The hybridization of iron atom in `[Fe(CN)_6]^(3-)` complex is

Options

A. `sp^3`
B. `d^2 sp^3`
C. `sp^3 d^2`
D. `dsp^2`

Explanation

To determine the hybridization of the iron atom in the complex ion \([Fe(CN)_6]^{3-}\), we can follow these steps:

### Step 1: Determine the oxidation state of iron (Fe)
Let the oxidation state of iron be \(x\). The cyanide ion (CN) has a charge of -1, and since there are 6 cyanide ions, their total contribution to the charge is -6. The overall charge of the complex is -3. Therefore, we can set up the equation:

\[ x + 6(-1) = -3 \]

Solving this gives:

\[ x - 6 = -3 \\ x = +3 \]

Thus, the oxidation state of iron in \([Fe(CN)_6]^{3-}\) is +3.

### Step 2: Write the electronic configuration of iron
The atomic number of iron (Fe) is 26. The electronic configuration of neutral iron is:

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

Since iron is in the +3 oxidation state, we need to remove three electrons. The two electrons from the 4s orbital and one from the 3d orbital will be removed, resulting in:

\[ \text{Fe}^{3+}: [Ar] 3d^5 \]

### Step 3: Analyze the ligand
Cyanide (CN) is a strong field ligand, which means it has the ability to cause pairing of electrons in the d-orbitals. In the case of \([Fe(CN)_6]^{3-}\), the 3d electrons will pair up due to the strong field nature of cyanide.

### Step 4: Determine the arrangement of electrons
After pairing, the electron configuration of \(\text{Fe}^{3+}\) can be represented as:

\[ 3d: \uparrow\downarrow \, \uparrow\downarrow \, \uparrow\downarrow \, \uparrow \, \text{(5 electrons)} \]

This means that there are 2 paired electrons and 3 unpaired electrons in the 3d orbitals.

### Step 5: Identify the hybridization
In the complex \([Fe(CN)_6]^{3-}\), there are 6 ligands (CN) surrounding the iron atom. The hybridization can be determined by the number of orbitals involved in bonding. Since we have 6 ligands, the hybridization will involve:

- 2 d-orbitals
- 1 s-orbital
- 3 p-orbitals

Thus, the hybridization is \(d^2sp^3\).

### Step 6: Determine the geometry
The geometry of the complex with \(d^2sp^3\) hybridization is octahedral.

### Final Answer
The hybridization of the iron atom in the complex \([Fe(CN)_6]^{3-}\) is \(d^2sp^3\).

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