Rank the following complex ions in order of increasing...

Rank the following complex ions in order of increasing wavelength of light absorbed.
$$\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}, \mathrm{Co}(\mathrm{CN})_{6}{ }^{3-}, \mathrm{Col}_{6}{ }^{3-}, \mathrm{Co}(\mathrm{en})_{3}{ }^{3+}$$

Key Concepts

Crystal Field Theory

This concept explains how the degeneracy of the d orbitals in a transition metal ion is broken when ligands approach to form a complex. The resulting splitting creates different energy levels, which are crucial for understanding the electronic transitions that occur when light is absorbed by the complex.

Spectrochemical Series

The spectrochemical series orders ligands by their field strength, indicating how much they split the metal's d orbitals. Ligands that are strong-field (such as cyanide) induce a larger splitting, leading to higher energy (shorter wavelength) absorption, whereas weak-field ligands (like water) result in smaller splitting and lower energy (longer wavelength) absorption.

d-d Transitions

These are electronic transitions between the split d orbitals in a coordination complex. The energy difference between these orbitals corresponds to the energy of the absorbed light, making d-d transitions central to understanding the color and the wavelength of light absorbed by the complex.

Energy-Wavelength Relationship

This principle, derived from the equation E = hc/?, explains that a larger energy gap (?) between orbitals results in the absorption of light with a shorter wavelength. Conversely, a smaller energy difference corresponds to absorption at a longer wavelength. This relationship is key to ranking complexes by their absorbed wavelengths.

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