Pick out the correct statement with respect `[Mn(CN)_(6)]^(4-)`

Options

A. It is `sp^(3)d^(2)` hybridised and octahedral
B. it is `sp^(3)d^(2)` hybridised and tetrahedral
C. It is `d^(2)sp^(3)` hybridised and octahedral
D. It is `dsp^(2)` hybridised and square planer

Answer

To solve the question regarding the complex ion \([Mn(CN)_{6}]^{4-}\), we will follow these steps:

### Step 1: Determine the oxidation state of manganese (Mn)
The complex \([Mn(CN)_{6}]^{4-}\) has a total charge of -4. Each cyanide ion (CN) has a charge of -1. Since there are 6 cyanide ions, the total contribution from the ligands is:
\[ 6 \times (-1) = -6 \]
Let the oxidation state of manganese be \(x\). The equation for the charge balance can be set up as follows:
\[ x + (-6) = -4 \]
Solving for \(x\):
\[ x - 6 = -4 \\ x = -4 + 6 \\ x = +2 \]
Thus, the oxidation state of manganese in the complex is +2.

### Step 2: Write the electron configuration of manganese
The atomic number of manganese (Mn) is 25. The ground state electron configuration is:
\[ [Ar] 4s^2 3d^5 \]
After losing 2 electrons (due to the +2 oxidation state), the configuration becomes:
\[ [Ar] 3d^5 \]

### Step 3: Analyze the ligand and its effect
Cyanide (CN) is a strong field ligand. Strong field ligands cause pairing of electrons in the d-orbitals. In the case of \(3d^5\), the electrons will pair up in the lower energy d-orbitals.

### Step 4: Determine the hybridization
Since there are 6 ligands (CN) coordinating to the manganese ion, we need to find the appropriate hybridization. The pairing of electrons and the presence of 6 coordination sites suggest that the hybridization will be:
\[ d^2sp^3 \]
This hybridization involves the use of two d-orbitals, one s-orbital, and three p-orbitals.

### Step 5: Determine the geometry of the complex
With 6 coordinate bonds formed and the hybridization being \(d^2sp^3\), the geometry of the complex will be octahedral.

### Conclusion
The correct statement regarding the complex \([Mn(CN)_{6}]^{4-}\) is that it has an octahedral geometry and is \(d^2sp^3\) hybridized.

### Final Answer
The correct statement is: **The complex \([Mn(CN)_{6}]^{4-}\) is octahedral and \(d^2sp^3\) hybridized.**

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