Consider the following four octahedral complexes of Mn(III): [ Mn ( H ₂ O )₆]³⁺ , [ Mn ( CN )₆]³⁻ , [ Mn ( en )₃]³⁺ , and [ MnF ₆]³⁻ . Let the magnitude of the crystal field stabilization energy (ignoring pairing energy) of the complex that absorbs light of the shortest wavelength be x ₀ . The value of 10x is ________.

Step-by-step solution

The energy of absorbed light is inversely proportional to its wavelength ( E = hc ). The complex that absorbs light of the shortest wavelength will have the largest crystal field splitting energy ( ₀ ). From the spectrochemical series, the strongest ligand among the given options is CN ⁻ . Therefore, [ Mn ( CN )₆]³⁻ absorbs the shortest wavelength. The central metal ion Mn ³⁺ has a 3 d ⁴ electronic configuration. Because CN ⁻ is a strong field ligand, ₀ > P , leading to a low-spin complex. The electrons will pair u