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 `Delta_(0)` for the given coordination compounds, we need to analyze the ligands and their field strengths, as well as the electronic configurations of the metal ions in these complexes.

### Step-by-Step Solution:

1. **Identify the Metal Ion and Its Oxidation State:**
- For all three complexes, the metal ion is Iron (Fe).
- In `[Fe(H₂O)₆]²⁺`, the oxidation state of Fe is +2.
- In `[Fe(CN)₂(H₂O)₄]`, the oxidation state of Fe is also +2.
- In `[Fe(CN)₄(H₂O)₂]²⁻`, the oxidation state of Fe is +2 as well.

2. **Determine the Electron Configuration of Fe²⁺:**
- The atomic number of Fe is 26. For Fe²⁺, the electron configuration is:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶
- Thus, Fe²⁺ has 6 electrons in the 3d subshell.

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

4. **Calculate CFSE for Each Complex:**
- **(I) `[Fe(H₂O)₆]²⁺`:**
- With 6 H₂O ligands (weak field), the configuration is t₂g⁴ e₁.
- CFSE = (-0.4 Δ₀ × 4) + (0.6 Δ₀ × 2) = -0.4 Δ₀ × 4 + 0 = -1.6 Δ₀.

- **(II) `[Fe(CN)₂(H₂O)₄]`:**
- With 2 CN⁻ (strong field) and 4 H₂O (weak field), the configuration is t₂g⁶.
- CFSE = (-0.4 Δ₀ × 6) = -2.4 Δ₀.

- **(III) `[Fe(CN)₄(H₂O)₂]²⁻`:**
- With 4 CN⁻ (strong field) and 2 H₂O (weak field), the configuration is t₂g⁶.
- CFSE = (-0.4 Δ₀ × 6) = -2.4 Δ₀.

5. **Order of `Delta_(0)`:**
- Based on the CFSE values calculated:
- For (I): CFSE = -1.6 Δ₀
- For (II): CFSE = -2.4 Δ₀
- For (III): CFSE = -2.4 Δ₀
- The order of `Delta_(0)` based on CFSE values is:
- `Delta_(0)(I) > Delta_(0)(II) = Delta_(0)(III)`

### Final Answer:
The correct order of `Delta_(0)` for the given compounds is:
**(a) `Delta_(0)(I) > Delta_(0)(II) = Delta_(0)(III)`**