Which of the following electronic configruation would be associated with the highest magnetic moment

Options

A. `[Ar]3d^(8)`
B. `[Ar]3d^(3)`
C. `[Ar]3d^(6)`
D. `[Ar]3d^(7)`

Answer

To determine which electronic configuration is associated with the highest magnetic moment, we need to analyze the number of unpaired electrons in each configuration. The magnetic moment is directly related to the number of unpaired electrons: the more unpaired electrons, the higher the magnetic moment.

### Step-by-Step Solution:

1. **Understand the Concept of Magnetic Moment**:
- The magnetic moment arises from unpaired electrons in an atom. The formula for calculating the magnetic moment (μ) is given by:
\[ μ = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

2. **Identify the Electronic Configurations**:
- Let's assume we have the following electronic configurations to analyze (for example):
- A) \( \text{[Ar]} \, 3d^8 \)
- B) \( \text{[Ar]} \, 3d^3 \)
- C) \( \text{[Ar]} \, 3d^6 \)
- D) \( \text{[Ar]} \, 3d^7 \)

3. **Count the Unpaired Electrons**:
- **Configuration A: \( \text{[Ar]} \, 3d^8 \)**
- In the \( 3d \) subshell, there are 8 electrons. The filling order is:
- 1, 2, 3, 4, 5 (first five fill singly), then 6, 7, 8 (pairing begins).
- Result: **2 unpaired electrons**.

- **Configuration B: \( \text{[Ar]} \, 3d^3 \)**
- In the \( 3d \) subshell, there are 3 electrons:
- 1, 2, 3 (all fill singly).
- Result: **3 unpaired electrons**.

- **Configuration C: \( \text{[Ar]} \, 3d^6 \)**
- In the \( 3d \) subshell, there are 6 electrons:
- 1, 2, 3, 4, 5 (first five fill singly), then 6 (pairs with one of the first five).
- Result: **4 unpaired electrons**.

- **Configuration D: \( \text{[Ar]} \, 3d^7 \)**
- In the \( 3d \) subshell, there are 7 electrons:
- 1, 2, 3, 4, 5 (first five fill singly), then 6, 7 (pairing begins).
- Result: **3 unpaired electrons**.

4. **Compare the Number of Unpaired Electrons**:
- Configuration A: 2 unpaired electrons
- Configuration B: 3 unpaired electrons
- Configuration C: 4 unpaired electrons
- Configuration D: 3 unpaired electrons

5. **Conclusion**:
- The configuration with the highest number of unpaired electrons is **Configuration C: \( \text{[Ar]} \, 3d^6 \)**, which has **4 unpaired electrons**. Therefore, this configuration is associated with the highest magnetic moment.

### Final Answer:
**The electronic configuration associated with the highest magnetic moment is \( \text{[Ar]} \, 3d^6 \).**