Complete the exercises below. a. Sketch a diagram that shows the definition of the crystal-field splitting energy (∆) for an octahedral crystal-field. b. What is the relationship between the magnitude of ∆ and the energy of the d-d transition for a d¹ complex? c. Calculate ∆ in kJ/mol if a d¹ complex has an absorption maximum at 545 nm.

Crystal-field theory explains how the arrangement of ligands around a central metal ion affects the energy levels of the d-orbitals. In an octahedral field, the d-orbitals split into two sets: the lower-energy t2g orbitals and the higher-energy eg orbitals. This splitting leads to differences in energy that influence the color and magnetic properties of coordination complexes.

Crystal-field splitting energy (∆) is the energy difference between the split d-orbitals in a coordination complex. It is crucial for understanding the electronic transitions that occur when electrons move between these orbitals. The magnitude of ∆ can be influenced by factors such as the nature of the metal ion and the type of ligands surrounding it.

d-d transitions refer to the electronic transitions between the split d-orbitals in transition metal complexes. For a d¹ complex, the energy of the d-d transition corresponds to the crystal-field splitting energy (∆). The wavelength of light absorbed during this transition can be used to calculate ∆, using the relationship between energy, wavelength, and Planck's equation.