The spectroscopic technique that can be used to determine the coordination number and geometry of a metal ion in a coordination compound is X-ray crystallography. This technique involves the diffraction of X-rays by the atoms in a crystalline solid, which produces a diffraction pattern that can be analyzed to determine the positions of the atoms within the crystal lattice. By analyzing the diffraction pattern, the coordination number, geometry, and overall structure of the metal ion and its surrounding ligands can be determined.Example:Suppose we have a coordination complex with an unknown structure, and we want to determine its coordination number and geometry. We can grow a single crystal of the complex and subject it to X-ray crystallography.1. Prepare a single crystal of the coordination complex: The complex is dissolved in a suitable solvent, and the solution is allowed to slowly evaporate, leading to the formation of a single crystal.2. Collect X-ray diffraction data: The crystal is mounted on a goniometer, and an X-ray beam is directed at the crystal. The X-rays are diffracted by the atoms in the crystal, producing a diffraction pattern that is recorded on a detector.3. Process and analyze the diffraction data: The diffraction pattern is processed using specialized software, which converts the raw data into a three-dimensional electron density map. This map represents the distribution of electrons in the crystal lattice and can be used to determine the positions of the atoms within the crystal.4. Determine the structure of the coordination complex: By analyzing the electron density map, the positions of the metal ion and its surrounding ligands can be determined. This information can be used to deduce the coordination number the number of ligands surrounding the metal ion and the geometry of the complex e.g., octahedral, tetrahedral, square planar, etc. .For example, if the electron density map reveals that a metal ion is surrounded by six ligands in an octahedral arrangement, we can conclude that the coordination number is 6, and the geometry is octahedral. This information, along with the positions of the other atoms in the crystal, allows us to determine the overall structure of the coordination complex.