Chapter 24: Problem 2

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

Short Answer

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Crystal Field Theory (CFT) accounts for the degeneracy distortions in metal-d orbitals, due to the presence of neighbouring anions. In an octahedral field, the \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals (forming \(e_g\) levels) are of higher energy while the \(d_{xy}\), \(d_{yz}\), \(d_{xz}\) (or \(t_{2g}\) levels) orbitals have lower energy. On the contrary, for a tetrahedral field, \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals have lower energy while \(d_{xy}\), \(d_{yz}\), \(d_{xz}\) orbitals are of higher energy due to a reversed alignment with the axes.

Step by step solution

Understanding Crystal Field Theory

Crystal Field Theory (CFT) is a model that describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding anion lattice. The interaction between the positive charge of the metal cation and negative charge from the surrounding anions results in a modification of the energy levels of the metal d orbitals.

Splitting in Octahedral Field

In an octahedral field, the five \(d\) orbitals split into two groups. The \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals align with the high electron density in the \(x\), \(y\), and \(z\) axis, making them of higher energy. They are known as \(e_g\) levels. The \(d_{xy}\), \(d_{yz}\), and \(d_{xz}\) orbitals lie in between these axes and are lower in energy, called \(t_{2g}\) levels.

Splitting in Tetrahedral Field

In a tetrahedral field, the splitting reverses. The \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals, which are \(e_g\) orbitals now fall between the axes and therefore have lower energy, whereas \(d_{xy}\), \(d_{yz}\), and \(d_{xz}\) orbitals align with the axes making them higher in energy. This inverted energy level scheme results from the axes of the tetrahedron pointing between the Cartesian axes.

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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

Understanding Crystal Field Theory

Splitting in Octahedral Field

Splitting in Tetrahedral Field

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