The CFSE for octahedral `[CoCl_(6)]^(4-)` is `18,000 cm^(-1)`. The CFSE for tetrahedral `[CoCl_(4)]^(2-)` will be

Options

A. `18, 000 cm^(-1)`
B. `16, 000 cm^(-1)`
C. `8, 000 cm^(-1)`
D. `20, 000 cm^(-1)`

Explanation

To find the Crystal Field Stabilization Energy (CFSE) for the tetrahedral complex \([CoCl_4]^{2-}\), we can use the relationship between the CFSE of octahedral and tetrahedral complexes.

### Step-by-Step Solution:

1. **Identify Given Data:**
- CFSE for the octahedral complex \([CoCl_6]^{4-}\) is given as \(18000 \, cm^{-1}\).

2. **Use the Relationship Between CFSE of Octahedral and Tetrahedral Complexes:**
- The formula to relate the CFSE of tetrahedral complexes to that of octahedral complexes is:
\[ \text{CFSE}_{\text{tetrahedral}} = \frac{4}{9} \times \text{CFSE}_{\text{octahedral}} \]

3. **Substitute the Given CFSE into the Formula:**
- Plugging in the value of the CFSE for the octahedral complex:
\[ \text{CFSE}_{\text{tetrahedral}} = \frac{4}{9} \times 18000 \, cm^{-1} \]

4. **Calculate the CFSE for the Tetrahedral Complex:**
- Performing the multiplication:
\[ \text{CFSE}_{\text{tetrahedral}} = \frac{4 \times 18000}{9} \]
- Simplifying the calculation:
\[ = \frac{72000}{9} = 8000 \, cm^{-1} \]

5. **Conclusion:**
- The CFSE for the tetrahedral complex \([CoCl_4]^{2-}\) is \(8000 \, cm^{-1}\).

### Final Answer:
The CFSE for \([CoCl_4]^{2-}\) is \(8000 \, cm^{-1}\).

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