The coordination number (C.N.) and oxidation number (O.N.) of central metal atom in the complex `K_3[Fe(CN)_6]` is :

Options

A. C.N. = 3, O.N. = +3
B. C.N. = 6, O.N. = +6
C. CN. =6, ON =+3
D. CN. =3, ON. =+6.

Explanation

To determine the coordination number (C.N.) and oxidation number (O.N.) of the central metal atom in the complex \( K_3[Fe(CN)_6] \), we can follow these steps:

### Step 1: Identify the central metal atom
The complex given is \( K_3[Fe(CN)_6] \). Here, the central metal atom is iron (Fe).

### Step 2: Determine the oxidation number of the central metal atom
1. **Assign the oxidation state**: Let the oxidation state of iron be \( x \).
2. **Identify the charge of the ligands**: The cyanide ion (CN) has a charge of \(-1\). Since there are 6 cyanide ligands, their total contribution to the charge is \( 6 \times (-1) = -6 \).
3. **Set up the equation**: The overall charge of the coordination complex is \(-3\) (from \( K_3 \), which contributes \( +3 \) to balance the complex). Therefore, we can set up the equation:
\[ x + (-6) = -3 \]
4. **Solve for \( x \)**:
\[ x - 6 = -3 \implies x = -3 + 6 \implies x = +3 \]
Thus, the oxidation number of iron is \( +3 \).

### Step 3: Determine the coordination number
1. **Identify the number of ligands surrounding the central metal atom**: In the complex \( [Fe(CN)_6] \), iron is surrounded by 6 cyanide ligands.
2. **Count the ligands**: Since there are 6 cyanide ions coordinated to the iron atom, the coordination number is \( 6 \).

### Final Answer
- Coordination Number (C.N.) = 6
- Oxidation Number (O.N.) = +3

### Summary
The coordination number and oxidation number of the central metal atom (iron) in the complex \( K_3[Fe(CN)_6] \) are:
- C.N. = 6
- O.N. = +3