a carbon atom has 6 electrons. in the lowest state, 2 electrons occupied the 1s shell and 4 electrons are in the 2s and 2p shell.

However, because of the interaction between electrons, the pure s-state and p-state is not an eigenstate, but the mixed state is, so called the Hybrid Orbit.

the mixed states are:

\Psi_{sp2}(1,0,0) = \frac{1}{\sqrt{2}} (\Psi_{2s} + \Psi_{2p_{x}})

\Psi_{sp2}(-1,\sqrt{3},0) = \frac{1}{\sqrt{2}} (\Psi_{2s} - \frac{1}{2} \Psi_{2p_{x}}+ \frac{\sqrt{3}}{2} \Psi_{2p_{y}})

\Psi_{sp2}(-1,-\sqrt{3},0) = \frac{1}{\sqrt{2}} (\Psi_{2s} - \frac{1}{2} \Psi_{2p_{x}}- \frac{\sqrt{3}}{2} \Psi_{2p_{y}})

and

\Psi_{2p_z}

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