Question

Given below are two statements :
Statement I : Presence of large number of unpaired electrons in transition metal atoms results in higher enthalpies of their atomisation.
Statement II : $d_{xy} = d_{xz} = d_{yz} < d_{x^2 - y^2} = d_{z^2}$ and $d_{x^2 - y^2} = d_{z^2} = d_{xy} <d_{xz} = d_{yz}$ are the d-orbital splittings in $[Fe(H_2O)_6]^{3+}$ and $[Ni(Cl)_4]^{2-}$ complex ions respectively.
In the light of the above statements, choose the correct answer from the options given below :

• A. Both Statement I and Statement II are correct
• B. Both Statement I and Statement II are incorrect
• C. Statement I is correct but Statement II is incorrect
• D. Statement I is incorrect but Statement II is correct

Hint:

For Statement I, recall how atomization enthalpy varies across the 3d series with the number of unpaired electrons. For Statement II, work out which orbitals point directly at the ligand positions in each geometry, since those are always the higher-energy set, rather than recalling the split pattern from memory.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Statement I relates the strength of metallic bonding to electronic configuration. Statement II concerns the Crystal Field Splitting patterns for octahedral and tetrahedral complexes.
Step 2: Detailed Explanation: 
Analysis of Statement I: 
Transition metals have unpaired d-electrons which participate in interatomic metallic bonding. The greater the number of unpaired electrons, the stronger the metallic bond, and hence higher is the enthalpy of atomisation. This is True. 

Analysis of Statement II: 
1. $[Fe(H_2O)_6]^{3+}$ is an octahedral complex. In octahedral field, d-orbitals split into $t_{2g} (d_{xy}, d_{xz}, d_{yz})$ and $e_g (d_{x^2-y^2}, d_{z^2})$. The $e_g$ set is higher in energy. The pattern given ($d_{xy} = d_{xz} = d_{yz} < d_{x^2 - y^2} = d_{z^2}$) is correct. 
2. $[Ni(Cl)_4]^{2-}$ is a tetrahedral complex (due to weak field $Cl^-$ ligand). In tetrahedral field, d-orbitals split into $e (d_{x^2-y^2}, d_{z^2})$ and $t_2 (d_{xy}, d_{xz}, d_{yz})$. The $t_2$ set is higher in energy. The second pattern given ($d_{x^2 - y^2} = d_{z^2} = d_{xy} < d_{xz} = d_{yz}$) is incorrect because $d_{xy}$ belongs to the $t_2$ set, not $e$. 
Thus, Statement II is Incorrect. 
Step 3: Final Answer: 
Statement I is correct but Statement II is incorrect.
 

Answer 2

Concept:

• Across the 3d transition series, the atomization enthalpy rises and falls with the number of unpaired d-electrons available for metallic bonding, peaking near the middle of the series and falling again toward the end.
• In an octahedral field, ligands approach directly along the $x$, $y$ and $z$ axes, so orbitals lying exactly on those axes feel the strongest repulsion.
• In a tetrahedral field, ligands approach between the axes (along the cube-diagonal directions), so the orbitals lying between the axes now feel the strongest repulsion instead.

Step 1: Check Statement I against the atomization enthalpy trend.
Moving across the 3d series, atomization enthalpy climbs as unpaired d-electrons increase, reaching a maximum around $Cr$, which has the maximum possible number of unpaired electrons for that series, then drops toward $Zn$, whose filled $d^{10}$ configuration leaves no unpaired electrons for bonding.
This confirms that more unpaired electrons directly raises the atomization enthalpy, so Statement I is correct.

Step 2: Work out the octahedral splitting for $[Fe(H_2O)_6]^{3+}$ from geometry.
The six ligands sit on the $+x, -x, +y, -y, +z, -z$ directions.
$d_{z^2}$ and $d_{x^2-y^2}$ point straight at these ligand positions, so they are pushed up in energy, forming the $e_g$ set.
$d_{xy}, d_{xz}, d_{yz}$ point between the axes, away from the ligands, so they stay lower in energy, forming the $t_{2g}$ set.
This matches the given pattern $d_{xy}=d_{xz}=d_{yz} < d_{x^2-y^2}=d_{z^2}$.

Step 3: Work out the tetrahedral splitting for $[NiCl_4]^{2-}$ from geometry.
In a tetrahedral arrangement, the four ligands sit along the cube-diagonal directions, which lie between the $x$, $y$, $z$ axes rather than on them.
Now $d_{xy}, d_{xz}, d_{yz}$ point closer to these ligand directions, so they are pushed up, forming the $t_2$ set.
$d_{z^2}$ and $d_{x^2-y^2}$ point closer to the axes themselves, farther from the ligands, so they stay lower, forming the $e$ set.
The correct order is therefore $d_{x^2-y^2}=d_{z^2} < d_{xy}=d_{xz}=d_{yz}$.

Step 4: Compare with the pattern given in Statement II.
The statement places $d_{xy}$ together with the lower $e$ set, but the geometric argument shows $d_{xy}$ belongs with the higher $t_2$ set.
So the given tetrahedral pattern is wrong, making Statement II incorrect.

Final Answer: Statement I is correct but Statement II is incorrect.