Among `|Ni(CO)_(4)|, |Ni(CN)_(4)|^(2-), |NiCl_(4)|^(2-)` species, the hybridisation state at Ni atom are respectively
]Atomic number of Ni = 28]

Options

A. `sp^(3),dsp^(2),dsp^(2)`
B. `sp^(3),dsp^(2),sp^(3)`
C. `sp^(3),sp^(3),dsp^(2)`
D. `dsp^(2),sp^(3),sp^(3)`

Explanation

To determine the hybridization state of the nickel (Ni) atom in the complexes \( Ni(CO)_4 \), \( Ni(CN)_4^{2-} \), and \( NiCl_4^{2-} \), we will follow these steps:

### Step 1: Determine the oxidation state of Ni in each complex.

1. **For \( Ni(CO)_4 \)**:
- CO is a neutral ligand.
- Let the oxidation state of Ni be \( x \).
- The equation becomes:
\[ x + 0 = 0 \implies x = 0 \]
- Therefore, Ni is in the 0 oxidation state.

2. **For \( Ni(CN)_4^{2-} \)**:
- CN is a -1 charged ligand.
- Let the oxidation state of Ni be \( x \).
- The equation becomes:
\[ x + 4(-1) = -2 \implies x - 4 = -2 \implies x = +2 \]
- Therefore, Ni is in the +2 oxidation state.

3. **For \( NiCl_4^{2-} \)**:
- Cl is a -1 charged ligand.
- Let the oxidation state of Ni be \( x \).
- The equation becomes:
\[ x + 4(-1) = -2 \implies x - 4 = -2 \implies x = +2 \]
- Therefore, Ni is also in the +2 oxidation state.

### Step 2: Determine the electronic configuration of Ni in each oxidation state.

- The atomic number of Ni is 28. The ground state electronic configuration is:
\[ [Ar] 4s^2 3d^8 \]

1. **For \( Ni(CO)_4 \)** (Ni in 0 oxidation state):
- The configuration remains \( [Ar] 4s^2 3d^8 \).
- Since CO is a strong field ligand, it causes pairing of electrons in the 3d orbitals. The configuration becomes:
\[ [Ar] 4s^0 3d^{10} \]
- The hybridization involves 4 orbitals (1 from 4s and 3 from 3d), leading to:
\[ \text{Hybridization: } sp^3 \]

2. **For \( Ni(CN)_4^{2-} \)** (Ni in +2 oxidation state):
- The configuration becomes \( [Ar] 4s^0 3d^8 \) (4s is lost).
- CN is also a strong field ligand, causing pairing:
\[ [Ar] 4s^0 3d^{10} \text{ (after pairing)} \]
- The hybridization involves 4 orbitals (3 from 3d and 1 from 4p), leading to:
\[ \text{Hybridization: } dsp^2 \]

3. **For \( NiCl_4^{2-} \)** (Ni in +2 oxidation state):
- The configuration remains \( [Ar] 4s^0 3d^8 \) (4s is lost).
- Cl is a weak field ligand, so no pairing occurs:
\[ [Ar] 4s^0 3d^8 \]
- The hybridization involves 4 orbitals (3 from 3d and 1 from 4s), leading to:
\[ \text{Hybridization: } sp^3 \]

### Summary of Hybridization States:
- \( Ni(CO)_4 \): Hybridization is **sp³**
- \( Ni(CN)_4^{2-} \): Hybridization is **dsp²**
- \( NiCl_4^{2-} \): Hybridization is **sp³**

### Final Answer:
- The hybridization states at Ni atom for the complexes are:
- \( Ni(CO)_4 \): **sp³**
- \( Ni(CN)_4^{2-} \): **dsp²**
- \( NiCl_4^{2-} \): **sp³**