Chapter 23, Problem 86AE

Interpretation Introduction

Interpretation:

At octahedral sites in the close packed oxide lattice of ${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$, the color of ruby being red due to the presence of $\text{Cr}\left(\text{III}\right)$ is given. The crystal field splitting diagram of $\text{Cr}\left(\text{III}\right)$ in the given environment, the variation of pressure in ruby crystal as a function of wavelength are to be determined.

Concept introduction:

A model that depicts the breakage of the degeneracies of the electron orbital states because of a static electric field is known as crystal field theory. The static field is produced by the surrounding charge distribution.

Crystal field theory is based on the degeneracy of d-orbitals when they come in contact with the ligand.

To determine:

The crystal field diagram of $\text{Cr}\left(\text{III}\right)$ and the variation of wavelength as a function of pressure.