Among the following complexes, the one which shows zero crystal field stabilization energy (CFSE) is

Options

A. `[Mn(H_(2)O)_(6)]^(3+)`
B. `[Fe(H_(2)O)_(6)]^(3+)`
C. `[Co(H_(2)O)_(6)]^(2+)`
D. `[Co(H_(2)O)_(6)]^(3+)`

Explanation

To determine which of the given complexes shows zero crystal field stabilization energy (CFSE), we will follow these steps:

### Step 1: Identify the oxidation states and electron configurations of the metal ions in the complexes.

1. **Manganese Complex (Mn³⁺)**:
- Manganese (Mn) has an atomic number of 25. Its ground state electron configuration is [Ar] 4s² 3d⁵.
- For Mn³⁺, we remove 3 electrons: 2 from 4s and 1 from 3d.
- Thus, the electron configuration for Mn³⁺ is [Ar] 3d⁴.

2. **Iron Complex (Fe³⁺)**:
- Iron (Fe) has an atomic number of 26. Its ground state electron configuration is [Ar] 4s² 3d⁶.
- For Fe³⁺, we remove 3 electrons: 2 from 4s and 1 from 3d.
- Thus, the electron configuration for Fe³⁺ is [Ar] 3d⁵.

### Step 2: Determine the distribution of electrons in the t2g and eg orbitals for each complex.

1. **For Mn³⁺ in a tetrahedral field**:
- Tetrahedral complexes have a splitting pattern where t2g (lower energy) and eg (higher energy) orbitals are filled.
- With 4 d-electrons, the filling will be as follows:
- t2g: 3 electrons (1, 2, 3)
- eg: 1 electron (4)
- Thus, t2g = 3, eg = 1.

2. **For Fe³⁺ in a tetrahedral field**:
- With 5 d-electrons, the filling will be:
- t2g: 3 electrons (1, 2, 3)
- eg: 2 electrons (4, 5)
- Thus, t2g = 3, eg = 2.

### Step 3: Calculate the CFSE for each complex.

The formula for CFSE in a tetrahedral complex is:
\[ \text{CFSE} = (-0.4 \times \text{t2g electrons}) + (0.6 \times \text{eg electrons}) \]

1. **For Mn³⁺**:
\[ \text{CFSE} = (-0.4 \times 3) + (0.6 \times 1) = -1.2 + 0.6 = -0.6 \]

2. **For Fe³⁺**:
\[ \text{CFSE} = (-0.4 \times 3) + (0.6 \times 2) = -1.2 + 1.2 = 0 \]

### Step 4: Conclusion

From the calculations, we find that the CFSE for Fe³⁺ is 0. Therefore, the complex that shows zero crystal field stabilization energy is the **Fe³⁺ complex**.

### Final Answer:
The complex that shows zero crystal field stabilization energy (CFSE) is **the Fe³⁺ complex**.

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