According to C.F.T, attraction between the central metal ion and ligands in a complex is purely electrostatic. The transition metal which forms the central atom cation in the complex is regarded as a positive ion. It is surrounded by negative ligands or neutral molecules which have a lone apir of electrons, if the ligand is a neutral molecule such as `NH_(3)`, the negative and of the dipole in the molecule is directed towards the metal cation. the electrons on the central metal ion are under repulsive forces from those on the ligands. thus the electrons occupy the d-orbitals remain away from the direction of approach ligands.
Q. The crystal field-spliting order for `Cr^(3+)` cation is octahedral field for ligands `CH_(3)COO^(-),NH_(3),H_(2)O,CN^(-)` is:

Options

A. `CH_(3)COO^(-) lt H_(2)O lt NH_(3) lt CN^(-)`
B. `CH_(3)COO^(-) lt NH_(3) lt H_(2)O lt CN^(-)`
C. `H_(2)O lt CH_(3)COO^(-) lt NH_(3) lt CN^(-)`
D. `NH_(3) lt CH_(3)COO^(-) lt H_(2)O lt CN^(-)`

Answer

To determine the crystal field splitting order for the `Cr^(3+)` cation in an octahedral field with the ligands `CH3COO^(-), NH3, H2O, CN^(-)`, we can follow these steps:

### Step 1: Identify the ligands and their strengths
The first step is to recognize the ligands provided in the question:
- `CH3COO^-` (acetate)
- `NH3` (ammonia)
- `H2O` (water)
- `CN^-` (cyanide)

### Step 2: Refer to the spectrochemical series
Next, we need to refer to the spectrochemical series, which ranks ligands according to their field strength (the ability to split the d-orbitals). The order from strongest to weakest ligands is as follows:
1. `CN^-` (strong field ligand)
2. `NH3` (moderate field ligand)
3. `H2O` (weak field ligand)
4. `CH3COO^-` (weakest field ligand)

### Step 3: Determine the crystal field splitting order
Based on the strength of the ligands from the spectrochemical series, we can establish the crystal field splitting order for the `Cr^(3+)` cation in the presence of these ligands. The stronger the ligand, the more it will influence the splitting of the d-orbitals.

Thus, the order of the ligands based on their field strength is:
1. `CN^-`
2. `NH3`
3. `H2O`
4. `CH3COO^-`

### Final Answer
The crystal field splitting order for `Cr^(3+)` cation in an octahedral field for the ligands `CH3COO^(-), NH3, H2O, CN^(-)` is:
**CN^- > NH3 > H2O > CH3COO^-**