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 can follow these steps:

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

Let the oxidation state of Mn be \(x\). The equation becomes:
\[ x + 0 \cdot 6 = +2 \]
Thus,
\[ x = +2 \]

### Step 2: Write the electron configuration of Mn
The atomic number of manganese (Mn) is 25. The ground state electron configuration of Mn is:
\[ [Ar] 3d^5 4s^2 \]

### Step 3: Determine the electron configuration of \(Mn^{2+}\)
When manganese loses 2 electrons to form \(Mn^{2+}\), the electrons are removed first from the 4s orbital. Therefore, the electron configuration of \(Mn^{2+}\) becomes:
\[ [Ar] 3d^5 \]

### Step 4: Analyze the ligand field
Since \(H_2O\) is a weak field ligand, it does not cause pairing of the electrons in the \(3d\) subshell. This means that the electrons will occupy the available \(d\) orbitals singly before pairing occurs.

### Step 5: Fill the \(3d\) orbitals
The \(3d\) subshell can hold a maximum of 10 electrons, and in the case of \(Mn^{2+}\) with \(3d^5\), the filling will be as follows:
- Each of the five \(d\) electrons will occupy separate orbitals due to the weak field nature of \(H_2O\).

The distribution of the five \(d\) electrons will look like this:
- \(d_{xy}\): 1 electron
- \(d_{xz}\): 1 electron
- \(d_{yz}\): 1 electron
- \(d_{x^2-y^2}\): 1 electron
- \(d_{z^2}\): 1 electron

### Step 6: Count the number of unpaired electrons
Since all five electrons are in separate orbitals and there is no pairing, all five electrons are unpaired.

Thus, the number of unpaired electrons in \([Mn(H_2O)_6]^{2+}\) is:
\[ \text{Number of unpaired electrons} = 5 \]

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

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