Atomisation Enthalpy and Crystal Field Splitting in Transition Metal Complexes

To determine the correctness of the given statements, let us analyze them individually:

Analysis of Statement I:

The enthalpy of atomisation ($\Delta_a H^\circ$) of transition metals is directly related to the strength of interatomic metallic bonding.

• In transition elements, interatomic bonds are formed due to the overlapping of $(n-1)d$ and $ns$ electrons.
• A higher number of unpaired electrons in the $d$-orbitals leads to stronger interatomic bonding (combining metallic character with covalent interaction between $d$-orbitals).
• Stronger bonding requires higher energy to break the lattice apart into individual gaseous atoms, resulting in a higher enthalpy of atomisation.

Thus, Statement I is correct.

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Analysis of Statement II:

1. Complex ion $[\text{Fe}(\text{H}_2\text{O})_6]^{3+}$:

   • The central metal ion is $\text{Fe}^{3+}$ with a coordination number of 6, giving it an octahedral geometry.
   • In an octahedral crystal field, ligand repulsion is greater along the Cartesian axes where the $d_{x^2-y^2}$ and $d_{z^2}$ ($e_g$ set) orbitals are oriented.
   • Consequently, the $d$-orbitals split into a lower energy triply degenerate $t_{2g}$ set ($d_{xy}, d_{xz}, d_{yz}$) and a higher energy doubly degenerate $e_g$ set ($d_{x^2-y^2}, d_{z^2}$): $d_{xy} = d_{xz} = d_{yz} < d_{x^2-y^2} = d_{z^2}$

2. Complex ion $[\text{Ni}(\text{Cl})_4]^{2-}$:

   • The central metal ion is $\text{Ni}^{2+}$ ($3d^8$ configuration) with a coordination number of 4. Since $\text{Cl}^-$ is a weak field ligand, it forms a tetrahedral complex.
   • In a tetrahedral crystal field, ligands approach between the Cartesian axes, causing greater repulsion for the $d_{xy}, d_{xz}, d_{yz}$ ($t_2$ set) orbitals than the $d_{x^2-y^2}, d_{z^2}$ ($e$ set) orbitals.
   • Consequently, the splitting pattern is reversed compared to octahedral complexes: $d_{x^2-y^2} = d_{z^2} < d_{xy} = d_{xz} = d_{yz}$

Thus, Statement II is correct.

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Conclusion:

Since both Statement I and Statement II are correct, the correct option is A.