(a) consider a carbon atom in its ground state. would such an atom offer a satisfactory model for the carbon of methane? if not, why not? (hint: consider whether a ground state carbon atom could be tetravalent, and consider the bond angles that would result if it were to combine with hydrogen atoms.)
(b) consider a carbon atom in the excited state. would such an atom offer a satisfactory model for the carbon of methane? if not, why not?

(a) No. Ground-state carbon has only 2 half-filled orbitals that could be used for bonding.

(b) No. The bond angles would be incorrect as the p-orbitals are all perpendicular to each other (90°).

Explanation:

See attachment for the ground-state and excited-state electron orbital diagrams of carbon.

A methane molecule has all four CH bonds the same length and at 109.5° from each other. Hybridization of the s and p orbitals to sp³ orbitals is necessary.

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