In which of the following paris both the ions are coloured in aqueous solution? (Atomic number, `Sc - 21, Ti = 22, Ni = 28, Cu = 29, Co = 27)`
(a)`Ni^(2+), Ti^(3+)`
(b)`Sc^(3+),Ti^(3+)`
(c)`Sc^(3+),Co^(2+)`
(d)`Ni^(2+),Cu^(+)`

Options

A. `Ni^(2+), Ti^(3+)`
B. `Sc^(3+),Ti^(3+)`
C. `Sc^(3+),Co^(2+)`
D. `Ni^(2+),Cu^(+)`

Explanation

To determine which pairs of ions are colored in aqueous solution, we need to analyze the electronic configurations of the ions given in the options. The presence of unpaired electrons in the d-orbitals of transition metals is responsible for the color of the solution.

### Step-by-Step Solution:

1. **Identify the Ions and Their Configurations**:
- **Nickel (Ni)**: Atomic number = 28
- Electronic configuration: \( \text{[Ar]} 3d^8 4s^2 \)
- For \( \text{Ni}^{2+} \): Remove 2 electrons from 4s:
- Configuration: \( \text{[Ar]} 3d^8 \)
- **Titanium (Ti)**: Atomic number = 22
- Electronic configuration: \( \text{[Ar]} 3d^2 4s^2 \)
- For \( \text{Ti}^{3+} \): Remove 3 electrons (2 from 4s and 1 from 3d):
- Configuration: \( \text{[Ar]} 3d^1 \)

2. **Check for Unpaired Electrons**:
- **Ni²⁺ (3d⁸)**:
- Configuration: \( \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \uparrow \uparrow \uparrow \) (2 unpaired electrons)
- **Colored**: Yes
- **Ti³⁺ (3d¹)**:
- Configuration: \( \uparrow \) (1 unpaired electron)
- **Colored**: Yes

3. **Evaluate the Other Pairs**:
- **Scandium (Sc)**: Atomic number = 21
- Electronic configuration: \( \text{[Ar]} 3d^1 4s^2 \)
- For \( \text{Sc}^{3+} \): Remove 3 electrons:
- Configuration: \( \text{[Ar]} \) (no unpaired electrons)
- **Colored**: No
- **Cobalt (Co)**: Atomic number = 27
- Electronic configuration: \( \text{[Ar]} 3d^7 4s^2 \)
- For \( \text{Co}^{2+} \): Remove 2 electrons:
- Configuration: \( \text{[Ar]} 3d^7 \) (3 unpaired electrons)
- **Colored**: Yes
- **Copper (Cu)**: Atomic number = 29
- Electronic configuration: \( \text{[Ar]} 3d^{10} 4s^1 \)
- For \( \text{Cu}^+ \): Remove 1 electron:
- Configuration: \( \text{[Ar]} 3d^{10} \) (no unpaired electrons)
- **Colored**: No

4. **Conclusion**:
- The only pair where both ions are colored is **(a) Ni²⁺ and Ti³⁺**.

### Final Answer:
(a) Ni²⁺, Ti³⁺