[susdujcrd]

I understand that the Carbon atom in C₂H₄ undergoes an sp² hybridization,
taking one 2s orbital with two half-filled 2p orbitals to create three sp² orbitals.
Why the newly arranged electrons occupy the third empty 2p orbital as well? isn't it of higher energy than the three new sp² obritals?

[AWK]

There is no empty 2p orbitals in ethylene. One electron at each C occupy  this orbital forming pi-bond.

[susdujcrd]

the pi-bond comes from the overlapping of the remaining 2p orbital in each of the carbons.

[AWK]

Exactly!
This are two different problems - isolated (or excited) atom and atom in molecule

[susdujcrd]

I think I got it, thank you.