The correct answer is option 'B', which states that the carbon atoms in allene (C3H4) are hybridized as sp and sp2. Let's explain this answer in detail:

The hybridization of an atom refers to the mixing of atomic orbitals to form new hybrid orbitals with different shapes and energies. In the case of carbon, the ground state electronic configuration is 1s^2 2s^2 2p^2. Carbon has four valence electrons, two in the 2s orbital and two in the 2p orbitals.

In allene (C3H4), there are three carbon atoms, each connected to two other carbon atoms. To determine the hybridization of the carbon atoms in allene, we need to look at the arrangement of the atoms and the number of sigma bonds formed by each carbon atom.

- Molecular structure of allene:

H H
\ /
C = C = C
/ \
H H

- Hybridization of the central carbon atom (C2):

The central carbon atom (C2) is connected to two other carbon atoms and two hydrogen atoms. It forms two sigma bonds with the adjacent carbon atoms and two sigma bonds with the hydrogen atoms.

1. Sigma bonds: Sigma bonds are formed by the overlap of sp hybrid orbitals from the central carbon atom (C2) with the 1s orbitals of the hydrogen atoms. Since the central carbon atom (C2) forms sigma bonds with two hydrogen atoms, it must have two unhybridized p orbitals available to form sigma bonds.

2. Hybridization: The presence of two sigma bonds and two unhybridized p orbitals suggests that the central carbon atom (C2) is hybridized as sp.

- Hybridization of the terminal carbon atoms (C1 and C3):

The terminal carbon atoms (C1 and C3) are each connected to one other carbon atom and two hydrogen atoms. They form one sigma bond with the adjacent carbon atom and two sigma bonds with the hydrogen atoms.

1. Sigma bonds: Sigma bonds are formed by the overlap of sp2 hybrid orbitals from the terminal carbon atoms (C1 and C3) with the 1s orbitals of the hydrogen atoms. Since the terminal carbon atoms (C1 and C3) form sigma bonds with two hydrogen atoms, they must have one unhybridized p orbital available to form sigma bonds.

2. Hybridization: The presence of one sigma bond and one unhybridized p orbital suggests that the terminal carbon atoms (C1 and C3) are hybridized as sp2.

Therefore, the correct answer is option 'B', which states that the carbon atoms in allene are hybridized as sp and sp2.