Given the following data about the absorption maxium of several complex ions what is the order of `Delta_(0)` for these ions? .
`{:(Compound,,lambda_(max),,),(I.[CrCI_(6)]^(3-),,758,,),(II.[Cr(NH_(3))_(6)]^(3+),,465,,),(III.[Cr(H_(2)O)_(6)]^(3+),,694,,):}`
(a) `Delta_(0)ltdelta_(0)(II)ltDelta_(0)(III)`
(b) `delta_(0)(II)ltDelta_(0)(III)ltDelta_(0)(III)`
(c) `Delta(0)ltdelta_(0)(III)ltDelta_(0)(II)`
(d) `Delta_(0)(III)ltDelta_(0)(II)ltDelta_(0)(I)` .

Explanation

To determine the order of Δ₀ (the crystal field splitting energy) for the given complex ions based on their absorption maxima (λ_max), we can follow these steps:

### Step 1: Understand the Relationship Between λ_max and Δ₀
The energy associated with the absorption of light is inversely proportional to the wavelength of that light. This means:
\[ E \propto \frac{1}{\lambda_{\text{max}}} \]
Where:
- E is the energy of the absorbed light.
- λ_max is the wavelength of the light absorbed.

### Step 2: List the Complex Ions and Their λ_max Values
We are given the following complex ions with their corresponding λ_max values:
1. [CrCl₆]³⁻: λ_max = 758 nm
2. [Cr(NH₃)₆]³⁺: λ_max = 465 nm
3. [Cr(H₂O)₆]³⁺: λ_max = 694 nm

### Step 3: Determine the Order of Δ₀ Based on λ_max
Since energy is inversely proportional to λ_max, we can determine the order of Δ₀ by looking at the λ_max values:
- For [CrCl₆]³⁻ (758 nm), the energy is the lowest (Δ₀ is the lowest).
- For [Cr(H₂O)₆]³⁺ (694 nm), the energy is moderate (Δ₀ is moderate).
- For [Cr(NH₃)₆]³⁺ (465 nm), the energy is the highest (Δ₀ is the highest).

### Step 4: Write the Order of Δ₀
From the above analysis, we can conclude:
\[ \Delta_0(\text{NH}_3) > \Delta_0(\text{H}_2O) > \Delta_0(\text{Cl}^-) \]
Thus, the order of Δ₀ is:
\[ \Delta_0(\text{II}) > \Delta_0(\text{III}) > \Delta_0(\text{I}) \]

### Step 5: Choose the Correct Option
Based on our findings, the correct order corresponds to option (d):
\[ \Delta_0(III) > \Delta_0(II) > \Delta_0(I) \]

### Final Answer
The correct order of Δ₀ for the given complex ions is:
(d) Δ₀(III) > Δ₀(II) > Δ₀(I)

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