The order of energy absorbed which is responsible for the color of complexes (i) \( [\text{Ni}(\text{H}_2\text{O})_2(\text{en})_2]^{2+} \) (ii) \( [\text{Ni}(\text{H}_2\text{O})_4(\text{en})_2]^{2+} \) and (iii) \( [\text{Ni}(\text{en})_3]^{2+} \) is

The energy absorbed for the color of the coordination complexes depends on the crystal field splitting energy (\( \Delta_o \)). According to the spectrochemical series, ethylenediamine (\( \text{en} \)) is a stronger field ligand than water (\( \text{H}_2\text{O} \)). Therefore, greater the number of \( \text{en} \) ligands coordinated to the nickel metal ion, larger will be the crystal field splitting energy (\( \Delta_o \)), and higher will be the energy absorbed (\( E = h\nu = \Delta_o \)).
- Complex (iii) \( [\text{Ni}(\text{en})_3]^{2+} \) contains 3 \( \text{en} \) ligands.
- Complex (i) \( [\text{Ni}(\text{H}_2\text{O})_2(\text{en})_2]^{2+} \) contains 2 \( \text{en} \) ligands.
- Complex (ii) \( [\text{Ni}(\text{H}_2\text{O})_4(\text{en})_2]^{2+} \) contains 2 \( \text{en} \) ligands (Wait, looking at the formula, complex (ii) has 2 \( \text{en} \) ligands and 4 \( \text{H}_2\text{O} \), whereas complex (i) has 2 \( \text{en} \) ligands and 2 \( \text{H}_2\text{O} \). Since \( \text{en} \) is a stronger ligand than \( \text{H}_2\text{O} \), complex (i) with two \( \text{en} \) and two \( \text{H}_2\text{O} \) has a higher \( \Delta_o \) than complex (ii) with two \( \text{en} \) and four \( \text{H}_2\text{O} \)).
Thus, the correct order of crystal field splitting energy and hence the absorbed energy is: (iii) > (i) > (ii).