The lobes of which \(d\) orbitals point directly between the ligands in (a) octahedral geometry, (b) tetrahedral geometry?

Short Answer

Expert verified
In (a) octahedral geometry, the lobes of the \(d_{xy}\), \(d_{yz}\), and \(d_{xz}\) orbitals point directly between the ligands. In (b) tetrahedral geometry, the lobes of the \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals point directly between the ligands.

Step by step solution

01

Understanding the d Orbitals

The d orbitals have a total of 5 different shapes. They can be represented as: 1. \(d_{xy}\): lobes lie in xy-plane, between x and y axes 2. \(d_{yz}\): lobes lie in yz-plane, between y and z axes 3. \(d_{xz}\): lobes lie in xz-plane, between x and z axes 4. \(d_{z^2}\): lobes lie along the z-axis, with a torus shape in the xy-plane 5. \(d_{x^2-y^2}\): lobes lie along the x and y axes
02

Understanding Octahedral Geometry

In octahedral geometry, six ligands are arranged around the central atom. The ligands form opposite pairs along each of the three axes (x, y, and z) in a symmetric manner.
03

Identifying the d Orbitals for Octahedral Geometry

As the ligands are arranged along the axes in octahedral geometry, we have to identify the d orbitals that point between the ligands. In this case, the \(d_{xy}\), \(d_{yz}\), and \(d_{xz}\) orbitals have lobes that point directly between the ligands, because their lobes lie between the axes.
04

Understanding Tetrahedral Geometry

In tetrahedral geometry, four ligands are arranged around the central atom. The ligands are placed at the vertices of a regular tetrahedron, which results in each ligand occupying a position between any two axes.
05

Identifying the d Orbitals for Tetrahedral Geometry

Since the ligands in tetrahedral geometry occupy positions between any two axes, the d orbitals with lobes pointing directly between the ligands are the ones with lobes along the axes. In this case, the \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals have lobes that point directly between the ligands.
06

Conclusion

In (a) octahedral geometry, the lobes of the \(d_{xy}\), \(d_{yz}\), and \(d_{xz}\) orbitals point directly between the ligands. In (b) tetrahedral geometry, the lobes of the \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals point directly between the ligands.

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