To solve the question of which metal ion forms complexes with the same magnetic moment and geometry irrespective of the nature of ligands, we will analyze the electronic configurations and the number of unpaired electrons for each metal ion provided in the options.
### Step-by-Step Solution:
1. **Identify the Metal Ions**: The question provides four metal ions. For this solution, we will consider the following ions: Ni²⁺, Fe²⁺, Cu²⁺, and Co²⁺.
2. **Determine the Electronic Configuration**:
- **Copper (Cu)**: The electronic configuration of neutral copper (Cu) is [Ar] 3d¹⁰ 4s¹. For Cu²⁺, it loses two electrons (one from 4s and one from 3d), resulting in the configuration 3d⁹.
- **Nickel (Ni)**: The electronic configuration of neutral nickel (Ni) is [Ar] 3d⁸ 4s². For Ni²⁺, it loses two electrons from 4s, resulting in the configuration 3d⁸.
- **Iron (Fe)**: The electronic configuration of neutral iron (Fe) is [Ar] 3d⁶ 4s². For Fe²⁺, it loses two electrons from 4s, resulting in the configuration 3d⁶.
- **Cobalt (Co)**: The electronic configuration of neutral cobalt (Co) is [Ar] 3d⁷ 4s². For Co²⁺, it loses two electrons from 4s, resulting in the configuration 3d⁷.
3. **Count the Unpaired Electrons**:
- **Cu²⁺ (3d⁹)**: Has 1 unpaired electron.
- **Ni²⁺ (3d⁸)**: Has 2 unpaired electrons (can vary with ligand field).
- **Fe²⁺ (3d⁶)**: Has 4 unpaired electrons (can vary with ligand field).
- **Co²⁺ (3d⁷)**: Has 3 unpaired electrons (can vary with ligand field).
4. **Analyze the Effect of Ligands**:
- For **Cu²⁺**, regardless of whether it is in the presence of strong field or weak field ligands, it retains 1 unpaired electron. Therefore, it will have the same magnetic moment and geometry.
- For **Ni²⁺**, **Fe²⁺**, and **Co²⁺**, the number of unpaired electrons can change depending on the ligand field strength (strong field ligands can cause pairing of electrons), leading to different magnetic moments and geometries.
5. **Conclusion**: The metal ion that forms complexes with the same magnetic moment and geometry irrespective of the nature of ligands is **Cu²⁺**.
### Final Answer:
**Cu²⁺**
