Spectroscopic techniques, such as UV-Visible UV-Vis spectroscopy, Infrared IR spectroscopy, and Nuclear Magnetic Resonance NMR spectroscopy, can be used to determine the coordination number and geometry of a transition metal complex. These techniques provide information about the electronic structure, vibrational modes, and magnetic properties of the complex, which can be correlated to its coordination number and geometry.1. UV-Visible UV-Vis spectroscopy: This technique is based on the absorption of light by the complex, which results in electronic transitions between different energy levels. The position, intensity, and shape of the absorption bands can provide information about the coordination number and geometry. For example, the d-d transitions in octahedral complexes usually result in weak and broad absorption bands, while square-planar complexes often exhibit more intense and sharper bands.Example: The complex [Cu NH3 4]2+ is a well-known example of a square-planar complex. Its UV-Vis spectrum shows a strong and sharp absorption band at around 600 nm, which is characteristic of a square-planar geometry.2. Infrared IR spectroscopy: This technique provides information about the vibrational modes of the complex, which can be related to the coordination number and geometry. The position and intensity of the IR bands can be used to identify the type of ligands and their coordination mode e.g., monodentate, bidentate, etc. .Example: The complex [Fe CO 5] is a well-known example of an octahedral complex. Its IR spectrum shows five strong absorption bands in the range of 1800-2100 cm-1, which are characteristic of the C-O stretching vibrations in carbonyl ligands. The presence of five CO ligands suggests an octahedral geometry.3. Nuclear Magnetic Resonance NMR spectroscopy: This technique provides information about the magnetic properties of the complex, which can be related to the coordination number and geometry. The chemical shift and coupling constants of the NMR signals can be used to determine the type of ligands and their coordination mode.Example: The complex [PtCl2 PPh3 2] is a well-known example of a square-planar complex. Its 31P NMR spectrum shows a single resonance at around 30 ppm, which is characteristic of the phosphorus atoms in the PPh3 ligands. The absence of any coupling between the phosphorus and platinum nuclei suggests a trans arrangement of the PPh3 ligands, which is consistent with a square-planar geometry.In summary, spectroscopic techniques can provide valuable information about the coordination number and geometry of a transition metal complex. By analyzing the electronic, vibrational, and magnetic properties of the complex using UV-Vis, IR, and NMR spectroscopy, it is possible to determine its structure and coordination environment.