The linear shape of $C{O}_2$ is due to

The correct option is D $sp$ hybridisation of
carbon

In $C{O}_2$ , C forms $2$ sigma bonds and $2pi$ bonds with $2$ different oxygen atoms.

Hybridisation of C atom due to $2$ sigma bonds is sp. There is no lone pair on C atom as it has only $4$ valence electrons and all of those are involved in bonding.

Carbon uses one $2s$ and one $2p$ electrons to form two sigma bonds with two different O atoms.

Both the O atom have configuration:



Both the O atoms use their one $2p$ electron to form a sigma bond with the C atom.

When both these O atoms form a second bond with the same C atom, it results in the formation of a pi bond.

These pi bond is formed by $2p$ electrons of C and $2p$ electrons of O atom and hence it is called $p\pi -p\pi$ bonding.

Due to sp hybridisation and no lone pair on C atom and $p\pi -p\pi$ bonding , $C{O}_2$ has a linear shape.