Which of the following complexes are diamagnetic?
(a) [Ni(H₂O)₆]²⁺
(b) [Co(CN)₆]^3-
(c) [HgI₄]^2- (tetrahedral) 
(d) [Cu(NH₃)₄]²⁺ (square planar) 

Verified step by step guidance

1. Identify the oxidation state and electron configuration of the central metal ion in each complex.
2. Determine the geometry of each complex and the type of ligands involved (strong field or weak field).
3. Apply crystal field theory to determine the electron distribution in the d-orbitals for each complex.
4. Check for unpaired electrons in the d-orbitals to determine if the complex is paramagnetic or diamagnetic.
5. Conclude which complexes are diamagnetic based on the absence of unpaired electrons.

Key Concepts

Magnetism in Coordination Complexes

Magnetism in coordination complexes is determined by the presence of unpaired electrons. A complex is diamagnetic if all its electrons are paired, resulting in no net magnetic moment. Conversely, if there are unpaired electrons, the complex is paramagnetic. Understanding the electron configuration and the ligand field theory helps predict the magnetic properties of these complexes.

Crystal Field Theory

Crystal Field Theory (CFT) explains how the arrangement of ligands around a central metal ion affects its electron distribution and energy levels. Ligands can cause the d-orbitals of the metal to split into different energy levels, influencing whether electrons are paired or unpaired. The geometry of the complex (e.g., octahedral, tetrahedral) plays a crucial role in this splitting and thus in determining the magnetic properties.

Ligand Field Strength

Ligand field strength refers to the ability of a ligand to influence the energy levels of the d-orbitals in a metal complex. Strong field ligands, such as CN⁻, cause greater splitting of the d-orbitals, often leading to pairing of electrons and resulting in diamagnetism. In contrast, weak field ligands, like H₂O, may not cause sufficient splitting, allowing unpaired electrons and resulting in paramagnetism.