The value of 'spin only' magnetic moment for one of the following configuration is `2.84B.M.` The correct one is:

Options

A. `d^(4)` (in strong ligand field )
B. `d^(4)` (in weak ligand field )
C. `d^(3)` (in weak as well as in strong fields)
D. `d^(5)` (in strong ligand field )

Explanation

To solve the problem regarding the spin-only magnetic moment of coordination compounds, we will analyze the given configurations step by step.

### Step-by-Step Solution:

1. **Understanding the Magnetic Moment Formula**:
The spin-only magnetic moment (μ) is calculated using the formula:
\[ μ = \sqrt{n(n + 2)} \text{ Bohr Magneton (B.M.)} \]
where \( n \) is the number of unpaired electrons.

2. **Analyzing the Configurations**:
We have four configurations to analyze:
- **Option 1**: \( d^4 \) strong field
- **Option 2**: \( d^4 \) weak field
- **Option 3**: \( d^3 \) (both strong and weak field)
- **Option 4**: \( d^5 \) strong field

3. **Calculating for Each Configuration**:
- **Option 1: \( d^4 \) Strong Field**:
- In a strong field, electrons pair up. The configuration is \( t_{2g}^4 e_g^0 \).
- Number of unpaired electrons \( n = 2 \).
- Magnetic moment:
\[ μ = \sqrt{2(2 + 2)} = \sqrt{8} = 2.84 \text{ B.M.} \]

- **Option 2: \( d^4 \) Weak Field**:
- In a weak field, electrons do not pair. The configuration is \( t_{2g}^3 e_g^1 \).
- Number of unpaired electrons \( n = 4 \).
- Magnetic moment:
\[ μ = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.89 \text{ B.M.} \]

- **Option 3: \( d^3 \) (Strong Field)**:
- In a strong field, the configuration is \( t_{2g}^3 e_g^0 \).
- Number of unpaired electrons \( n = 3 \).
- Magnetic moment:
\[ μ = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \text{ B.M.} \]

- **Option 4: \( d^5 \) Strong Field**:
- In a strong field, the configuration is \( t_{2g}^5 e_g^0 \).
- Number of unpaired electrons \( n = 5 \).
- Magnetic moment:
\[ μ = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \text{ B.M.} \]

4. **Conclusion**:
The only configuration that gives a magnetic moment of \( 2.84 \text{ B.M.} \) is **Option 1: \( d^4 \) Strong Field**.

### Final Answer:
The correct configuration is **Option 1: \( d^4 \) Strong Field**.