Magnetic moment 2.83 BM is given by which of the following ions?
`"At. nos. Ti=22, Cr=24, Mn=25,Ni=28"`

Options

A. `Mn^(2+)`
B. `Ni^(2+)`
C. `Ti^(3+)`
D. `Cr^(3+)`

Answer

To determine which ion has a magnetic moment of 2.83 Bohr Magneton (BM), we need to analyze the electronic configurations of the given ions and calculate their magnetic moments. The ions we need to consider are Titanium (Ti), Chromium (Cr), Manganese (Mn), and Nickel (Ni).

### Step 1: Identify the electronic configurations of the ions.

1. **Titanium (Ti)** - Atomic number 22
- Electronic configuration: [Ar] 3d² 4s²
- For Ti²⁺ (losing 2 electrons): [Ar] 3d²
- Unpaired electrons: 2

2. **Chromium (Cr)** - Atomic number 24
- Electronic configuration: [Ar] 3d⁵ 4s¹
- For Cr³⁺ (losing 3 electrons): [Ar] 3d³
- Unpaired electrons: 3

3. **Manganese (Mn)** - Atomic number 25
- Electronic configuration: [Ar] 3d⁵ 4s²
- For Mn²⁺ (losing 2 electrons): [Ar] 3d⁵
- Unpaired electrons: 5

4. **Nickel (Ni)** - Atomic number 28
- Electronic configuration: [Ar] 3d⁸ 4s²
- For Ni²⁺ (losing 2 electrons): [Ar] 3d⁸
- Unpaired electrons: 2

### Step 2: Calculate the magnetic moments using the formula.

The magnetic moment (μ) can be calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \text{ BM} \]
where \( n \) is the number of unpaired electrons.

1. **For Ti²⁺ (n = 2)**:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} \approx 2.83 \text{ BM} \]

2. **For Cr³⁺ (n = 3)**:
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \text{ BM} \]

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

4. **For Ni²⁺ (n = 2)**:
\[ \mu = \sqrt{2(2 + 2)} = \sqrt{8} \approx 2.83 \text{ BM} \]

### Step 3: Compare the calculated magnetic moments with the given value.

From the calculations:
- Ti²⁺ has a magnetic moment of approximately 2.83 BM.
- Cr³⁺ has a magnetic moment of approximately 3.87 BM.
- Mn²⁺ has a magnetic moment of approximately 5.92 BM.
- Ni²⁺ has a magnetic moment of approximately 2.83 BM.

### Conclusion:
Both Ti²⁺ and Ni²⁺ have a magnetic moment of approximately 2.83 BM. However, since the question asks for the ion corresponding to the magnetic moment of 2.83 BM, we can conclude that the answer is **Nickel (Ni)**.