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Chapter 25: Problem 13

Discuss the Jahn-Teller effect with the help of an octahedral complex of \(\mathrm{Cu}^{2+}\) ion.

Short Answer

Expert verified
The Jahn-Teller effect in the octahedral complex of \(\mathrm{Cu}^{2+}\) ion is due to its \(d^9\) electronic configuration. The effect induces a distortion in the complex leading to a decrease in the degeneracy of the \(e_g\) orbitals and as a result, a decrease in energy and increase in stability of the complex.

Step by step solution

01

Introduction to the Octahedral Complex of Cu^2+

An octahedral complex is a molecular complex shaped like an octahedron where a central atom is surrounded by six ligands. For \(\mathrm{Cu}^{2+}\), the configuration is \(d^9\) in the octahedral field.
02

Description of the Jahn-Teller Effect

The Jahn-Teller theorem postulates that any non-linear molecule with a spatially degenerate ground-state electron configuration will spontaneously distort to remove that degeneracy. The distortion results in stabilization of the system and is known as the Jahn-Teller effect. In simple terms, it is the distortion of degenerate molecules to lower symmetry to lower energy and achieve greater stability.
03

Application of the Jahn-Teller Effect to the Cu^2+ Octahedral Complex

In a \(\mathrm{Cu}^{2+}\) octahedral complex, the electron configuration is \(d^9\). This configuration is degenerate with two electrons in the \(e_g\) orbital and seven electrons in the \(t_{2g}\) orbital. The \(d^9\) high-spin configuration is not spherical symmetrically and gives rise to Jahn-Teller distortion. The octahedral complex distorts to elongate along one of its molecular axes which leads to a distribution of the \(e_g\) subset into \(e_{g}\) ( \(z^2\) ) and \(e_{g}\) ( \(x^2-y^2\) ) which are different in energy. This leads to the reduction in the degeneracy of the orbitals and stabilization of the complex through the Jahn-Teller effect.

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Most popular questions from this chapter

$$ \text { Show that } \Delta_{t}=\frac{-4}{9} \Delta_{0} \text { with the help of mathematical derivations. } $$

Explain the following: (a) The ionic radii of \(\mathrm{Ca}^{2+}, \mathrm{Mn}^{2+}\) and \(\mathrm{Zn}^{2+}\) decrease regularly. (b) The ionic radius of \(\mathrm{Ni}^{2+}\) is smaller than that of \(\mathrm{Cu}^{2+}\) in presence of octahedral crystal-field environment of halide ions. (c) \(\mathrm{Co}^{3+}\) preferably adopts octahedral geometry under the effect of strong field ligands. (d) \(\mathrm{Mn}_{2} \mathrm{O}_{4}\) exists in normal spinel structure while \(\mathrm{Fe}_{2} \mathrm{O}_{1}\) exists in inverse spinel structure.

Derive and expression for the tetrahedral and cubic crystal-field potential.

Discuss the quantitative basis of crystal-field theory in presence of octahedral crystal-field potential.

Discuss the crystal-field effects on lattice energy and hydration energies of transition metal ions.
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