Part 1. sp3 Hybridization of Carbon
The simplest way to illustrate hybridization of atomic orbitals is to look at the case of methane, CH4.Obviously, we need to make four bonds using the atomic valence orbitals of hydrogen and those of carbon. Two ways of representing the molecule are shown below. Note especially that the molecule is symmetrical, i.e. all four bonds are of equal length and all bond angles are equal to the perfect tetrahedral angle (109.5o).
Of course, we need four such orbitals to make a methane molecule. They are arranged around the carbon atom as shown below. Use the mouse to rotate it and have a good look at it.
Finally, the electron from each hydrogen pairs up with the electron in one of the sp3 hybrids, forming a (two electron) single bond. The methane molecule thus looks like the following. Note the hydrogen atoms (white) around the carbon atom (grey) and note, by rotating the molecule, that all H-C-H bond angles are the same.
On to part 2, sp2 hybridization