Magnetic moment, ionic conductance and colligative properties are useful in deciding structure/constitution of a given unknown complex compound.
Q. A metal M having elecftronic configuration `(n-1)d^(8)ns^(2)` forms complexes with co-ordination No.=4 and 6, if it forms diamagnetic complexes then permissible oxidation states of metal cation and geometry is:

Options

A. `+2`, octahedral
B. `+4`, octahedral
C. `+2`, square planar
D. (b) and (c) both

Answer

To solve the problem regarding the metal M with the electronic configuration (n-1)d^8 ns^2 that forms diamagnetic complexes with coordination numbers 4 and 6, we will follow these steps:

### Step 1: Identify the Electronic Configuration
The given electronic configuration is (n-1)d^8 ns^2. This indicates that the metal has 8 d-electrons and 2 s-electrons.

**Hint:** Remember that the electronic configuration helps determine the oxidation states and the number of unpaired electrons.

### Step 2: Determine Possible Oxidation States
For a metal with the configuration (n-1)d^8 ns^2, the possible oxidation states can be:
- +2: This involves losing the two s-electrons, resulting in a (n-1)d^8 configuration.
- +4: This involves losing two s-electrons and two d-electrons, resulting in a (n-1)d^6 configuration.

**Hint:** The oxidation state is determined by the number of electrons lost from the outermost shell.

### Step 3: Analyze Diamagnetic Condition
Diamagnetic complexes have all electrons paired. We need to check the configurations for both oxidation states to see if they can lead to diamagnetic complexes.

1. **For +2 Oxidation State:**
- Configuration: (n-1)d^8
- The d-orbitals can be filled as follows: ↑↓ ↑↓ ↑↓ ↑↓ ↑ (8 electrons).
- All electrons are paired, leading to a diamagnetic complex.

**Hint:** A diamagnetic complex will have no unpaired electrons.

2. **For +4 Oxidation State:**
- Configuration: (n-1)d^6
- The d-orbitals can be filled as follows: ↑↓ ↑↓ ↑↓ ↑ (6 electrons).
- All electrons can be paired, leading to a diamagnetic complex.

**Hint:** Check the pairing of electrons in the d-orbitals for the oxidation state.

### Step 4: Determine the Geometry of the Complexes
1. **For +2 Oxidation State with Coordination Number 4:**
- The hybridization will be dsp^2, leading to a square planar geometry.

**Hint:** Coordination number and hybridization help determine the geometry of the complex.

2. **For +4 Oxidation State with Coordination Number 6:**
- The hybridization will be d^2sp^3, leading to an octahedral geometry.

**Hint:** Different hybridizations correspond to different geometries.

### Conclusion
- The permissible oxidation states of the metal cation are +2 and +4.
- The geometries corresponding to these oxidation states are:
- +2: Square planar geometry (coordination number 4).
- +4: Octahedral geometry (coordination number 6).

**Final Answer:**
Permissible oxidation states: +2 and +4; Geometry: Square planar (for +2) and Octahedral (for +4).