The wavelength of absorbed electromagnetic radiation for CoBr4^2- is 3.4 ×10^-6 m. Will the com

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The wavelength of absorbed electromagnetic radiation for...

The wavelength of absorbed electromagnetic radiation for $\mathrm{CoBr}_{4}^{2-}$ is $3.4 \times 10^{-6} \mathrm{~m}$. Will the complex ion $\mathrm{CoBr}_{6}^{4-}$ absorb electromagnetic radiation having a wavelength longer or shorter than $3.4 \times 10^{-6} \mathrm{~m}$ ? Explain.

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Key Concepts

Crystal Field Theory

This concept explains how the degenerate d orbitals of a transition metal split into groups of different energies when ligands approach and form a complex. The magnitude of this splitting is influenced by both the geometry of the complex and the nature of the ligands, which in turn affects the wavelengths of light the complex can absorb.

Energy-Wavelength Relationship in Electromagnetic Radiation

According to the relationship E = hc/? (where E is energy, h is Planck's constant, c is the speed of light, and ? is the wavelength), the energy absorbed during electronic transitions is inversely proportional to the wavelength. Therefore, a larger energy gap corresponds to the absorption of shorter-wavelength (higher-energy) radiation.

Coordination Geometry and Ligand Number Effects

The geometry and overall coordination number of a complex significantly affect the crystal field splitting energy. Complexes with a higher number of ligands, such as octahedral complexes, typically exhibit larger splitting gaps compared to tetrahedral complexes. This increased splitting results in electronic transitions that absorb radiation of higher energy or shorter wavelengths.

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