Which of the following statement is correct for the complex `Ca_(2)[Fe(CN)_(5)O_(2)]` having `t_(2g)^(6),e_(g)^(0)` electronic configuration ? .

Options

A. `d^(2)sp^(3)` hybridised and diamagnetic
B. `sp^(3)d^(2)` hybridised and paramagnetic
C. `sp^(3)d^(2)` hybridised and diamagnetic
D. `d^(2)sp^(3)` hybridised and paramagnetic

Explanation

To solve the question regarding the complex \( \text{Ca}_2[\text{Fe(CN)}_5\text{O}_2] \) with the electronic configuration \( t_{2g}^6, e_g^0 \), we will follow these steps:

### Step 1: Determine the Oxidation State of Iron
1. **Identify the overall charge of the complex**: The complex has a total charge of -2 (from the \( \text{Ca}^{2+} \)).
2. **Set up the equation**: Let the oxidation state of iron be \( x \). The cyanide ion \( \text{CN}^- \) contributes -1 for each of the 5 ligands, and the \( \text{O}^{2-} \) contributes -2.
\[ x + 5(-1) + (-2) = -2 \]
3. **Solve for \( x \)**:
\[ x - 5 - 2 = -2 \implies x - 7 = -2 \implies x = +5 \]
Thus, the oxidation state of iron is +5.

### Step 2: Determine the Electron Configuration of Iron
1. **Find the ground state configuration of iron**: Iron (Fe) has an atomic number of 26, with a ground state electron configuration of \( [\text{Ar}] 4s^2 3d^6 \).
2. **Adjust for oxidation state**: In the +5 oxidation state, iron loses 5 electrons:
- 2 from \( 4s \) and 3 from \( 3d \).
- Therefore, the configuration becomes \( [\text{Ar}] 3d^3 \).

### Step 3: Analyze the Ligands
1. **Identify the ligands**: The complex contains 5 cyanide ions (strong field ligands) and one \( \text{O}^{2-} \) ligand.
2. **Determine the field strength**: Since cyanide is a strong field ligand, it causes pairing of electrons in the \( 3d \) orbitals.

### Step 4: Determine the Hybridization
1. **Count the number of ligands**: There are 6 ligands (5 \( \text{CN}^- \) and 1 \( \text{O}^{2-} \)).
2. **Determine the hybridization**: The hybridization that accommodates 6 orbitals is \( d^2sp^3 \), indicating an octahedral geometry.

### Step 5: Determine the Magnetic Properties
1. **Check for unpaired electrons**: With the configuration \( 3d^3 \) and strong field ligands causing pairing, all electrons are paired.
2. **Conclusion on magnetism**: The complex is diamagnetic because there are no unpaired electrons.

### Conclusion
The correct statement regarding the complex \( \text{Ca}_2[\text{Fe(CN)}_5\text{O}_2] \) is that it is an inner orbital complex with \( d^2sp^3 \) hybridization and is diamagnetic.

### Final Answer
The correct option is: **d2sp3 hybridization and diamagnetic nature**.

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