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The necessity of the hybridization of orbitals can be traced back to Valence Bond theory, the theory that calculates covalent bonds angles and lengths. When we try to apply this theory to a compound like methane (CH4), it begins to fall apart. This is due to something called Electron Promotion, in which an electron from a lower energy shell is "promoted" to an empty higher energy orbital. For example, the shorthand electron configuration of Carbon is [He]2s2,2px1,2py1. In a compound such as methane, Carbons configuration can more accurately depicted as [He]2s1,2px1,2py1,2pz1, because this is a lower energy and more stable configuration(atoms love that).The latter configuration is lower in energy because the 2s electron that got moved up to an empty p orbital here experiences less repulsion from the other electrons. As a result, a very small amount of energy is required to "promote" this electron. The resulting s orbital and p orbitals are combined into four "sp3" hybrid orbitals because of the property of s and p orbitals to act as waves of electron density that interfere with each other and form brand new patterns. In carbon, we have one 2s orbital and three 2p orbitals (Px, Py and Pz). This means you can mix the s orbital with x, y or z of the 3 p orbitals, which will result in the SP, SP2, and SP3 orbitals respectively.
There is also conservation of orbitals. Even when carbon orbitals are hybridized into sp or sp2, there are 2 and 1 p orbitals left over, respectively. The total number of orbitals following hybridization stays the same.
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