Energy required for the excitation of carbon atom is
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Ab initio hybridisation is a concept taught in schools to help understand how carbon with its one s- and three p-orbitals can achieve a tetrahedral environment. As part of this process, it is required to formally excite an electron.
Formally is the key word here. The entire process is a formal process that has practically nothing to do with real-life atoms (especially because these real-life atoms rather rarely end up in a vacuum without anything around them as the theory assumes). Thus, in real life this formal energy is not needed.
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The energy required for the excitation of C atom is $$\Delta E = hcRZ^2 (\frac {1}{n_1^2} - \frac {1}{n_2^2})$$.
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