Hybridisation: sp³, sp² and sp orbitals

Ground-state carbon is $1\text{s}^2\,2\text{s}^2\,2\text{p}^2$. Only two unpaired electrons, so you'd expect two bonds.

Yet methane has four C–H bonds, all identical, all at 109.5°. Plain s and p orbitals can't explain either fact.

One 2s electron moves up into the empty 2p orbital:

$1\text{s}^2\,2\text{s}^2\,2\text{p}^2 \;\rightarrow\; 1\text{s}^2\,2\text{s}^1\,2\text{p}^3$

Now there are four unpaired electrons, so four bonds. Promotion costs a little energy, but forming two extra bonds releases much more.

The 2s orbital and some or all of the 2p orbitals mix to make new, identical hybrid orbitals.

• Mix 1 s + 3 p → 4 sp³ orbitals.
• Mix 1 s + 2 p → 3 sp² orbitals (1 p left over).
• Mix 1 s + 1 p → 2 sp orbitals (2 p left over).

Orbitals in = orbitals out: mixing four orbitals gives four.