Predict the order of `Delta_(0)`for the following compounds
(a) `[Fe(H_(2)O))_(6)]^(2+)`
(II) `[Fe(CN)_(2)(H_(2)O))_(4)]`
(III) `[fe(CN)_(4)(H_(2)O))_(2)]^(2-)`
(a) `delta_(0)ltDelta_(0)(II)ltdelta_(0)(III)`
(b) `delta_(0)ltDelta_(0)(I)ltdelta_(0)(III)`
(c ) `delta_(0)ltDelta_(0)(III)ltdelta_(0)(II) ltDelta_(0)(I)`
`delta_(0)ltDelta_(0)(II)ltdelta_(0)(III)ltDelta_(0)(I)` .

Explanation

To predict the order of `Δ₀` for the given coordination compounds, we need to analyze the ligands and their field strengths, as well as the electronic configurations of the central metal ion (Fe in this case) in each complex.

### Step-by-Step Solution:

1. **Identify the oxidation state of Iron (Fe)**:
- For `[Fe(H₂O)₆]²⁺`, the oxidation state of Fe is +2.
- For `[Fe(CN)₂(H₂O)₄]`, the oxidation state is also +2.
- For `[Fe(CN)₄(H₂O)₂]²⁻`, the oxidation state remains +2.

2. **Determine the electronic configuration of Fe²⁺**:
- Iron (Fe) has an atomic number of 26. Its ground state electronic configuration is `[Ar] 3d⁶ 4s²`.
- For Fe²⁺, we remove two electrons (from the 4s orbital), resulting in the configuration: `3d⁶`.

3. **Analyze the ligands**:
- H₂O is a weak field ligand.
- CN⁻ is a strong field ligand.

4. **Determine the splitting of d-orbitals**:
- In `[Fe(H₂O)₆]²⁺`, with H₂O as a weak field ligand, the d-orbitals will split into two sets (T₂g and Eₕ), but no pairing occurs. The configuration will be T₂g⁴ Eₕ².
- In `[Fe(CN)₂(H₂O)₄]`, there are 2 CN⁻ ligands (strong field) and 4 H₂O ligands (weak field). The presence of strong field ligands will cause some pairing, but not all electrons will pair due to the weak field ligands. The configuration will be influenced by the strong field ligands.
- In `[Fe(CN)₄(H₂O)₂]²⁻`, there are 4 CN⁻ ligands, which are strong field ligands, leading to maximum pairing of electrons. The configuration will be T₂g⁶ Eₕ⁰.

5. **Calculate the Crystal Field Stabilization Energy (CFSE)**:
- For `[Fe(H₂O)₆]²⁺`:
- CFSE = (-0.4 * 4 + 0.6 * 2)Δ₀ = -0.4Δ₀ (magnitude = 0.4Δ₀).
- For `[Fe(CN)₂(H₂O)₄]`:
- The CFSE will be higher than that of the first complex but lower than that of the third due to the presence of both strong and weak ligands.
- For `[Fe(CN)₄(H₂O)₂]²⁻`:
- CFSE = -0.4 * 6Δ₀ = -2.4Δ₀ (magnitude = 2.4Δ₀).

6. **Order of Δ₀**:
- Based on the analysis, we can conclude:
- `[Fe(CN)₄(H₂O)₂]²⁻` has the highest Δ₀ due to the maximum number of strong field ligands.
- `[Fe(CN)₂(H₂O)₄]` has a moderate Δ₀.
- `[Fe(H₂O)₆]²⁺` has the lowest Δ₀ due to the presence of only weak field ligands.

Thus, the order of `Δ₀` is:
\[ \Delta₀(III) > \Delta₀(II) > \Delta₀(I) \]

### Final Answer:
The correct option is (c) `Δ₀(III) > Δ₀(II) > Δ₀(I)`.