Highest magnetic moments, shown by the transition metal ion with the outermost electronic configuration is:

Options

A. `3d^(5)`
B. `3d^(2)`
C. `3d^(7)`
D. `3d^(9)`

Answer

To determine which transition metal ion has the highest magnetic moment based on the given outermost electronic configurations (3d5, 3d2, 3d7, and 3d9), we will calculate the magnetic moment for each configuration using the formula:

\[ \mu = \sqrt{n(n + 2)} \]

where \( n \) is the number of unpaired electrons.

### Step 1: Calculate for 3d5
1. **Determine the number of unpaired electrons**:
- The configuration 3d5 has 5 electrons, which can be arranged in 5 d-orbitals. All 5 electrons will occupy separate orbitals due to Hund's rule, resulting in 5 unpaired electrons.
- \( n = 5 \)

2. **Calculate the magnetic moment**:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{5 \times 7} = \sqrt{35} \approx 5.92 \text{ BM} \]

### Step 2: Calculate for 3d2
1. **Determine the number of unpaired electrons**:
- The configuration 3d2 has 2 electrons. They will occupy separate orbitals, resulting in 2 unpaired electrons.
- \( n = 2 \)

2. **Calculate the magnetic moment**:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{2 \times 4} = \sqrt{8} \approx 2.83 \text{ BM} \]

### Step 3: Calculate for 3d7
1. **Determine the number of unpaired electrons**:
- The configuration 3d7 has 7 electrons. Filling the orbitals, we will have 3 unpaired electrons (the first 5 will be filled singly, and the next 2 will pair up).
- \( n = 3 \)

2. **Calculate the magnetic moment**:
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{3 \times 5} = \sqrt{15} \approx 3.87 \text{ BM} \]

### Step 4: Calculate for 3d9
1. **Determine the number of unpaired electrons**:
- The configuration 3d9 has 9 electrons. Filling the orbitals, we will have 1 unpaired electron (the first 5 will be filled singly, and the next 4 will pair up).
- \( n = 1 \)

2. **Calculate the magnetic moment**:
\[ \mu = \sqrt{1(1 + 2)} = \sqrt{1 \times 3} = \sqrt{3} \approx 1.73 \text{ BM} \]

### Conclusion
After calculating the magnetic moments for all configurations:
- 3d5: \( \approx 5.92 \text{ BM} \)
- 3d2: \( \approx 2.83 \text{ BM} \)
- 3d7: \( \approx 3.87 \text{ BM} \)
- 3d9: \( \approx 1.73 \text{ BM} \)

The highest magnetic moment is shown by the transition metal ion with the outermost electronic configuration of **3d5**.