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The complex with the shortest wavelength in its absorption spectrum will be [Cr(en)3]3+.
Here's why:
Ligand Field Theory: The color of a coordination complex is related to the splitting of the d orbitals of the metal ion by the ligands. Stronger field ligands cause a larger splitting, resulting in higher energy transitions and shorter wavelength light absorbed.
Spectrochemical Series: The spectrochemical series ranks ligands based on their ability to split d orbitals. Ethylenediamine (en) is a strong field ligand, while chloride (Cl-), water (H2O), and oxalate (ox) are weaker field ligands.
Energy and Wavelength: The energy of absorbed light is inversely proportional to wavelength. Higher energy transitions correspond to shorter wavelengths of light.
Since [Cr(en)3]3+ has the strongest field ligands, it will have the largest d-orbital splitting, resulting in the highest energy transition and the shortest wavelength of light absorbed.