Which of the following complex ions is expected to absorb visible light?

Options

A. (a) `[Zn(NH_3)_6]^(2+)`
B. (b) `[Cr(NH_3)_6]^(3+)`
C. (c) `[Ti(en)_2(NH_3)_2]^(4+)`
D. (d) `[Sc(H_2O)_(3)(NH_3)_3]^(3+)`

Explanation

To determine which of the given complex ions is expected to absorb visible light, we need to analyze the electronic configurations of the metal ions involved and their ability to undergo d-d transitions, which are responsible for the color observed in coordination compounds.

### Step-by-Step Solution:

1. **Identify the Metal Ions and Their Oxidation States:**
- The metal ions mentioned are Zinc (Zn²⁺), Chromium (Cr³⁺), and Titanium (Ti⁴⁺).

2. **Determine the Electronic Configuration:**
- **Zinc (Zn²⁺):** The electronic configuration of Zn is [Ar] 3d¹⁰ 4s². For Zn²⁺, it loses 2 electrons from the 4s orbital, resulting in 3d¹⁰. This means all d-orbitals are fully filled.
- **Chromium (Cr³⁺):** The electronic configuration of Cr is [Ar] 3d⁵ 4s¹. For Cr³⁺, it loses 3 electrons (2 from 4s and 1 from 3d), resulting in 3d³. This means there are 3 unpaired electrons.
- **Titanium (Ti⁴⁺):** The electronic configuration of Ti is [Ar] 3d² 4s². For Ti⁴⁺, it loses 4 electrons (2 from 4s and 2 from 3d), resulting in 3d⁰. This means all d-orbitals are empty.

3. **Analyze the Absorption of Visible Light:**
- Complexes with d⁰ (like Ti⁴⁺) and d¹⁰ (like Zn²⁺) configurations do not absorb visible light because they cannot undergo d-d transitions (no available d electrons to transition).
- Complexes with unpaired electrons (like Cr³⁺ with 3d³) can absorb visible light due to the presence of unpaired electrons, allowing for d-d transitions.

4. **Conclusion:**
- Among the given metal ions, only Chromium (Cr³⁺) with its 3 unpaired electrons is expected to absorb visible light, making it the only complex ion that can exhibit color.

### Final Answer:
The complex ion expected to absorb visible light is **Chromium (Cr³⁺)**.