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The pale yellow color of [Mn(H2O)3]2+ is due to a combination of factors:
1. Weak Crystal Field Strength: The water ligands in the complex are weak-field ligands. This means they do not cause a large splitting of the d-orbitals in the manganese ion.
2. High Spin Configuration: With a weak field, the manganese ion adopts a high-spin configuration. This means that the electrons occupy all five d-orbitals before pairing up, leading to a smaller energy gap for electronic transitions.
3. Limited d-d Transitions: The relatively small energy gap makes the d-d transitions (electronic transitions between d-orbitals) less energetic, resulting in the absorption of light in the higher energy (UV) region. This leaves the visible light spectrum relatively unabsorbed, resulting in a pale yellow color.
Essentially, the complex absorbs less visible light, making it appear pale yellow.