To analyze the magnetic properties of the complexes \( Ni(CO)_4 \), \( [NiCl_4]^{2-} \), and \( [Ni(CN)_4]^{2-} \), we will follow these steps:
### Step 1: Determine the oxidation state and electron configuration of Nickel in \( Ni(CO)_4 \)
- **Oxidation State**: In \( Ni(CO)_4 \), CO is a neutral ligand, so the oxidation state of Ni is 0.
- **Electron Configuration**: The electron configuration of Ni (atomic number 28) is \( [Ar] 4s^2 3d^8 \).
### Step 2: Analyze the ligand field strength of CO
- CO is a strong field ligand, which means it will cause pairing of electrons in the d-orbitals.
- In the presence of 4 CO ligands, the \( 4s \) electrons will be promoted to the \( 3d \) orbitals, leading to a configuration of \( d^{10} \) (all electrons paired).
### Step 3: Determine the geometry and magnetic properties of \( Ni(CO)_4 \)
- The geometry of \( Ni(CO)_4 \) is tetrahedral (due to 4 ligands).
- Since all electrons are paired, \( Ni(CO)_4 \) is **diamagnetic**.
### Step 4: Determine the oxidation state and electron configuration of Nickel in \( [NiCl_4]^{2-} \)
- **Oxidation State**: In \( [NiCl_4]^{2-} \), Cl is a -1 ligand, so the oxidation state of Ni is +2.
- **Electron Configuration**: The electron configuration for \( Ni^{2+} \) is \( [Ar] 3d^8 \).
### Step 5: Analyze the ligand field strength of Cl
- Cl is a weak field ligand, which means it does not cause significant pairing of electrons.
- Therefore, the \( 3d \) orbitals will have unpaired electrons.
### Step 6: Determine the geometry and magnetic properties of \( [NiCl_4]^{2-} \)
- The geometry of \( [NiCl_4]^{2-} \) is typically tetrahedral.
- Since there are unpaired electrons, \( [NiCl_4]^{2-} \) is **paramagnetic**.
### Step 7: Determine the oxidation state and electron configuration of Nickel in \( [Ni(CN)_4]^{2-} \)
- **Oxidation State**: In \( [Ni(CN)_4]^{2-} \), CN is a -1 ligand, so the oxidation state of Ni is +2.
- **Electron Configuration**: The electron configuration for \( Ni^{2+} \) is \( [Ar] 3d^8 \).
### Step 8: Analyze the ligand field strength of CN
- CN is a strong field ligand, which means it will cause pairing of electrons in the d-orbitals.
- In this case, the \( 3d \) electrons will pair up, leading to a configuration of \( d^{10} \) (all electrons paired).
### Step 9: Determine the geometry and magnetic properties of \( [Ni(CN)_4]^{2-} \)
- The geometry of \( [Ni(CN)_4]^{2-} \) is square planar.
- Since all electrons are paired, \( [Ni(CN)_4]^{2-} \) is **diamagnetic**.
### Summary of Magnetic Properties:
- \( Ni(CO)_4 \): Diamagnetic
- \( [NiCl_4]^{2-} \): Paramagnetic
- \( [Ni(CN)_4]^{2-} \): Diamagnetic
