According to crystal field therory the electronic configuration of the `[FeCI_(4)]^(Θ)` ion is .

Options

A. `a.(t_(2g)^(2)e_(g)^(2))`
B. `b.(e_(g)^(2) t_(2g)^(3))`
C. `c.(e_(g)^(1) t_(2g)^(3))`
D. `d.(e_(g)^(3)t_(2g)^(1))`

Explanation

To find the electronic configuration of the `[FeCl₄]^(Θ)` ion according to crystal field theory, we can follow these steps:

### Step 1: Determine the oxidation state of iron in `[FeCl₄]^(Θ)`.
- The complex ion `[FeCl₄]^(Θ)` has four chloride ions (Cl⁻), each with a charge of -1.
- Let the oxidation state of iron (Fe) be \( x \). The total charge of the complex is 0 (neutral).

\[ x + 4(-1) = 0 \implies x - 4 = 0 \implies x = +4 \]

### Step 2: Write the electronic configuration of iron in its elemental form.
- The atomic number of iron (Fe) is 26. Therefore, its electronic configuration is:

\[ \text{Fe: } [Ar] 3d^6 4s^2 \]

### Step 3: Adjust the electronic configuration based on the oxidation state.
- Since iron is in the +4 oxidation state in `[FeCl₄]^(Θ)`, it loses 4 electrons. Typically, electrons are removed from the 4s orbital first and then from the 3d orbital.

\[ \text{Fe}^{4+}: [Ar] 3d^4 \]

### Step 4: Identify the nature of the ligand and its effect on the d-orbitals.
- Chloride (Cl⁻) is a weak field ligand, which means it does not cause significant splitting of the d-orbitals and leads to high spin complexes.

### Step 5: Fill the d-orbitals according to crystal field theory.
- In a high spin complex, we fill the d-orbitals to maximize the number of unpaired electrons.
- The d-orbitals split into two sets: \( t_{2g} \) (lower energy) and \( e_g \) (higher energy).
- For \( 3d^4 \), we fill the orbitals as follows:
- Place one electron in each of the three \( t_{2g} \) orbitals first, and then place the fourth electron in the \( e_g \) orbital.

\[ t_{2g}^3 e_g^1 \]

### Step 6: Write the final electronic configuration.
- The final electronic configuration of the `[FeCl₄]^(Θ)` ion is:

\[ t_{2g}^3 e_g^1 \]

### Conclusion
The electronic configuration of the `[FeCl₄]^(Θ)` ion according to crystal field theory is \( t_{2g}^3 e_g^1 \).

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