`[Co(NH_(3))_(6)]^(3+)` is diamagnetic while `[CoF_(6)]^(3-)` is_____ .

Answer

To determine the magnetic nature of the complex `[CoF6]^(3-)`, we will follow these steps:

### Step 1: Determine the Oxidation State of Cobalt
The complex is `[CoF6]^(3-)`. The oxidation state of cobalt (Co) can be calculated as follows:
- Let the oxidation state of Co be \( x \).
- Each fluorine (F) has an oxidation state of -1, and there are 6 fluorine atoms.
- The overall charge of the complex is -3.

The equation is:
\[ x + 6(-1) = -3 \]
\[ x - 6 = -3 \]
\[ x = +3 \]

**Hint:** Remember that the sum of the oxidation states in a complex ion equals the overall charge of the ion.

### Step 2: Write the Electronic Configuration of Cobalt
The ground state electronic configuration of cobalt (Co) is:
\[ \text{Co: } [Ar] 3d^7 4s^2 \]

When cobalt is in the +3 oxidation state, it loses two 4s electrons and one 3d electron, resulting in:
\[ \text{Co}^{3+}: [Ar] 3d^6 \]

**Hint:** For transition metals, the 4s electrons are lost before the 3d electrons when forming cations.

### Step 3: Determine the Type of Ligand
Fluoride (F-) is a weak field ligand. Weak field ligands do not cause significant splitting of the d-orbitals and typically lead to high-spin complexes.

**Hint:** Identify the strength of the ligand to determine the type of spin state (high-spin or low-spin).

### Step 4: Fill the d-Orbitals
In a high-spin configuration for \( 3d^6 \) with weak field ligands, the electrons will occupy the orbitals to maximize unpaired electrons:
- The d-orbitals will be filled as follows:
- 1 electron in each of the five d-orbitals (3dxy, 3dxz, 3dyz, 3dx2-y2, 3dz2).
- The sixth electron will pair up in one of the orbitals.

Thus, the filling will look like this:
- 3dxy: ↑
- 3dxz: ↑
- 3dyz: ↑
- 3dx2-y2: ↑
- 3dz2: ↑↓ (pairing occurs here)

**Hint:** For high-spin complexes, always fill each orbital singly before pairing.

### Step 5: Count the Number of Unpaired Electrons
From the filling of the d-orbitals, we can see that there are 4 unpaired electrons (one in each of the first four orbitals and one paired in the last orbital).

**Hint:** Count the number of electrons that are not paired to determine if the complex is paramagnetic or diamagnetic.

### Step 6: Determine the Magnetic Nature
Since there are 4 unpaired electrons in `[CoF6]^(3-)`, this complex is **paramagnetic**.

**Final Answer:** `[CoF6]^(3-)` is paramagnetic.