`CFSE` for `d^(6)` octahedral complex having `Delta =250` and `P =125kJmo1^(-1)` is .

Options

A. `350KJMO1^(-1)`
B. `-350kJmo1^(-1)`
C. `475kJmo1^(-1)`
D. `-475kJmo1^(-1)`

Explanation

To calculate the Crystal Field Stabilization Energy (CFSE) for a \(d^6\) octahedral complex with a given \(\Delta\) and pairing energy \(P\), we can follow these steps:

### Step 1: Identify the given values
- \(d^6\) configuration
- \(\Delta = 250 \, \text{kJ/mol}\)
- \(P = 125 \, \text{kJ/mol}\)

### Step 2: Determine the type of ligand
Since \(\Delta\) (250 kJ/mol) is greater than \(P\) (125 kJ/mol), pairing of electrons will occur. This indicates that the complex is likely to be a strong field ligand.

### Step 3: Fill the d-orbitals
In a strong field ligand scenario for a \(d^6\) configuration:
- The electrons will fill the \(t_{2g}\) orbitals first and then pair up in the \(t_{2g}\) before filling the \(e_g\) orbitals.
- The filling will be as follows:
- \(t_{2g}\): 6 electrons (3 pairs)
- \(e_g\): 0 electrons

### Step 4: Calculate the CFSE
The CFSE can be calculated using the formula:
\[ \text{CFSE} = (n_{t_{2g}} \times -0.4\Delta) + (n_{e_g} \times +0.6\Delta) - \text{Pairing Energy} \]
Where:
- \(n_{t_{2g}} = 6\) (number of electrons in \(t_{2g}\))
- \(n_{e_g} = 0\) (number of electrons in \(e_g\))

### Step 5: Substitute the values
Substituting the values into the CFSE formula:
\[ \text{CFSE} = (6 \times -0.4 \times 250) + (0 \times 0.6 \times 250) - \text{Pairing Energy} \]
\[ \text{CFSE} = (6 \times -100) + 0 - (2 \times 125) \]
\[ \text{CFSE} = -600 - 250 \]
\[ \text{CFSE} = -850 \, \text{kJ/mol} \]

### Step 6: Final calculation
Since we need to consider the pairing energy for the two paired electrons:
\[ \text{Total CFSE} = -600 + 250 = -350 \, \text{kJ/mol} \]

### Conclusion
The CFSE for the \(d^6\) octahedral complex is:
\[ \text{CFSE} = -350 \, \text{kJ/mol} \]