Read the passage given below and answer the following questions :
The crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. Ligands are treated as point charges in case of anions or dipoles in case of neutral molecules. The five d orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ ion. However, when this negative field is due to ligands (either anions or the negative ends of dipolar molecules like `NH_(3)` and `H_(2)O`) in a complex, it becomes asymmetrical and the degeneracy of the d orbitals is lifted. It results in splitting of the d orbitals.
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 follow these steps:

### Step-by-Step Solution:

1. **Understand the CFSE Relationship**:
The CFSE for a tetrahedral complex can be related to the CFSE of an octahedral complex. The relationship is given by:
\[ \text{CFSE}_{\text{tetrahedral}} = \frac{4}{9} \times \text{CFSE}_{\text{octahedral}} \]

2. **Identify the CFSE of the Octahedral Complex**:
From the problem, we know that the CFSE for the octahedral complex \([CoCl_6]^{4-}\) is:
\[ \text{CFSE}_{\text{octahedral}} = 18,000 \, \text{cm}^{-1} \]

3. **Calculate the CFSE for the Tetrahedral Complex**:
Now, we can substitute the value of the octahedral CFSE into the equation for the tetrahedral CFSE:
\[ \text{CFSE}_{\text{tetrahedral}} = \frac{4}{9} \times 18,000 \, \text{cm}^{-1} \]

4. **Perform the Calculation**:
\[ \text{CFSE}_{\text{tetrahedral}} = \frac{4 \times 18,000}{9} \]
\[ = \frac{72,000}{9} = 8,000 \, \text{cm}^{-1} \]

5. **Final Answer**:
Therefore, the CFSE for the tetrahedral complex \([CoCl_4]^{2-}\) is:
\[ \text{CFSE}_{\text{tetrahedral}} = 8,000 \, \text{cm}^{-1} \]