The geometry of some complex ions are given against them -
(1) `[Ag(NH_3)_(2)]^(+)` - Linear
(2) `
(2) `[MnCl_(4)]^(2+)` - Tetrahedral
(3) `[Cu(NH_3)_(4)]^(2+)` - square planar
(4) `[Ni(CN_4)]^(2-)` - square planar
The correct match is -

Options

A. 1 and 4
B. 1,2, and 3
C. 1, 3 and 4
D. 1, 2, 3 and 4

Answer

To solve the problem of matching the geometries of the given complex ions, we will analyze each complex ion one by one based on their electronic configurations and the nature of the ligands involved.

### Step-by-Step Solution:

1. **Analyze `[Ag(NH₃)₂]⁺`:**
- Silver (Ag) in its elemental state has the electronic configuration of [Kr] 4d¹⁰ 5s².
- In the +1 oxidation state, Ag loses one electron, resulting in [Kr] 4d¹⁰.
- The d-orbitals are fully filled (d¹⁰), which leads to a linear geometry due to the sp hybridization of the orbitals.
- **Match:** `[Ag(NH₃)₂]⁺` - Linear

2. **Analyze `[MnCl₄]²⁺`:**
- Manganese (Mn) has the electronic configuration of [Ar] 3d⁵ 4s².
- In the +2 oxidation state, Mn loses two electrons, resulting in [Ar] 3d⁵.
- Chloride (Cl) is a weak field ligand and does not cause pairing of electrons. The geometry is tetrahedral due to sp³ hybridization.
- **Match:** `[MnCl₄]²⁺` - Tetrahedral

3. **Analyze `[Cu(NH₃)₄]²⁺`:**
- Copper (Cu) has the electronic configuration of [Ar] 3d¹⁰ 4s¹.
- In the +2 oxidation state, Cu loses two electrons, resulting in [Ar] 3d⁹.
- Ammonia (NH₃) is a strong field ligand that causes pairing of electrons. The geometry is square planar due to dsp² hybridization.
- **Match:** `[Cu(NH₃)₄]²⁺` - Square planar

4. **Analyze `[Ni(CN)₄]²⁻`:**
- Nickel (Ni) has the electronic configuration of [Ar] 3d⁸ 4s².
- In the +2 oxidation state, Ni loses two electrons, resulting in [Ar] 3d⁸.
- Cyanide (CN) is a strong field ligand that causes pairing of electrons. The geometry is also square planar due to dsp² hybridization.
- **Match:** `[Ni(CN)₄]²⁻` - Square planar

### Final Matches:
- (1) `[Ag(NH₃)₂]⁺` - Linear
- (2) `[MnCl₄]²⁺` - Tetrahedral
- (3) `[Cu(NH₃)₄]²⁺` - Square planar
- (4) `[Ni(CN)₄]²⁻` - Square planar

### Conclusion:
The correct match for the geometries of the complex ions is:
1. `[Ag(NH₃)₂]⁺` - Linear
2. `[MnCl₄]²⁺` - Tetrahedral
3. `[Cu(NH₃)₄]²⁺` - Square planar
4. `[Ni(CN)₄]²⁻` - Square planar