Which of the following energy level diagram for `[FeF_(6)]^(3-)` is correct on the basis of crystal field theory ?

Options

A.
B.
C.
D.

Answer

To determine the correct energy level diagram for the complex ion \([FeF_6]^{3-}\) based on crystal field theory, we will follow these steps:

### Step 1: Determine the oxidation state of Iron (Fe)
1. The complex ion is \([FeF_6]^{3-}\).
2. Each fluorine (F) has an oxidation state of -1.
3. Let the oxidation state of Fe be \(x\).
4. The equation can be set up as follows:
\[ x + 6(-1) = -3 \]
\[ x - 6 = -3 \implies x = +3 \]
Therefore, the oxidation state of Fe in \([FeF_6]^{3-}\) is +3.

### Step 2: Write the electronic configuration of Fe
1. The atomic number of Fe is 26, and its ground state electronic configuration is:
\[ [Ar] 3d^6 4s^2 \]
2. Since Fe is in the +3 oxidation state, it loses 3 electrons. The electrons are removed first from the 4s orbital and then from the 3d orbital:
\[ [Ar] 3d^5 \]

### Step 3: Identify the geometry of the complex
1. \([FeF_6]^{3-}\) is an octahedral complex because it has six ligands (F) surrounding the central metal ion (Fe).

### Step 4: Determine the splitting of d-orbitals
1. In an octahedral field, the 3d orbitals split into two sets: \(t_{2g}\) (lower energy) and \(e_g\) (higher energy).
2. The energy level diagram for the d-orbitals in an octahedral field is as follows:
- \(t_{2g}\) (three orbitals)
- \(e_g\) (two orbitals)

### Step 5: Consider the nature of the ligand
1. Fluoride (F) is a weak field ligand, which means it does not cause strong pairing of electrons.
2. Therefore, the electrons will occupy the available orbitals singly before pairing occurs.

### Step 6: Fill the d-orbitals according to Hund's rule
1. Since we have \(3d^5\) configuration and F is a weak field ligand:
- The first three electrons will fill the \(t_{2g}\) orbitals singly.
- The next two electrons will fill the \(e_g\) orbitals singly.

The filling will look like this:
- \(t_{2g}\): 3 electrons
- \(e_g\): 2 electrons

### Step 7: Draw the energy level diagram
1. The correct energy level diagram will show:
- \(t_{2g}\) with 3 electrons
- \(e_g\) with 2 electrons

### Conclusion
The correct energy level diagram for \([FeF_6]^{3-}\) based on crystal field theory is that there are 3 electrons in the \(t_{2g}\) level and 2 electrons in the \(e_g\) level.