Step 1: Understanding the Concept:
To determine the hybridization and magnetic property of a coordination complex, we must first determine the oxidation state of the central metal ion, find its electronic configuration, and consider the nature of the ligand (strong field vs. weak field) to determine if electron pairing occurs.
Step 2: Detailed Explanation:
1. Oxidation State: Let the oxidation state of Co be \(x\). Since NH\(_3\) is a neutral ligand, \(x + 6(0) = +3\), so \(x = +3\).
2. Electronic Configuration: Cobalt (Co) has an atomic number of 27. The ground state configuration is [Ar] 3d\(^7\) 4s\(^2\). Therefore, Co\(^{3+}\) has a configuration of [Ar] 3d\(^6\).
3. Ligand Effect: NH\(_3\) is a strong field ligand, which forces the pairing of electrons in the 3d orbitals of the Co\(^{3+}\) ion.
4. Orbital Filling: The 6 electrons of 3d\(^6\) are forced into the first three 3d orbitals (t\(_{2g}\)), leaving two 3d orbitals, one 4s orbital, and three 4p orbitals vacant.
5. Hybridization: These six empty orbitals (two 3d, one 4s, and three 4p) hybridize to form d\(^2\)sp\(^3\) hybrid orbitals, which accept the lone pairs from the six NH\(_3\) ligands.
Step 3: Magnetic Properties:
Because the strong field ligand (NH\(_3\)) caused all 3d electrons to pair up, there are no unpaired electrons remaining. A substance with no unpaired electrons is diamagnetic.
Step 4: Final Answer:
The complex [Co(NH\(_3\))\(_6\)]\(^{3+}\) is d\(^2\)sp\(^3\) hybridised and diamagnetic.