon ground state valence electrons are the 2s and 2p. The 2s has paired
electrons. This must un-pair and one of the two electrons populate a higher energy 2p
orbital
2. One 2s orbital and three 2p orbitals each have one unpaired electron. But they are
not equal in energy as shown on the left. By hybridization, the 2s and three 2p mixing
will result in four equal energy orbitals (sp 3 orbitals). Note the energy of sp 3 orbitals is
slightly less than a 2p, but higher than the 2s

Similarly, the C three 2sp 2 orbitals are equal in energy and must occupy a trigonal
planar arrangement. Note, one 2p orbital remains pure (not hybridized.)
Types of overlaps shown below

3. Similarly, the Csp orbital require hybridization of one 2s and one 2p orbital to give
two 2sp hybrid orbitals (blue) that are arranged linearly. This leaves two 2p orbitals for
pi bonding (green)