Transition metal complex with highest value of crystal field splitting $$(\Delta_0)$$ will be

We need to determine which complex has the highest crystal field splitting energy ($$\Delta_0$$). The crystal field splitting energy depends on several factors:

1. Nature of the ligand: All four complexes have the same ligand ($$H_2O$$), so this factor is the same for all. 2. Oxidation state of the metal: All four metal ions have a +3 oxidation state, so this factor is also the same.

3. Period of the transition metal: As we move down a group in the d-block (from 3d to 4d to 5d), the crystal field splitting energy increases. The general trend is:

$$\Delta_0 (\text{3d}) < \Delta_0 (\text{4d}) < \Delta_0 (\text{5d})$$ The increase is approximately 40-50% on moving from one period to the next.

Now let us classify each metal ion by its period: $$Cr^{3+}$$: 3d series (Period 4), $$Fe^{3+}$$: 3d series (Period 4), $$Mo^{3+}$$: 4d series (Period 5), $$Os^{3+}$$: 5d series (Period 6).

Since $$Os^{3+}$$ is a 5d transition metal, it has the largest d-orbitals with the greatest spatial extent. This leads to the strongest interaction with the ligands and therefore the highest crystal field splitting.

$$\Delta_0: [Os(H_2O)_6]^{3+} > [Mo(H_2O)_6]^{3+} > [Cr(H_2O)_6]^{3+} \approx [Fe(H_2O)_6]^{3+}$$

The correct answer is Option C: $$[Os(H_2O)_6]^{3+}$$.