Briefly? ?

(a) The observation that [Co(NH3)6]3+ is diamagnetic and orange-yellow while [CoF6]3- is blue can be explained qualitatively using ligand field theory. In [Co(NH3)6]3+, the ammonia ligands are weak field ligands, causing a small splitting of the d orbitals in the cobalt ion. This results in a low-spin configuration and diamagnetic behavior. The orange-yellow color is due to the absorption of light in the visible spectrum. On the other hand, in [CoF6]3-, the fluoride ligands are strong field ligands, causing a large splitting of the d orbitals and resulting in a high-spin configuration and blue color.

(b) The observation that [Fe(H2O)6]2+ is paramagnetic while [Os(H2O)6]2+ is diamagnetic can also be explained using ligand field theory. In [Fe(H2O)6]2+, the water ligands are weak field ligands, causing a small splitting of the d orbitals in the iron ion. This results in unpaired electrons and paramagnetic behavior. On the other hand, in [Os(H2O)6]2+, the water ligands are strong field ligands, causing a large splitting of the d orbitals and resulting in a low-spin configuration with no unpaired electrons, leading to diamagnetic behavior.

(a) [Co(NH3)6]3+ has a t2g6eg0 configuration, which gives rise to a diamagnetic complex. The orange-yellow color is due to metal-to-ligand charge transfer (MLCT) transitions, which are allowed for d6 metal ions in octahedral complexes. [CoF6]3- has a t2g3eg2 configuration, which gives rise to a paramagnetic complex. The blue color is due to d-d transitions within the t2g set of orbitals.

(b) [Fe(H2O)6]2+ has a t2g4eg2 configuration, which gives rise to a paramagnetic complex with four unpaired electrons. [Os(H2O)6]2+ has a t2g6eg0 configuration, which gives rise to a diamagnetic complex with no unpaired electrons.