Which of the following options are correct for `[Fe(CN)_(6)]^(3-)` complex ?

Options

A. `d^(2)sp^(3)` hybridisation
B. `sp^(3) d^(2)` hybridisation
C. Paramagnetic
D. Diamagnetic

Explanation

To determine the correct options for the complex \([Fe(CN)_{6}]^{3-}\), we will follow these steps:

### Step 1: Determine the oxidation state of Iron (Fe)
The charge of the complex is \(-3\). The cyanide ion (CN) has a charge of \(-1\). Since there are 6 cyanide ions, their total contribution to the charge is \(6 \times -1 = -6\).

Let the oxidation state of iron be \(x\). The equation can be set up as follows:
\[ x + 6(-1) = -3 \]
\[ x - 6 = -3 \]
\[ x = +3 \]

### Step 2: Determine the electronic configuration of Iron in this oxidation state
Iron has an atomic number of 26, and its electron configuration is:
\[ [Ar] 3d^6 4s^2 \]
When it loses 3 electrons to form \(Fe^{3+}\), the configuration becomes:
\[ [Ar] 3d^5 \]

### Step 3: Analyze the ligand field
Cyanide (CN\(^-\)) is a strong field ligand. Strong field ligands cause pairing of electrons in the lower energy d-orbitals (t2g) before occupying the higher energy orbitals (eg).

### Step 4: Fill the d-orbitals
For \(Fe^{3+}\) with a \(3d^5\) configuration in the presence of a strong field ligand, the electrons will pair up in the t2g orbitals. The filling will be as follows:
- The 5 electrons will occupy the t2g orbitals, resulting in:
- t2g: ↑↑↑↑↑ (5 electrons in t2g, no electrons in eg)

### Step 5: Determine the hybridization
In an octahedral complex like \([Fe(CN)_{6}]^{3-}\), the hybridization can be determined by the number of orbitals involved in bonding. For this complex:
- 2 d-orbitals, 1 s-orbital, and 3 p-orbitals are used for hybridization.
Thus, the hybridization is:
\[ d^2sp^3 \]

### Step 6: Determine magnetic properties
Since there is 1 unpaired electron in the t2g orbitals, the complex is paramagnetic.

### Final Conclusion
Based on the analysis:
1. The hybridization is \(d^2sp^3\) - **True**
2. The hybridization is \(sp^3d^2\) - **False**
3. The complex is paramagnetic - **True**
4. The complex is diamagnetic - **False**

### Correct Options
The correct options for the complex \([Fe(CN)_{6}]^{3-}\) are:
- \(d^2sp^3\) hybridization (True)
- Paramagnetic (True)