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The complex with the shortest wavelength absorption would be (Cr(en)3)3+. Here's why:
Ligand Field Theory: The color of transition metal complexes arises from the absorption of light, which causes electronic transitions within the d orbitals of the metal ion. The energy difference between these d orbitals is influenced by the ligands surrounding the metal.
Strong-Field Ligands: Ethylenediamine (en) is a strong-field ligand. Strong-field ligands cause a larger splitting of the d orbitals, leading to a higher energy difference between the ground and excited states.
Wavelength and Energy: Higher energy transitions correspond to shorter wavelengths of light.
Therefore, the complex with the strongest-field ligand, (Cr(en)3)3+, will absorb the highest energy light, resulting in the shortest wavelength absorption.