Nickel `(Z=28)` combines with a uninegative monodentate ligand `X^(-)` to form a paramagnetic complex `[NiX_4]^(2-)`. The number of unpaired electron(s) in the nickel and geometry of this complex ion are, respectively:

Options

A. one, tetrahedral
B. two, tetrahedral
C. one, square planar
D. two, square planar

Answer

To solve the question, we need to determine the oxidation state of nickel in the complex \([NiX_4]^{2-}\), the number of unpaired electrons in nickel, and the geometry of the complex. Let's break this down step by step.

### Step 1: Determine the Oxidation State of Nickel
In the complex \([NiX_4]^{2-}\):
- Each ligand \(X^-\) has a charge of \(-1\).
- There are four ligands, so the total negative charge contributed by the ligands is \(4 \times (-1) = -4\).
- The overall charge of the complex is \(-2\).

Let the oxidation state of nickel be \(x\). The equation for the oxidation state can be set up as follows:
\[ x + (-4) = -2 \]
Solving for \(x\):
\[ x - 4 = -2 \\ x = +2 \]
Thus, the oxidation state of nickel in this complex is \(+2\).

### Step 2: Determine the Electronic Configuration of Nickel
The atomic number of nickel (Ni) is 28. The electronic configuration of neutral nickel is:
\[ [Ar] \, 3d^8 \, 4s^2 \]
In the \(+2\) oxidation state, nickel loses two electrons, typically from the \(4s\) orbital first:
\[ \text{Ni}^{2+}: [Ar] \, 3d^8 \]

### Step 3: Determine the Number of Unpaired Electrons
In the \(3d\) subshell, the distribution of electrons for \(3d^8\) is:
- The \(3d\) orbitals can hold a maximum of 10 electrons.
- The filling of \(3d\) orbitals follows Hund's rule and the Pauli exclusion principle.

The configuration of \(3d^8\) can be represented as:
- \(3d\) orbitals: ↑↓ ↑↓ ↑↓ ↑ ↑

This shows that there are 2 paired electrons and 2 unpaired electrons in the \(3d\) orbitals.

### Step 4: Determine the Geometry of the Complex
Given that the ligand \(X^-\) is a uninegative monodentate ligand, and there are four such ligands surrounding the nickel ion, we can infer the hybridization:
- The coordination number is 4, which typically leads to \(sp^3\) hybridization.
- The geometry of an \(sp^3\) hybridized complex is tetrahedral.

### Final Answer
The number of unpaired electrons in nickel is **2**, and the geometry of the complex ion \([NiX_4]^{2-}\) is **tetrahedral**.

### Summary
- **Number of unpaired electrons**: 2
- **Geometry**: Tetrahedral