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Here's how to determine the electronic configuration of a complex ion using crystal field theory:
1. Identify the central metal ion and its oxidation state. This determines the number of d electrons involved.
2. Determine the geometry of the complex ion. This will dictate the splitting pattern of the d orbitals. Common geometries include octahedral, tetrahedral, and square planar.
3. Draw the d orbital splitting diagram. The specific splitting pattern depends on the geometry. For instance, in an octahedral complex, the d orbitals split into two sets: a lower-energy set (t2g) and a higher-energy set (eg).
4. Fill the d orbitals with electrons. Start by filling the lower-energy orbitals first, following Hund's rule and the Pauli exclusion principle. The number of electrons you fill corresponds to the metal ion's oxidation state.
5. Determine the electronic configuration. Write the configuration by listing the filled d orbitals, with their respective subscripts indicating the number of electrons in each. For example, [Cr(H2O)6]3+ has a d3 configuration, which means it has three electrons in the lower-energy t2g orbitals.