The allene molecule has the following Lewis structure:

Must all four hydrogen atoms lie in the same plane? If not, what is the spatial relationship among them? Why?

We know that the $\mathrm{\pi }$ bond is formed due to sidewise overlapping of the p orbital. Thus for the formation of $\mathrm{\pi }$ bond the p orbitals need to be in the same plane. The central carbon in the allene molecule is sp hybridized. This means that it has two p orbitals for forming $\pi$ bond. But the p orbitals will be perpendicular to each other. As a result when the terminal carbons will form $\pi$ bond with the p orbitals of the central carbon, the bonds formed will be perpendicular to each other.

The$\mathrm{\pi }$ bonds formed will be perpendicular to each other. The sp hybrid orbitals will be perpendicular to the p orbitals. The terminal carbons are ${\text{sp}}^{\text{2}}$ hybridised and will have trigonal planar geometry. Therefore the two hydrogen on the left will be perpendicular to the two hydrogen on the left.