The value of the magnetic moment of a particular ion is `2.83` Bohr magneton. The ion is :-

Options

A. `Fe^(2+)`
B. `Ni^(2+)`
C. `Mn^(2+)`
D. `Co^(3+)`

Explanation

To determine the ion with a magnetic moment of 2.83 Bohr magnetons, we can follow these steps:

### Step 1: Understand the formula for magnetic moment
The magnetic moment (μ) of an ion can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \text{ Bohr magneton} \]
where \( n \) is the number of unpaired electrons in the ion.

### Step 2: Identify possible ions and their electronic configurations
We will consider the following ions and their respective electronic configurations:
1. **Ferrous ion (Fe²⁺)**: Electronic configuration is \( [Ar] 3d^6 \)
2. **Nickel ion (Ni²⁺)**: Electronic configuration is \( [Ar] 3d^8 \)
3. **Manganese ion (Mn²⁺)**: Electronic configuration is \( [Ar] 3d^5 \)
4. **Cobalt ion (Co³⁺)**: Electronic configuration is \( [Ar] 3d^6 \)

### Step 3: Calculate unpaired electrons for each ion
1. **Fe²⁺ (3d⁶)**:
- Configuration: \( \uparrow\downarrow \uparrow \uparrow \uparrow \)
- Unpaired electrons: 4

2. **Ni²⁺ (3d⁸)**:
- Configuration: \( \uparrow\downarrow \uparrow\downarrow \uparrow \uparrow \uparrow \uparrow \)
- Unpaired electrons: 2

3. **Mn²⁺ (3d⁵)**:
- Configuration: \( \uparrow \uparrow \uparrow \uparrow \uparrow \)
- Unpaired electrons: 5

4. **Co³⁺ (3d⁶)**:
- Configuration: Similar to Fe²⁺
- Unpaired electrons: 4

### Step 4: Calculate magnetic moments for each ion
1. **Fe²⁺**:
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.89 \text{ Bohr magneton} \]

2. **Ni²⁺**:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} \approx 2.83 \text{ Bohr magneton} \]

3. **Mn²⁺**:
\[ \mu = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \text{ Bohr magneton} \]

4. **Co³⁺**:
\[ \mu = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.89 \text{ Bohr magneton} \]

### Step 5: Identify the correct ion
From the calculations, we find that the only ion with a magnetic moment of approximately 2.83 Bohr magnetons is **Ni²⁺**.

### Conclusion
The ion with a magnetic moment of 2.83 Bohr magneton is **Nickel ion (Ni²⁺)**.

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