Step 1 : Understanding the Question:
The topic of this question is Crystal Field Theory (CFT). CFT explains the bonding and properties of coordination complexes by considering the electrostatic interactions between the central metal ion's $d$-orbitals and the surrounding ligands. In an octahedral field, the five degenerate $d$-orbitals split into two sets: $t_{2g}$ (lower energy) and $e_g$ (higher energy). The question asks for the electron distribution and magnetic nature of a specific Iron(II) complex.
Step 2 : Key Formulas and approach:
The approach involves these logical steps:
1. Determine the oxidation state of the metal: $Fe + 6(0) = +2 \implies Fe^{2+}$.
2. Find the $d$-electron count: $Fe$ is $[Ar]3d^6 4s^2$, so $Fe^{2+}$ is $3d^6$.
3. Assess ligand strength: $H_2O$ is a weak-field ligand (from the spectrochemical series).
4. Apply the High-Spin vs. Low-Spin rule: For weak-field ligands, $\Delta_o<P$ (pairing energy), resulting in a "High-Spin" complex.
Step 3 : Detailed Explanation:
We have an $Fe^{2+}$ ion which has a $d^6$ configuration. These 6 electrons need to be distributed among the $t_{2g}$ and $e_g$ levels.
Because $H_2O$ is a weak-field ligand, the energy gap ($\Delta_o$) between the $t_{2g}$ and $e_g$ levels is relatively small. It is energetically "cheaper" for an electron to jump to the $e_g$ level than to pair up in the $t_{2g}$ level.
Following Hund's Rule of maximum multiplicity, we fill the orbitals one by one:
- Electrons 1, 2, and 3 go into the three $t_{2g}$ orbitals.
- Electrons 4 and 5 go into the two $e_g$ orbitals (instead of pairing).
- The 6th electron must now pair up in one of the $t_{2g}$ orbitals.
This results in the configuration: $t_{2g}^4 e_g^2$.
To determine the magnetic behavior, we look for unpaired electrons. In this configuration, there are 4 unpaired electrons (two in $t_{2g}$ and two in $e_g$).
Any substance with one or more unpaired electrons is "Paramagnetic" (attracted by a magnetic field).
Thus, the complex is high-spin, paramagnetic, and has a $t_{2g}^4 e_g^2$ configuration.
Step 4 : Final Answer:
The weak-field ligand results in a $t_{2g}^4 e_g^2$ high-spin paramagnetic configuration. The correct option is (A).