Of the ions `Zn^(2+),Ni^(2+) and Cr^(3+)` (atomic number Zn=30,Ni=28,Cr=24):

Options

A. Only `Zn^(2+)` is colourless and `Ni^(2+) and Cr^(3+)` are coloured.
B. all three are colourless.
C. all three are coloured
D. only `Ni^(2+)` is coloured and `Zn^(2+)` and `Cr^(3+)` are colourless.

Explanation

To determine which of the ions \( \text{Zn}^{2+}, \text{Ni}^{2+}, \text{Cr}^{3+} \) are colored and which are colorless, we need to analyze their electronic configurations and the presence of unpaired electrons. Here's a step-by-step solution:

### Step 1: Write the electronic configurations of the neutral atoms
- **Zinc (Zn)**: Atomic number = 30
- Electronic configuration: \( \text{[Ar]} 3d^{10} 4s^2 \)

- **Nickel (Ni)**: Atomic number = 28
- Electronic configuration: \( \text{[Ar]} 3d^8 4s^2 \)

- **Chromium (Cr)**: Atomic number = 24
- Electronic configuration: \( \text{[Ar]} 3d^5 4s^1 \)

### Step 2: Determine the electronic configurations of the ions
- **For \( \text{Zn}^{2+} \)**:
- Remove 2 electrons from \( 4s \) (since \( 4s \) is filled before \( 3d \)):
- Configuration: \( \text{[Ar]} 3d^{10} \)

- **For \( \text{Ni}^{2+} \)**:
- Remove 2 electrons from \( 4s \):
- Configuration: \( \text{[Ar]} 3d^8 \)

- **For \( \text{Cr}^{3+} \)**:
- Remove 3 electrons (2 from \( 4s \) and 1 from \( 3d \)):
- Configuration: \( \text{[Ar]} 3d^3 \)

### Step 3: Analyze the number of unpaired electrons
- **For \( \text{Zn}^{2+} \)**:
- Configuration: \( 3d^{10} \) (0 unpaired electrons)

- **For \( \text{Ni}^{2+} \)**:
- Configuration: \( 3d^8 \) (2 unpaired electrons)

- **For \( \text{Cr}^{3+} \)**:
- Configuration: \( 3d^3 \) (3 unpaired electrons)

### Step 4: Determine the color of the ions
- **Colored ions**: Ions with unpaired electrons can undergo d-d transitions, which result in color.
- \( \text{Ni}^{2+} \): 2 unpaired electrons → colored
- \( \text{Cr}^{3+} \): 3 unpaired electrons → colored

- **Colorless ions**: Ions with all paired electrons do not undergo d-d transitions.
- \( \text{Zn}^{2+} \): 0 unpaired electrons → colorless

### Conclusion
- \( \text{Zn}^{2+} \) is colorless.
- \( \text{Ni}^{2+} \) and \( \text{Cr}^{3+} \) are colored.

### Final Answer
- **Only \( \text{Zn}^{2+} \) is colorless, while \( \text{Ni}^{2+} \) and \( \text{Cr}^{3+} \) are colored.**

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