Question

Can two `2p` orbitals of an atom hybridize to give two hybridized orbitals?

Answer 1

No. They are the same in energy, so it would lose the point to hybridize them. They have no necessity to hybridize with other `2p` orbitals.

As a result, if you attempt to hybridize two different `2p` orbitals, it will not work. There is no energy benefit.

On the other hand, a `2s` can hybridize with some `2p` orbitals to form `sp`, `sp^2`, or `sp^3` hybridizations depending on how many `2p` orbitals hybridize.

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Since methane must make four identical `"C"-"H"` bonds, it must use four identical orbitals, so it hybridizes one `2s` with all three `2p` orbitals to form four `sp^3` hybrid orbitals, one for each `"C"-"H"` `sigma` bond.

All four of these `\mathbf(sp^3)` orbitals are lower in energy than the original `\mathbf(2p)` orbitals.