The coordination number in transition metal complexes plays a significant role in determining their color. The coordination number refers to the number of ligands atoms, ions, or molecules that are directly bonded to the central metal ion in a complex. This number can vary from 2 to 12, but the most common coordination numbers are 4 and 6.The color of transition metal complexes arises from the absorption of visible light, which causes electronic transitions between different energy levels d-orbitals of the central metal ion. The energy difference between these levels corresponds to the energy of the absorbed light, which in turn determines the color of the complex.The coordination number influences the color of the complex in several ways:1. Geometry: The coordination number determines the geometry of the complex e.g., tetrahedral, square planar, or octahedral . Different geometries lead to different arrangements of the d-orbitals and their energy levels, which affects the energy of the absorbed light and the color of the complex.2. Crystal field splitting: The interaction between the ligands and the central metal ion causes the d-orbitals to split into different energy levels. The magnitude of this splitting crystal field splitting depends on the coordination number and the nature of the ligands. Larger splitting results in the absorption of higher energy light, leading to a different color.3. Ligand field strength: The strength of the ligand field, which is related to the type of ligands and their arrangement around the central metal ion, also depends on the coordination number. Stronger ligand fields cause greater splitting of the d-orbitals, leading to different colors.4. Charge transfer: In some cases, the color of the complex may arise from charge transfer transitions, where an electron is transferred from the ligand to the metal ion or vice versa. The coordination number can influence the likelihood of such transitions and thus affect the color of the complex.In summary, the coordination number plays a crucial role in determining the geometry, crystal field splitting, ligand field strength, and charge transfer transitions in transition metal complexes, all of which contribute to their color.