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: Use 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.

### Step 2: Set up the equation
Given that the magnetic moment is 2.83 Bohr magnetons, we can set up the equation:
\[ 2.83 = \sqrt{n(n + 2)} \]

### Step 3: Square both sides
Squaring both sides of the equation gives:
\[ (2.83)^2 = n(n + 2) \]
Calculating \( (2.83)^2 \):
\[ 8.0089 \approx 8 \]
So, we have:
\[ n(n + 2) = 8 \]

### Step 4: Rearrange the equation
Rearranging the equation gives:
\[ n^2 + 2n - 8 = 0 \]

### Step 5: Solve the quadratic equation
We can solve the quadratic equation using the quadratic formula:
\[ n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \( a = 1, b = 2, c = -8 \):
\[ n = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 1 \cdot (-8)}}{2 \cdot 1} \]
Calculating the discriminant:
\[ n = \frac{-2 \pm \sqrt{4 + 32}}{2} = \frac{-2 \pm \sqrt{36}}{2} = \frac{-2 \pm 6}{2} \]
This gives us two potential solutions:
\[ n = \frac{4}{2} = 2 \quad \text{or} \quad n = \frac{-8}{2} = -4 \]
Since the number of unpaired electrons cannot be negative, we take \( n = 2 \).

### Step 6: Identify the ion
Now, we need to check the possible ions to find one with 2 unpaired electrons.

1. **Fe²⁺ (Iron)**:
- Atomic number = 26, loses 2 electrons → 24 electrons.
- Electronic configuration: [Ar] 3d⁶ 4s⁰.
- Unpaired electrons: 4 (not the answer).

2. **Ni²⁺ (Nickel)**:
- Atomic number = 28, loses 2 electrons → 26 electrons.
- Electronic configuration: [Ar] 3d⁸ 4s⁰.
- Unpaired electrons: 2 (this could be the answer).

3. **Mn²⁺ (Manganese)**:
- Atomic number = 25, loses 2 electrons → 23 electrons.
- Electronic configuration: [Ar] 3d⁵ 4s⁰.
- Unpaired electrons: 5 (not the answer).

4. **Co³⁺ (Cobalt)**:
- Atomic number = 27, loses 3 electrons → 24 electrons.
- Electronic configuration: [Ar] 3d⁶ 4s⁰.
- Unpaired electrons: 4 (not the answer).

### Conclusion
The ion with a magnetic moment of 2.83 Bohr magnetons is **Ni²⁺ (Nickel 2+)**, which has 2 unpaired electrons.

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