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Chapter 25: Problem 1

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

Short Answer

Expert verified
In the octahedral crystal-field potential, the d orbitals split into two levels: \(t_{2g}\) and \(e_{g}\). The energy difference between the \(t_{2g}\) and \(e_{g}\) levels is \(10Dq\), where \(Dq\) is the crystal field splitting parameter. The lower energy \(t_{2g}\) orbitals are lower in energy by \(-4Dq\) and the higher energy \(e_{g}\) orbitals are higher in energy by \(6Dq\). The size of this energy gap determines the spectral properties and magnetic behavior of the transition metal complex.

Step by step solution

01

Understand Octahedral Field Splitting

Identify the relevant d orbitals in the system. In an octahedron, there are three lower energy d orbitals known as \(t_{2g}\) (dxz, dyz, dxy) and two higher energy d orbitals known as \(e_{g}\) (dx^2-y^2, dz^2) due to the spatial arrangement of the ligands.
02

Calculate the Energy Splitting

Calculate the energy splitting between the orbitals using the crystal field splitting energy (\(10 Dq\), where Dq is the crystal field splitting parameter) - a characteristic energy of the resulting field. This can be found experimentally. The energy separation (\(E\)) between the \(e_{g}\) and \(t_{2g}\) orbitals is given by the formula: \(E= 10Dq\). The \(t_{2g}\) orbitals are lower in energy by \(-4Dq\) and the \(e_{g}\) orbitals are higher in energy by \(6Dq\).
03

Plot the Energy Levels

Plot the energy levels of the d-orbitals under the influence of the octahedral crystal field potential. On the \(y\)-axis is the energy, on the \(x\)-axis are the d-orbitals. Place the \(t_{2g}\) and \(e_{g}\) orbitals on the y-axis according to the calculated energy levels.
04

Discuss Result

Use these results to discuss the spectral properties, magnetic behavior, and geometry of the coordination complexes. For instance, the energy gap size determines the spectral properties of the complex. A large energy gap will absorb light in the visible portion of the spectrum while a smaller gap could mean that light is absorbed in the infrared region.

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Most popular questions from this chapter

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

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

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.

Discuss the crystal-field effects on spinel structures.

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) \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\)
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