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Hybridization is the idea that when an atom is exposed to an amount of energy, the energy levels surrounding it get jumbled enough to migrate from one orbital to another. I think Lavelle said in class that we cannot externally determine the hybridization state of an atom without knowing what it's bonded to so you shouldn't have to derive the hybridization state out of thin air.
Hybridization is basically when atomic orbitals combine to be more suitable for chemical bonds. For example, Carbon has a ground state configuration of 1s2 2s2 2p2, indicating it has two lone electrons. This would mean Carbon is inclined to only bond two electrons, however we know that is not the case. Taking methane, CH4, we know that Carbon bonds with 4 Hydrogen atoms because an electron from the carbon's 2s orbital can be excited into a 2p orbital, allowing there to be 4 unpaired electrons (in the 2s and 3p orbitals) and resulting sp3 hybridized orbitals.
The way that we determine hybridization is generally by drawing the Lewis Structure of the given compound and counting the number of regions of electron density that the compound has. If we have COF2, which has three regions of electron density, the number of orbitals filled when they merge together (or hybridize) is three, so your exponents in your hybridization have to add up to three. COF2 would have an sp^2 hybridization for this reason.
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