Question

How are hybridization orbitals found?

Answer 1

Hybridized orbitals are mathematical "averages" (I know it's more complicated) of the s and p orbitals of the atom participating in the bonding.

Conventionally, we cannot understand why methane exists, since carbon has four identical bonds to hydrogen but only three p orbitals and one s orbital in its valence shell.

Hence, if it hybridizes its valence orbitals into four identical orbitals, (`"sp"^3`), it can achieve this molecular structure.

Here's a link to a page from a more advanced chemistry class at NYU regarding the calculus involved if you're interested in the quantitative methodology.

http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_16/node2.html