Where do vacant p-orbitals come from?

[ProfuselyQuarky]

Forgive me for such a such a question; it's probably sleep deprivation or my inherent stupidity. Either way, where do vacant p-orbitals come from?? When carbon's valence electrons find themselves in a bonding situation that requires them to hybridize, their 2s and 2p orbitals merge into a single $sp^3$ orbital. Apparently the "3" refers to the number of 2p orbitals that merged, but I don't understand why there are three?? There are only two unpaired electrons from 2p.

 

[Wrichik Basu]

Orbitals are inherent to atoms. Absence of electrons in the orbitals does not mean that the orbitals are absent. Quantum mechanically, these orbitals are obtained by solving the Schrödinger Equation. If you look at how the orbitals are derived based on quantum numbers, you will understand that these are inherent to the atoms. For example, elements of period 2 don't have d-orbitals. That is because the solutions of Schrödinger Equation says that you don't have d-orbitals for principal quantum number 2.

Once you look under the hood (study things through QM), things will become clearer. It's not true that I know everything, but I have studied bits and parts, and orbitals are truly inherent to atoms.

 

[ProfuselyQuarky]

Orbitals are inherent to atoms. Absence of electrons in the orbitals does not mean that the orbitals are absent. Quantum mechanically, these orbitals are obtained by solving the Schrödinger Equation. If you look at how the orbitals are derived based on quantum numbers, you will understand that these are inherent to the atoms. For example, elements of period 2 don't have d-orbitals. That is because the solutions of Schrödinger Equation says that you don't have d-orbitals for principal quantum number 2.

Quantum mechanics aside, how am I supposed to look at a carbon atom and know that it has 3 2p orbitals?

 

[Borek]

Quantum mechanics aside, how am I supposed to look at a carbon atom and know that it has 3 2p orbitals?

You can't put quantum mechanics aside and ask about number of orbitals, as it is quantum mechanics that tels us how many orbitals there are. It is all in the quantum numbers and their relationships: m_l can take any value from -l to l, so for every n>=2 there are always three p orbitals.

I feel like you are mistaking orbital with an occupied orbital. My desk has three drawers, doesn't mean they can't be empty.