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The pale yellow color of [Mn(H2O)6]^2+ is due to a combination of factors:
1. d-orbital splitting: Transition metal ions like Mn^2+ have partially filled d-orbitals. When these ions are surrounded by ligands (like water molecules), the d-orbitals split into two energy levels. The energy difference between these levels corresponds to the energy of visible light.
2. Electronic transitions: When a photon of light with the right energy is absorbed, an electron can be excited from a lower d-orbital to a higher one. The color we see is the complementary color of the light absorbed.
3. Weak field ligands: Water molecules are relatively weak-field ligands, meaning they do not cause a large splitting of the d-orbitals in Mn^2+. This results in a smaller energy difference and lower energy light absorption, leading to the pale yellow color.
In summary, the pale yellow color of [Mn(H2O)6]^2+ is a result of the weak field ligands, the resulting small splitting of the d-orbitals, and the absorption of light in the blue/violet region, leading to the perception of yellow.