What are the correct oxidation state , coordination number , configuration , magnetic character and magnetic moment of `K_(4)[Mn(CN)_(6)] ? `

Options

A. `{:(O.S. , C.N, "Configuration" , "Magnetic Character" , "Magnetic Moment "), (+6 , 6 , t_(2g)^(5) , "Diamagnetic " , 0):}`
B. `{:(O.S. , C.N, "Configuration" , "Magnetic Character" , "Magnetic Moment "), (+4 , 6 , t_(2g)^(4) e_(g)^(1) , "Paramagnetic " , 1.732 B.M):}`
C. `{:(O.S. , C.N, "Configuration" , "Magnetic Character" , "Magnetic Moment "), (+2 , 6 , t_(2g)^(5) , "Paramagnetic " , 1.732 B.M):}`
D. `{:(O.S. , C.N, "Configuration" , "Magnetic Character" , "Magnetic Moment "), (+4 , 6 , t_(2g)^(3) e_(g)^(2) , "Diamagnetic " , 0):}`

Answer

To solve the question regarding the oxidation state, coordination number, configuration, magnetic character, and magnetic moment of \( K_4[Mn(CN)_6] \), we will follow these steps:

### Step-by-Step Solution:

1. **Determine the Oxidation State of Manganese (Mn)**:
- The complex ion is \( [Mn(CN)_6]^{4-} \).
- Each cyanide ion (CN) has a charge of -1. Therefore, for 6 cyanide ions, the total charge is -6.
- Let the oxidation state of manganese be \( x \).
- The equation becomes:
\[ x + 6(-1) = -4 \implies x - 6 = -4 \implies x = +2 \]
- **Oxidation state of Mn is +2**.

2. **Determine the Coordination Number**:
- The coordination number is determined by the number of ligands attached to the central metal ion.
- In this case, there are 6 cyanide ions coordinated to manganese.
- **Coordination number is 6**.

3. **Determine the Electron Configuration**:
- Manganese (Mn) has an atomic number of 25, so its ground state electron configuration is \( [Ar] 3d^5 4s^2 \).
- In the +2 oxidation state, Mn loses two electrons, typically from the 4s orbital first, leading to \( [Ar] 3d^5 \).
- Since cyanide (CN) is a strong field ligand, it causes a large splitting of the d-orbitals, leading to the configuration \( t_{2g}^5 e_g^0 \).
- **Configuration is \( t_{2g}^5 \)**.

4. **Determine the Magnetic Character**:
- The magnetic character depends on the presence of unpaired electrons.
- In the \( t_{2g}^5 \) configuration, there are 5 electrons in the \( t_{2g} \) level, which means there are no paired electrons.
- Therefore, the complex is **paramagnetic**.

5. **Calculate the Magnetic Moment**:
- The magnetic moment (\( \mu \)) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
- Here, \( n \) is the number of unpaired electrons. For \( t_{2g}^5 \), there are 5 unpaired electrons.
- Thus, \( n = 5 \):
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{5 \times 7} = \sqrt{35} \approx 5.92 \, \text{BM} \]
- **Magnetic moment is approximately 5.92 BM**.

### Summary of Results:
- **Oxidation State**: +2
- **Coordination Number**: 6
- **Configuration**: \( t_{2g}^5 \)
- **Magnetic Character**: Paramagnetic
- **Magnetic Moment**: Approximately 5.92 BM