Which of the following ion has magnetic moment is 3.87 BM :-

Options

A. `Ti^(3+)`
B. `Sc^(3+)`
C. `Ti^(+)`
D. `Mn^(+5)`

Explanation

To determine which ion has a magnetic moment of 3.87 BM, we can use the formula for magnetic moment, which is given by:

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

where \( n \) is the number of unpaired electrons. We will evaluate the magnetic moment for each ion provided in the options.

### Step 1: Evaluate Ti³⁺
1. **Determine the electron configuration of Ti³⁺**:
- Titanium (Ti) has the electron configuration: \( [Ar] 3d^2 4s^2 \).
- For Ti³⁺, we remove 3 electrons (2 from 4s and 1 from 3d), resulting in: \( 3d^1 \).

2. **Count unpaired electrons**:
- Ti³⁺ has 1 unpaired electron.

3. **Calculate magnetic moment**:
\[ n = 1 \quad \Rightarrow \quad \mu = \sqrt{1(1 + 2)} = \sqrt{3} \approx 1.73 \, \text{BM} \]
- This is incorrect.

### Step 2: Evaluate Sc³⁺
1. **Determine the electron configuration of Sc³⁺**:
- Scandium (Sc) has the electron configuration: \( [Ar] 3d^1 4s^2 \).
- For Sc³⁺, we remove 3 electrons (2 from 4s and 1 from 3d), resulting in: \( [Ar] \) (all electrons paired).

2. **Count unpaired electrons**:
- Sc³⁺ has 0 unpaired electrons.

3. **Calculate magnetic moment**:
\[ n = 0 \quad \Rightarrow \quad \mu = \sqrt{0(0 + 2)} = 0 \, \text{BM} \]
- This is incorrect.

### Step 3: Evaluate Ti⁺
1. **Determine the electron configuration of Ti⁺**:
- For Ti⁺, we remove 1 electron from titanium's configuration: \( [Ar] 3d^2 4s^2 \) becomes \( 3d^2 4s^1 \).

2. **Count unpaired electrons**:
- Ti⁺ has 3 unpaired electrons (2 in 3d and 1 in 4s).

3. **Calculate magnetic moment**:
\[ n = 3 \quad \Rightarrow \quad \mu = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \, \text{BM} \]
- This is correct.

### Step 4: Evaluate Mn⁵⁺
1. **Determine the electron configuration of Mn⁵⁺**:
- Manganese (Mn) has the electron configuration: \( [Ar] 3d^5 4s^2 \).
- For Mn⁵⁺, we remove 5 electrons (2 from 4s and 3 from 3d), resulting in: \( 3d^2 \).

2. **Count unpaired electrons**:
- Mn⁵⁺ has 2 unpaired electrons.

3. **Calculate magnetic moment**:
\[ n = 2 \quad \Rightarrow \quad \mu = \sqrt{2(2 + 2)} = \sqrt{8} \approx 2.82 \, \text{BM} \]
- This is incorrect.

### Conclusion
The ion with a magnetic moment of 3.87 BM is **Ti⁺**.