Question

The energy levels of the d orbitals split upon ligand binding according to the crystal-field theory on the basis of the Coulomb's law. Which d orbital is expected to be at the highest energy level in a linear complex such as AgCl₂⁻ ?

a. dxy ,dxz and dyz
b. dxz and dyz
c. dx²−y²
d. dz²
e. dxy
f. both dz² and dx²-y²

Answer 1

In a linear complex such as AgCl₂⁻, the (d) dz² orbital will have the highest energy due to direct alignment with the ligands causing increased electrostatic repulsion, as explained by crystal field theory.

Step-by-step explanation:

According to crystal field theory (CFT), in a linear complex, the d orbitals split into different energy levels due to electrostatic interactions with the ligands. For a linear complex such as AgCl₂⁻, the approximate arrangement of ligands aligns with the z-axis, causing a change in energy levels.

The energy of the dz² orbital will be the highest because it points directly along the line of the two ligands, resulting in greater electrostatic repulsion and higher energy relative to a spherical distribution of negative charge.

The other d orbitals (dxy, dxz, dyz, and dx²-y²) will have lower energies, with the dx²-y² orbital being affected by the repulsions less due to its orientation relative to the z-axis.

Consequently, the correct answer to which d orbital would be at the highest energy level in AgCl₂⁻ is dz².