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What is the derivation of the formula for finding number of pure and hybrid orbital?

I am studying Organic Chemistry. Recently I came up with the formula for finding number of Pure and Hybrid orbital that can be present in a organic compound , That is

Number of Hybrid Orbital = number of "Carbons" * (number denoting the hybridisation of carbon) and

Number of Pure Orbital = number of Hydrogens present + 2* (no of pi orbitals present )

Example Benzene

  1. number of hybrid orbital = 6*(3) = 18 (Hybridisation is sp2 = 1s + 2p = 3)
  2. number of pure orbital = 6 + 2*3 = 12

which tells that there are 18 hybrid orbital and 12 pure orbital present in Benzene.

My question is , What is the derivation of this formula ? Thanks.

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