Question

Why isn't allene planar?

Answer 1

I assume you mean the twisted propadiene.

Well, the left half of allene is perpendicular to the right half. In order for a molecule to be planar, the whole molecule has to be planar.

A simplified explanation is that the central carbon atom's `p_x` and `p_y` orbitals are aligned to make perpendicular `pi` bonds, corresponding to perpendicular `"CH"_2` groups. The same `p` orbital cannot (easily) make two parallel `pi` bonds on either side, especially if they both contain localized electrons.

(A planar allene exists, but for a much shorter amount of time than the twisted allene as it equilibrates into the twisted form.)