Number of unpaired electrons in `Mn^(3+)` is

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To determine the number of unpaired electrons in the \( \text{Mn}^{3+} \) ion, we can follow these steps:

### Step 1: Determine the electronic configuration of manganese (Mn)
Manganese (Mn) has an atomic number of 25. The electronic configuration of Mn is:
\[ \text{Mn: } [\text{Ar}] 3d^5 4s^2 \]

### Step 2: Identify the oxidation state of manganese in \( \text{Mn}^{3+} \)
In the \( \text{Mn}^{3+} \) ion, manganese loses three electrons. The two electrons from the 4s subshell and one electron from the 3d subshell are removed.

### Step 3: Write the electronic configuration for \( \text{Mn}^{3+} \)
After removing three electrons, the electronic configuration of \( \text{Mn}^{3+} \) becomes:
\[ \text{Mn}^{3+}: [\text{Ar}] 3d^4 \]

### Step 4: Determine the distribution of electrons in the 3d subshell
The 3d subshell can hold a maximum of 10 electrons (5 orbitals, 2 electrons each). For \( \text{Mn}^{3+} \) with a \( 3d^4 \) configuration, we distribute the 4 electrons according to Hund's rule, which states that electrons will fill degenerate orbitals singly before pairing up.

1. Fill the first orbital: 1 electron
2. Fill the second orbital: 1 electron
3. Fill the third orbital: 1 electron
4. Pair one electron in the first orbital: 1 electron

This results in the following distribution:
- Orbital 1: ↑↓ (2 electrons, paired)
- Orbital 2: ↑ (1 electron, unpaired)
- Orbital 3: ↑ (1 electron, unpaired)
- Orbital 4: ↑ (1 electron, unpaired)

### Step 5: Count the number of unpaired electrons
From the distribution:
- There are 3 unpaired electrons (one in each of the last three orbitals).

### Final Answer:
The number of unpaired electrons in \( \text{Mn}^{3+} \) is **4**.

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