Give the number of unpaired electron present in the d-orbitals (whose lobes are present along the axis) for the complex `[Co(SCN)_(4)]^(2-)` .

Explanation

To determine the number of unpaired electrons present in the d-orbitals (whose lobes are present along the axis) for the complex \([Co(SCN)_{4}]^{2-}\), we can follow these steps:

### Step 1: Determine the oxidation state of cobalt in the complex
The overall charge of the complex is \(-2\). The thiocyanate ion (SCN) has a charge of \(-1\). Since there are four SCN ligands, their total contribution to the charge is \(-4\).

Let the oxidation state of cobalt be \(x\). The equation can be set up as follows:

\[ x + 4(-1) = -2 \]

Solving for \(x\):

\[ x - 4 = -2 \\ x = +2 \]

Thus, cobalt is in the +2 oxidation state.

### Step 2: Write the electron configuration of cobalt
Cobalt (Co) has an atomic number of 27. The ground state electron configuration of cobalt is:

\[ [Ar] 4s^2 3d^7 \]

For the +2 oxidation state, cobalt loses the two 4s electrons, resulting in:

\[ [Ar] 3d^7 \]

### Step 3: Determine the nature of the ligand
The ligand SCN is a weak field ligand. Weak field ligands do not cause pairing of electrons in the d-orbitals. Therefore, the electrons in the 3d orbitals will remain unpaired.

### Step 4: Fill the d-orbitals according to Hund's rule
In the 3d subshell, we have 7 electrons to place. According to Hund's rule, we fill each orbital singly before pairing. The filling of the 3d orbitals will look like this:

- 3d orbital filling:
- \(d_{xy}\): 1
- \(d_{yz}\): 1
- \(d_{zx}\): 1
- \(d_{x^2-y^2}\): 2 (pairing starts here)
- \(d_{z^2}\): 2 (pairing continues)

This results in the following distribution:
- \(d_{xy}\): 1 unpaired
- \(d_{yz}\): 1 unpaired
- \(d_{zx}\): 1 unpaired
- \(d_{x^2-y^2}\): 1 paired
- \(d_{z^2}\): 1 paired

### Step 5: Identify the axial orbitals
The d-orbitals that are oriented along the axes are \(d_{x^2-y^2}\) and \(d_{z^2}\).

### Step 6: Count the unpaired electrons in the axial orbitals
In the axial orbitals:
- \(d_{x^2-y^2}\): 1 paired (no unpaired)
- \(d_{z^2}\): 1 paired (no unpaired)

Thus, there are **0 unpaired electrons** in the axial d-orbitals.

### Final Answer
The number of unpaired electrons present in the d-orbitals (whose lobes are present along the axis) for the complex \([Co(SCN)_{4}]^{2-}\) is **0**.

---