Step 1: Analyzing Statement I.
Statement I compares the crystal field stabilisation energy (CFSE) of the complexes \( [\text{Co}(H_2O)_6]^{2+} \) and \( [\text{Ni}(H_2O)_6]^{2+} \). The CFSE depends on the \( d \)-orbital splitting, which in turn depends on the metal ion and its electronic configuration.
- \( \text{Co}^{2+} \) has a \( d^7 \) electronic configuration, while \( \text{Ni}^{2+} \) has a \( d^8 \) configuration.
- For octahedral complexes, the CFSE is typically larger for \( d^7 \) (Co\(^{2+}\)) due to the lower repulsion between the electrons in the \( d \)-orbitals, resulting in a larger stabilization energy compared to \( d^8 \) (Ni\(^{2+}\)).
Therefore, Statement I is incorrect because the CFSE of \( [\text{Co}(H_2O)_6]^{2+} \) is actually smaller than \( [\text{Ni}(H_2O)_6]^{2+} \).
Step 2: Analyzing Statement II.
Statement II gives the order of bond energy for halogens. The bond dissociation energy increases as you go from iodine to chlorine because:
- Chlorine, being smaller, forms stronger bonds compared to iodine.
- Therefore, the bond energy order is \( \text{Cl}_2>\text{Br}_2>\text{F}_2>\text{I}_2 \), which is correct.
Thus, Statement II is correct.