Among the following least 3rd ionization energy is for

Options

A. Mn
B. Co
C. Fe
D. Ni

Explanation

To determine which element among manganese (Mn), cobalt (Co), iron (Fe), and nickel (Ni) has the least third ionization energy, we need to analyze the electronic configurations and stability of the ions formed by these elements.

### Step 1: Write the electronic configurations of the elements

1. **Manganese (Mn)**:
- Atomic number = 25
- Electronic configuration = \( [Ar] 3d^5 4s^2 \)

2. **Cobalt (Co)**:
- Atomic number = 27
- Electronic configuration = \( [Ar] 3d^7 4s^2 \)

3. **Iron (Fe)**:
- Atomic number = 26
- Electronic configuration = \( [Ar] 3d^6 4s^2 \)

4. **Nickel (Ni)**:
- Atomic number = 28
- Electronic configuration = \( [Ar] 3d^8 4s^2 \)

### Step 2: Determine the ionization processes

For each element, we will consider the ionization processes leading to the formation of \( M^{3+} \):

- **Manganese**:
- \( \text{Mn} \rightarrow \text{Mn}^+ \) (1st ionization)
- \( \text{Mn}^+ \rightarrow \text{Mn}^{2+} \) (2nd ionization)
- \( \text{Mn}^{2+} \rightarrow \text{Mn}^{3+} \) (3rd ionization)

- **Cobalt**:
- \( \text{Co} \rightarrow \text{Co}^+ \) (1st ionization)
- \( \text{Co}^+ \rightarrow \text{Co}^{2+} \) (2nd ionization)
- \( \text{Co}^{2+} \rightarrow \text{Co}^{3+} \) (3rd ionization)

- **Iron**:
- \( \text{Fe} \rightarrow \text{Fe}^+ \) (1st ionization)
- \( \text{Fe}^+ \rightarrow \text{Fe}^{2+} \) (2nd ionization)
- \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} \) (3rd ionization)

- **Nickel**:
- \( \text{Ni} \rightarrow \text{Ni}^+ \) (1st ionization)
- \( \text{Ni}^+ \rightarrow \text{Ni}^{2+} \) (2nd ionization)
- \( \text{Ni}^{2+} \rightarrow \text{Ni}^{3+} \) (3rd ionization)

### Step 3: Analyze the stability of the resulting ions

- **Manganese**:
- After losing 3 electrons, \( \text{Mn}^{3+} \) has the configuration \( 3d^4 \). This is less stable compared to \( \text{Mn}^{2+} \) which has a half-filled \( 3d^5 \) configuration.

- **Cobalt**:
- After losing 3 electrons, \( \text{Co}^{3+} \) has the configuration \( 3d^6 \). This is not particularly stable compared to \( \text{Co}^{2+} \).

- **Iron**:
- After losing 3 electrons, \( \text{Fe}^{3+} \) has the configuration \( 3d^5 \). This is a stable half-filled configuration, which means it requires less energy to remove the third electron.

- **Nickel**:
- After losing 3 electrons, \( \text{Ni}^{3+} \) has the configuration \( 3d^7 \). This is less stable than \( \text{Ni}^{2+} \).

### Step 4: Conclusion

Among the four elements, the least third ionization energy will be for iron (\( \text{Fe} \)), as it achieves a stable half-filled configuration after the third ionization.

### Final Answer:
The least third ionization energy is for **iron (Fe)**.

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