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Chapter 25: Problem 4

Discuss the splitting of energy of degenerate \(d\) -orbitals in presence of tetrahedral crystal-field potential.

Short Answer

Expert verified
The d-orbitals split into two energy levels in a tetrahedral crystal field. The three orbitals \(d_{xy}, d_{yz}\), and \(d_{xz}\) increase in energy to become \(e\), while the other two \(d_{x^{2}-y^{2}}\) and \(d_{z^{2}}\) decrease in energy to form \(t_{2}\). The \(t_{2}\) orbitals are at a lower energy level than the \(e\) orbitals.

Step by step solution

01

- Understand the Tetrahedral Crystal Field

Let's first comprehend the configuration of a tetrahedral crystal field. It's a specific form of crystal field where the central metal atom/ion is surrounded by four ligands.place at the corners of a tetrahedron. This crystal field induces interactions between the ligands and the d-orbitals of the metal, splitting the degenerate energy levels into two distinct groups further.
02

- Energy Levels of d Orbitals

In the absence of a crystal field, all five d-orbitals are degenerate, possessing the same energy. These are usually represented as \(d_{xy}, d_{yz}, d_{xz}, d_{x^{2}-y^{2}}\) and \(d_{z^{2}}\). When influenced by the tetrahedral crystal field, these degenerate orbitals split into two. It's important to note that the energy splitting of d orbitals in a tetrahedral field is a direct contrast to the splitting in an octahedral field.
03

- Splitting Pattern

The d-orbitals under the influence of a tetrahedral crystal field split into two energy levels. The three orbitals \(d_{xy}, d_{yz}\), and \(d_{xz}\) rise in energy to become \(e\), while the two other orbitals, \(d_{x^{2}-y^{2}}\) and \(d_{z^{2}}\), decrease in energy, forming \(t_{2}\). This happens due to the different spatial arrangement and directional properties of the orbitals referring to the axes.
04

- Understand the Plot

Finally, looking at the energy diagram, you will notice that the \(t_{2}\) orbitals are on a lower energy level than the \(e\) orbitals. This arrangement is the opposite of what occurs in an octahedral field, helping distinguish between the effects of the two types of fields.

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Most popular questions from this chapter

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.

Predict the effect of Jahn-Teller distortion following complexes: (a) \(\mathrm{CuF}_{2}\) (b) \(\mathrm{CuBr}_{2}\) (c) \(\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) (d) \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\)

Discuss the structural effects of crystal field splitting.

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