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The coordination complex that will give the least intense peaks in the UV-Vis spectrum is [Mn(H2O)6]2+. Here's why:
d-orbital splitting and electronic transitions: The intensity of UV-Vis absorption bands is related to the magnitude of the d-orbital splitting in the metal complex. Larger splitting leads to higher energy transitions and more intense absorption.
Mn(II) d-electron configuration: Mn(II) has a d5 configuration. In an octahedral complex like [Mn(H2O)6]2+, the d-orbitals split into two sets: t2g and eg. All five d-electrons occupy the lower energy t2g orbitals. Since there are no electrons in the higher energy eg orbitals, there are no allowed d-d transitions, which are typically responsible for the color (and UV-Vis absorption) of transition metal complexes.
Other complexes: The other complexes have partially filled eg orbitals, allowing for d-d transitions and thus more intense UV-Vis absorption.