Question

# In Allene (${{\text{C}}_{\text{3}}}{{\text{H}}_{\text{4}}}$), the type(s) of hybridization of the carbon atoms is (are)? A sp and ${\text{s}}{{\text{p}}^3}$ B sp and ${\text{s}}{{\text{p}}^{\text{2}}}$  C only ${\text{s}}{{\text{p}}^{\text{2}}}$ D ${\text{s}}{{\text{p}}^{\text{2}}}$and ${\text{s}}{{\text{p}}^3}$

Hint:
The atomic orbitals of an atom combine with each other to form a new set of hybrid orbitals, which are more prominent to bonding with upcoming elements. This process of forming new hybrid orbitals is called hybridization. Hybridization also defines the structure of the molecules. For a specific hybridization there is a specific structure of the molecules. Which is called molecular geometry.
Formula used: $H = \dfrac{1}{2}\left[ {V + X - C + A} \right]$

Allene is an organic compound ,where every carbon atom are bounded with another carbon atom with double bond. These compounds are also called cumulated dienes. The structure of the simplest allene is shown below.

The formula to calculate the hybridization of the central molecule is, $H = \dfrac{1}{2}\left[ {V + X - C + A} \right]$. where V is the number of valence electrons of the central atom, X is the number of monovalent atoms attached to the central atom, C is the total cationic charge and A is the total anionic charge.
Now for allene ${{\text{c}}_1}$ carbon hybridization is,
$H = \dfrac{1}{2}\left[ {V + X - C + A} \right] \\ = \dfrac{1}{2}\left[ {4 + 2 - 0 + 0} \right] \\ = \dfrac{1}{2}\left[ 6 \right] \\ = 3 \\$
For H=3 hybridization is ${\text{s}}{{\text{p}}^2}$.
Now for allene ${{\text{c}}_2}$ carbon hybridization is,
$H = \dfrac{1}{2}\left[ {V + X - C + A} \right] \\ = \dfrac{1}{2}\left[ {4 + 0 - 0 + 0} \right] \\ = \dfrac{1}{2} \times 4 \\ = 2 \\$
For H=2 hybridization is${\text{sp}}$.
Now for allene ${{\text{c}}_3}$ carbon hybridization is,
$H = \dfrac{1}{2}\left[ {V + X - C + A} \right] \\ = \dfrac{1}{2}\left[ {4 + 2 - 0 + 0} \right] \\ = \dfrac{1}{2}\left[ 6 \right] \\ = 3 \\$
For H=3 hybridization is $s{p^2}$.
Therefore the hybridizations of allene is ${\text{sp}}$ and $s{p^2}$.

The correct option is, B.

Note: Atomic orbitals of an atom combine with each other to form a new set of hybrid orbitals, which are more prominent to bonding with upcoming elements. This process of forming new hybrid orbitals is called hybridization.