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 field ligand)
B. `d^(2)` (in weak field ligand)
C. `d^(3)` (In weak as well as in strong field ligand)
D. `d^(5)` (in strong field ligand)

Answer

To solve the question regarding the value of 'spin only' magnetic moment being `2.84 B.M.`, we need to analyze the given configurations and determine which one corresponds to this magnetic moment value. The magnetic moment can be calculated using the formula:

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

where \( n \) is the number of unpaired electrons.

### Step-by-Step Solution:

1. **Understanding the Magnetic Moment Formula**:
- The formula for calculating the spin-only magnetic moment is given as \(\mu = \sqrt{n(n + 2)}\).
- We need to find the value of \( n \) (the number of unpaired electrons) that will give us a magnetic moment of `2.84 B.M.`.

2. **Calculate the Number of Unpaired Electrons**:
- We set up the equation:
\[ \sqrt{n(n + 2)} = 2.84 \]
- Squaring both sides gives:
\[ n(n + 2) = (2.84)^2 \]
- Calculating \( (2.84)^2 \):
\[ (2.84)^2 = 8.0656 \]
- Thus, we have:
\[ n(n + 2) = 8.0656 \]

3. **Forming a Quadratic Equation**:
- Rearranging gives:
\[ n^2 + 2n - 8.0656 = 0 \]
- We can use the quadratic formula \( n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 1, b = 2, c = -8.0656 \).

4. **Calculating the Discriminant**:
- First, calculate the discriminant:
\[ b^2 - 4ac = 2^2 - 4 \cdot 1 \cdot (-8.0656) = 4 + 32.2624 = 36.2624 \]

5. **Finding the Roots**:
- Now, substituting into the quadratic formula:
\[ n = \frac{-2 \pm \sqrt{36.2624}}{2} \]
- Calculating \( \sqrt{36.2624} \):
\[ \sqrt{36.2624} \approx 6.02 \]
- Thus:
\[ n = \frac{-2 \pm 6.02}{2} \]
- This gives us two possible values for \( n \):
\[ n_1 = \frac{4.02}{2} = 2.01 \quad \text{(not valid since n must be an integer)} \]
\[ n_2 = \frac{-8.02}{2} \quad \text{(not valid since n cannot be negative)} \]

6. **Analyzing the Given Configurations**:
- Now we will analyze the options provided:
- **Option 1: D4 in strong field**: All electrons paired → \( n = 0 \) (not valid).
- **Option 2: D2 in weak field**: 2 unpaired electrons → \( n = 2 \) (valid).
- **Option 3: D3 in weak field**: 3 unpaired electrons → \( n = 3 \) (not valid).
- **Option 4: D5 in strong field**: 1 unpaired electron → \( n = 1 \) (not valid).

7. **Conclusion**:
- The only configuration that yields 2 unpaired electrons is **Option 2: D2 in weak field**, which corresponds to the magnetic moment of `2.84 B.M.`.

### Final Answer:
The correct configuration is **Option 2: D2 in weak field**.