The number of unpaired electrons in `[CoF_(6)]^(3-)` are

Answer

To determine the number of unpaired electrons in the complex \([CoF_6]^{3-}\), we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Oxidation State of Cobalt:**
- The formula for the complex is \([CoF_6]^{3-}\).
- Let the oxidation state of cobalt be \(X\).
- Each fluorine (\(F\)) has an oxidation state of \(-1\).
- Therefore, the equation for the oxidation state can be set up as:
\[ X + 6(-1) = -3 \]
- Simplifying this gives:
\[ X - 6 = -3 \implies X = +3 \]
- Thus, the oxidation state of cobalt in this complex is \(+3\).

2. **Write the Electron Configuration of Cobalt:**
- The atomic number of cobalt (Co) is 26.
- The electron configuration of cobalt in its elemental state is:
\[ [Ar] 3d^7 4s^2 \]
- Since cobalt is in the \(+3\) oxidation state, it loses 3 electrons. The electrons are removed first from the \(4s\) orbital and then from the \(3d\) orbital:
\[ [Ar] 3d^6 \]
- Therefore, the electron configuration of \([Co]^{3+}\) is \(3d^6\).

3. **Identify the Type of Ligand:**
- Fluoride (\(F^-\)) is a weak field ligand, which means it does not cause pairing of electrons in the \(d\) orbitals.

4. **Determine the Arrangement of Electrons in the \(d\) Orbitals:**
- In an octahedral field, the \(d\) orbitals split into two sets: \(t_{2g}\) (lower energy) and \(e_g\) (higher energy).
- The \(3d^6\) configuration will fill the orbitals as follows:
- The \(t_{2g}\) orbitals will be filled first, and since \(F^-\) is a weak ligand, there will be no pairing.
- The filling order will be:
- \(t_{2g}\): 3 electrons (1 in each orbital)
- \(e_g\): 3 electrons (1 in each of the three orbitals)
- This results in the following arrangement:
- \(t_{2g}\): ↑ ↑ ↑ (3 unpaired electrons)
- \(e_g\): ↑ ↑ (2 unpaired electrons)

5. **Count the Number of Unpaired Electrons:**
- In total, there are 4 unpaired electrons in the \(3d\) orbitals of \([CoF_6]^{3-}\).

### Final Answer:
The number of unpaired electrons in \([CoF_6]^{3-}\) is **4**.