Question

A filled d orbital (\[{d^{10}}\])
A. Spherically symmetrical
B. Has octahedral symmetry
C. Has tetrahedral symmetry
D. Depends on the atom

Answer 1

Hint: The s orbital can obtain two electrons while p, d, and f orbitals can carry 6, 10, and 14 electrons separately.
The d-orbitals have 5 degenerate orbitals which if carry two electrons each will have
\[{d^{10}}\] configuration.

Complete step by step solution:Crystal field theory (CFT) depicts the breakage of orbital degeneracy in transition metal complexes due to the existence of ligands.
In this theory, it is presumed that the ions are simple point charges.
There are five d-orbitals.
\[{d_{xy}}\] lies in between the x and the y axes.
\[{d_{xz}}\] lies in between the x and the z axes.
\[{d_{yz}}\] lying between the y and the z axes.
\[{d_{{x^2} - {y^2}}}\] lies on the x and y axes.
In\[{d_{{z^2}}}\] are two lobes on the z axes and there is a donut-shaped ring that lies on the XY plane of the other two lobes.
In a tetrahedral complex, there are four ligands connected to the central metal.
The d orbitals also divide into two distinct energy levels.
The top three have \[{d_{xy}}\], \[{d_{xz}}\], and \[{d_{yz}}\] orbitals. The lowest two consist of the \[{d_{{x^2} - {y^2}}}\] and \[{d_{{z^2}}}\] orbitals.
The explanation for this is inadequate orbital overlap between the metal and the ligand orbitals. The orbitals are directed on the axes, but the ligands are not.
The CFT diagram for tetrahedral complexes has \[{d_{{x^2} - {y^2}}}\]and \[{d_{{z^2}}}\] orbitals equally inadequate in energy as they are between the ligand axis and face small repulsion.
In tetrahedral molecular geometry, a central atom is found at the center of four substituents, which comprise the corners of a tetrahedron.
Tetrahedral geometry is typical for complexes where the metal has d0 or d10 electron configuration.
A filled d orbital (\[{d^{10}}\]) has tetrahedral symmetry.

So, option C is correct.

Note: In square planar molecular geometry, a central atom is encircled by constituent atoms, which constitute the corners of a square on the same plane.
The square planar geometry is dominant for transition metal complexes with a \[{d^8}\] configuration.