Jawaharlal Nehru Technological University Hyderabad B.Tech I CHEMISTRY Previous Question Paper (July/August - 2021 - R18)

Crystal field splitting occurs because the degeneracy of the d-orbitals of a central metal ion is lifted when it is surrounded by ligands. As ligands approach the metal ion, the electrostatic repulsion between the metal's d-electrons and the ligand's lone pairs depends on the spatial orientation of the d-orbitals, causing them to split into different energy levels.

In a tetrahedral field, the four ligands approach along the axes of a tetrahedron, which lie between the Cartesian axes. Consequently, the d_xy, d_yz, and d_zx orbitals (collectively termed t₂) point more directly toward the ligands than the d_x²-y² and d_z² orbitals (collectively termed e). This results in the t₂ set being at a higher energy level than the e set. The splitting energy in a tetrahedral field, denoted as Δ_t, is significantly smaller than in an octahedral field, specifically Δ_t ≈ 4/9 Δ_o, because there are fewer ligands and their approach does not align perfectly with any d-orbital.

1,3-Butadiene (CH₂=CH-CH=CH₂) consists of four sp² hybridized carbon atoms, each possessing one unhybridized p-orbital perpendicular to the molecular plane. These four p-orbitals overlap laterally to form a conjugated system of four π molecular orbitals.

The four π orbitals are generated by the linear combination of the four atomic p-orbitals:

1. ψ₁ (Bonding): Lowest energy, zero nodes, all four p-orbitals have the same phase.
2. ψ₂ (Bonding): One node between C₂ and C₃, two regions of constructive overlap.
3. ψ₃* (Antibonding): Two nodes, one between C₁-C₂ and one between C₃-C₄.
4. ψ₄* (Antibonding): Highest energy, three nodes, all adjacent p-orbitals have opposite phases.

In the ground state, the four π electrons occupy the two lowest energy bonding orbitals (ψ₁ and ψ₂), resulting in a stable conjugated system with partial double-bond character between C₂ and C₃.