Question
What is meant by hybridisation of atomic orbitals? Describe the shapes of $sp, sp^2 , sp^3$ hybrid orbitals.

Answer

Hybridization is defined as an intermixing of a set of atomic orbitals of slightly different energies, thereby forming a new set of orbitals having equivalent energies and shapes.
For example, one 2s-orbital hybridizes with two 2p-orbitals of carbon to form three new $0sp^2$ hybrid orbitals.
These hybrid orbitals have minimum repulsion between their electron pairs and thus, are more stable. Hybridization helps indicate the geometry of the molecule.
Shape of sp hybrid orbitals: sp hybrid orbitals have a linear shape. They are formed by the intermixing of s and p orbitals as:

Shape of $sp^2$ hybrid orbitals:
$sp^2$ hybrid orbitals are formed as a result of the intermixing of one s-orbital and two 2p-orbitals. The hybrid orbitals are oriented in a trigonal planar arrangement as:

Shape of $sp^3$ hybrid orbitals:
Four $sp^3$ hybrid orbitals are formed by intermixing one s-orbital with three p-orbitals. The four $sp^3$ hybrid orbitals are arranged in the form of a tetrahedron as:

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