Chapter 23: Problem 2

Discuss in brief the crystal field theory and represent the splitting of ' \(d\) ' orbitals in octahedral and tetrahedral fields.

Short Answer

Expert verified

The Crystal Field Theory describes the variations in the energy levels of the 'd' orbitals due to repulsion with ligands in a complex. The orbitals split into two groups based on their orientation. This splitting is different for octahedral (eg and t2g) and tetrahedral (t2 and e) fields.

Step by step solution

Introduction to Crystal Field Theory

Crystal Field Theory (CFT) is a model that describes the electronic structure of transition metal compounds. It considers how the interaction between a central metal ion and its surrounding ligands can lead to changes in the energy levels of the metal's 'd' orbitals.

Understand 'd' Orbitals

In an isolated atom, the five 'd' orbitals (dz², dx²-y², dxy, dxz, dyz) are degenerate - they have the same energy. However, in the presence of an electric field created by surrounding ligands, the energies of the 'd' orbitals can be altered.

Octahedral Field Splitting

In an octahedral field, the 'd' orbitals split into two energy levels. The \[d_{z^{2}}\] and \[d_{x^{2}-y^{2}}\] orbitals point directly at the ligands, so they experience more repulsion and are raised in energy, forming the \( e_{g} \) set. The other three orbitals (\[d_{xy}\], \[d_{xz}\], \[d_{yz}\]) lie in between the ligands, so they experience less repulsion and are lowered in energy, forming the \( t_{2g} \) set.

Tetrahedral Field Splitting

In a tetrahedral field, the 'd' orbitals also split, but in the opposite manner. Here, the \[d_{z^{2}}\] and \[d_{x^{2}-y^{2}}\] orbitals are farther from the ligands and form a lower energy group \( t_{2} \) and \[d_{xy}\], \[d_{xz}\], \[d_{yz}\] orbitals point closer towards the ligands forming the higher energy group \( e \).

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Discuss in brief the crystal field theory and represent the splitting of ' \(d\) ' orbitals in octahedral and tetrahedral fields.

Short Answer

Step by step solution

Introduction to Crystal Field Theory

Understand 'd' Orbitals

Octahedral Field Splitting

Tetrahedral Field Splitting

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