Complete the exercises below. The red color of ruby is due to the presence of Cr(III) ions at octahedral sites in the close-packed oxide lattice of Al₂O₃. Draw the crystal-field splitting diagram for Cr(III) in this environment. Suppose that the ruby crystal is subjected to high pressure. What do you predict for the variation in the wavelength of absorption of the ruby as a function of pressure? Explain.

Crystal Field Theory (CFT) explains how the arrangement of ligands around a central metal ion affects its electronic energy levels. In octahedral coordination, the d-orbitals split into two energy levels: the lower-energy t2g and the higher-energy eg orbitals. This splitting is crucial for understanding the color and absorption properties of transition metal complexes, such as Cr(III) in ruby.

The strength of the ligands surrounding a metal ion influences the extent of d-orbital splitting. Strong field ligands cause greater splitting, leading to larger energy differences between the t2g and eg levels. In the case of Cr(III) in ruby, the presence of oxide ions contributes to the ligand field strength, affecting the wavelength of light absorbed and thus the color observed.

Applying pressure to a crystal lattice can alter the distances between ions and the overall geometry of the lattice. In the case of ruby, increased pressure may lead to changes in the crystal field splitting due to altered ligand interactions, which can shift the wavelength of absorption. Typically, higher pressure can increase the energy gap between split d-orbitals, resulting in a shift to shorter wavelengths (blue shift) in the absorption spectrum.