Calculate the number of unpaired electrons in `[Mn(H_(2)O)_6]^(2+)` , Considering `H_(2)O` as a weak field ligand (At . No of Mn = 25 )

Options

A. Two
B. Three
C. Four
D. Five

Answer

To calculate the number of unpaired electrons in the complex ion \([Mn(H_2O)_6]^{2+}\), we will follow these steps:

### Step 1: Determine the oxidation state of manganese in \([Mn(H_2O)_6]^{2+}\)
The complex has a charge of \(+2\) and water (\(H_2O\)) is a neutral ligand. Therefore, the oxidation state of manganese (Mn) can be calculated as follows:

\[ \text{Oxidation state of Mn} + \text{(Number of water ligands)} \times \text{(Charge of water)} = \text{Charge of complex} \]

Let \(x\) be the oxidation state of Mn:

\[ x + 0 = +2 \implies x = +2 \]

So, the oxidation state of Mn in \([Mn(H_2O)_6]^{2+}\) is \(+2\).

### Step 2: Determine the electronic configuration of Mn
The atomic number of manganese (Mn) is \(25\). The electronic configuration of neutral Mn is:

\[ \text{Mn: } [Ar] 3d^5 4s^2 \]

### Step 3: Adjust the electronic configuration for Mn\(^{2+}\)
When Mn loses two electrons to form Mn\(^{2+}\), it loses the two \(4s\) electrons first. Therefore, the electronic configuration of Mn\(^{2+}\) is:

\[ \text{Mn}^{2+}: [Ar] 3d^5 \]

### Step 4: Analyze the \(3d\) electrons in the presence of a weak field ligand
Since water is a weak field ligand, it does not cause significant splitting of the \(d\) orbitals. In an octahedral field, the \(3d\) orbitals split into two sets: \(t_{2g}\) (lower energy) and \(e_g\) (higher energy). However, because water is a weak field ligand, the electrons will occupy the \(3d\) orbitals singly before pairing up.

The \(3d^5\) configuration means that all five \(3d\) electrons will occupy the \(t_{2g}\) and \(e_g\) orbitals singly:

- \(t_{2g}\): 3 electrons
- \(e_g\): 2 electrons

### Step 5: Count the number of unpaired electrons
Since all five \(3d\) electrons are unpaired, we conclude that:

\[ \text{Number of unpaired electrons} = 5 \]

### Final Answer
The number of unpaired electrons in \([Mn(H_2O)_6]^{2+}\) is **5**.

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