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We are given the Lewis structure of the allene molecule. The Lewis structure for allene is: H2C=C=CH2

Let's analyze the geometry of each carbon atom in the allene molecule. There are two types of carbon atoms - the central one and the two terminal ones. For terminal carbon atoms (HC=C): These carbon atoms are sp-hybridized since they form a double bond with the central carbon atom and a single bond with hydrogen. Each sp-hybridized carbon atom will have a linear geometry due to the linear arrangement of the hybrid orbitals. For the central carbon atom (C=C=C): The central carbon atom is also sp-hybridized since it forms a double bond with each of the terminal carbon atoms. The geometry around this atom will also be linear.

Now that we know the geometries around each carbon atom, we can understand the spatial arrangement of hydrogen atoms in the allene molecule. The two terminal carbon atoms (HC=C) have their hybrid orbitals (one sp-hybrid orbital and one unhybridized p-orbital) arranged linearly. The double bond between the terminal carbon atoms and the central carbon atom is formed by the overlap of an sp-hybrid orbital from each terminal carbon atom with an sp-hybrid orbital from the central carbon atom, along with a π bond involving their unhybridized p-orbitals. Since the π bond between the central carbon atom and each of the terminal carbon atoms involves p-orbitals that are perpendicular to each other, the allene molecule has a non-planar arrangement. In other words, π bonding in the allene molecule forces the groups attached to the terminal carbons to be perpendicular.

As a result of the non-planar arrangement of the allene molecule, the hydrogen atoms are also not in the same plane. There are two planes for hydrogen atoms: 1. The first plane contains two hydrogen atoms attached to a terminal carbon atom (on one side of the linear C=C=C unit). 2. The second plane contains the other two hydrogen atoms attached to the other terminal carbon atom (on the opposite side of the linear C=C=C unit). These two planes are perpendicular to each other. In conclusion, all hydrogen atoms in the allene molecule do not lie in the same plane. Instead, they are arranged in two distinct planes perpendicular to each other due to the non-planar arrangement of the allene molecule.