Which of the following statements is correct in the context of the allene molecule, $C_{3} H_{4}$ ?

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The central carbon atom is $s p$ hybridized

The terminal carbon atoms are ${sp}^{2}$ hybridized

$C_{3} H_{4}$ is a planar molecule.

The planes containing the ${CH}_{2}$ groups are mutually perpendicular to permit the formation of two separate $π$ -bonds

answer is A, B, C.

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Detailed Solution

The central C atom in the allene molecule is sp hybridised, and the remaining two C atoms are $s p^{2}$ hybridised.
As a result, the central C atom possesses two double bonds, compared to just one double bond for each of the other two C atoms.
On the centre carbon atom, there are two unhybridized, mutually perpendicular p orbitals. Two pi bonds are created between these two unhybridized p orbitals and two nearby C atoms.
As a result, the planes that include the ${CH}_{2}$ groups are perpendicular to one another.

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