The magnetic nature of elements depends on the presence of unpaired electrons. Identify the configuration of transition element, which shows highest magnetic moment.

Options

A. `3d^7`
B. `3d^5`
C. `3d^8`
D. `3d^2`

Answer

To solve the problem of determining the configuration of the transition element that shows the highest magnetic moment, we will follow these steps:

### Step 1: Understand the Magnetic Moment Formula
The magnetic moment (\( \mu \)) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
where \( n \) is the number of unpaired electrons.

### Step 2: Analyze Each Given Electron Configuration
We will analyze the given configurations: 3d7, 3d5, 3d8, and 3d2, to find the number of unpaired electrons in each.

#### Configuration 1: 3d7
- Fill the d-orbitals:
- 1, 2, 3, 4, 5 (first five electrons fill each orbital singly)
- 6 (pairs with one of the orbitals)
- 7 (pairs with another orbital)
- Unpaired electrons: 3
- Calculate magnetic moment:
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \]

#### Configuration 2: 3d5
- Fill the d-orbitals:
- 1, 2, 3, 4, 5 (all five electrons fill each orbital singly)
- Unpaired electrons: 5
- Calculate magnetic moment:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.91 \]

#### Configuration 3: 3d8
- Fill the d-orbitals:
- 1, 2, 3, 4, 5 (first five electrons fill each orbital singly)
- 6, 7 (pairing begins)
- 8 (pairs with another orbital)
- Unpaired electrons: 2
- Calculate magnetic moment:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} \approx 2.82 \]

#### Configuration 4: 3d2
- Fill the d-orbitals:
- 1, 2 (two electrons fill two orbitals singly)
- Unpaired electrons: 2
- Calculate magnetic moment:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} \approx 2.82 \]

### Step 3: Compare the Magnetic Moments
Now we compare the calculated magnetic moments:
- For 3d7: \( \mu \approx 3.87 \)
- For 3d5: \( \mu \approx 5.91 \)
- For 3d8: \( \mu \approx 2.82 \)
- For 3d2: \( \mu \approx 2.82 \)

### Conclusion
The configuration with the highest magnetic moment is **3d5**, with a magnetic moment of approximately 5.91.

### Final Answer
**The configuration of the transition element that shows the highest magnetic moment is 3d5.**

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