`CFSE(Delta_(0))` for metal ion in `d^7` configuration in presence of strong ligand field is

Options

A. `-0.6Delta_(0)`
B. `-0.8Delta_(0)`
C. `-1.6Delta_(0)`
D. `-1.8Delta_(0)`

Answer

To find the crystal field splitting energy (CFSE) for a metal ion with a d^7 configuration in the presence of a strong ligand field, we can follow these steps:

### Step 1: Understand the d^7 Configuration
A d^7 configuration means that there are 7 electrons in the d orbitals. In an octahedral field, the d orbitals split into two sets: the lower energy set (t2g) and the higher energy set (eg).

### Step 2: Electron Filling in a Strong Field
In a strong ligand field, electrons tend to pair up in the lower energy t2g orbitals before occupying the higher energy eg orbitals. For a d^7 configuration, this means:
- 6 electrons will fill the t2g orbitals (3 orbitals, each can hold 2 electrons).
- 1 electron will occupy the eg orbital.

### Step 3: Determine the Electron Distribution
The electron distribution for d^7 in a strong field will be:
- t2g: 6 electrons (fully filled)
- eg: 1 electron (partially filled)

### Step 4: Calculate the CFSE
The formula for calculating the CFSE is:
\[ \text{CFSE} = (n_{t2g} \times -0.4 \Delta_0) + (n_{eg} \times 0.6 \Delta_0) \]
Where:
- \( n_{t2g} \) = number of electrons in t2g
- \( n_{eg} \) = number of electrons in eg

Substituting the values:
- \( n_{t2g} = 6 \)
- \( n_{eg} = 1 \)

So,
\[ \text{CFSE} = (6 \times -0.4 \Delta_0) + (1 \times 0.6 \Delta_0) \]
\[ \text{CFSE} = -2.4 \Delta_0 + 0.6 \Delta_0 \]
\[ \text{CFSE} = -1.8 \Delta_0 \]

### Step 5: Conclusion
The crystal field splitting energy (CFSE) for a metal ion in a d^7 configuration in the presence of a strong ligand field is:
\[ \text{CFSE} = -1.8 \Delta_0 \]

Thus, the correct answer is **Option D - 1.8 Δ0**.

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