Which of the following ion is colourless?

Options

A. `Mn^(2+)`
B. `Cu^(+)`
C. `Cr^(3+)`
D. `Fe^(2+)`

Answer

To determine which of the given ions is colorless, we need to analyze the electronic configurations of each ion and check for the presence of unpaired electrons. Here's a step-by-step solution:

### Step 1: Understand the Concept of Color in Ions
Ions are colored if they have unpaired electrons in their d-orbitals. The presence of unpaired electrons allows for d-d transitions, which absorb certain wavelengths of light and impart color to the ion. Conversely, if all electrons are paired, the ion will be colorless as d-d transitions cannot occur.

### Step 2: Analyze Each Ion
We will analyze the electronic configuration of each ion provided in the question.

#### Ion 1: Mn²⁺
- **Electronic Configuration**: The electronic configuration of Mn is [Ar] 3d⁵ 4s². For Mn²⁺, two electrons are removed from the 4s orbital and one from the 3d orbital.
- **Resulting Configuration**: Mn²⁺ = [Ar] 3d⁵
- **Unpaired Electrons**: There are 5 unpaired electrons in the 3d orbitals.
- **Conclusion**: Mn²⁺ is colored.

#### Ion 2: Cu⁺
- **Electronic Configuration**: The electronic configuration of Cu is [Ar] 3d¹⁰ 4s¹. For Cu⁺, one electron is removed from the 4s orbital.
- **Resulting Configuration**: Cu⁺ = [Ar] 3d¹⁰
- **Unpaired Electrons**: There are no unpaired electrons (all 10 electrons in 3d are paired).
- **Conclusion**: Cu⁺ is colorless.

#### Ion 3: Cr³⁺
- **Electronic Configuration**: The electronic configuration of Cr is [Ar] 3d⁵ 4s². For Cr³⁺, three electrons are removed (two from 4s and one from 3d).
- **Resulting Configuration**: Cr³⁺ = [Ar] 3d³
- **Unpaired Electrons**: There are 3 unpaired electrons in the 3d orbitals.
- **Conclusion**: Cr³⁺ is colored.

#### Ion 4: Fe²⁺
- **Electronic Configuration**: The electronic configuration of Fe is [Ar] 3d⁶ 4s². For Fe²⁺, two electrons are removed (both from 4s).
- **Resulting Configuration**: Fe²⁺ = [Ar] 3d⁶
- **Unpaired Electrons**: There are 4 unpaired electrons in the 3d orbitals.
- **Conclusion**: Fe²⁺ is colored.

### Step 3: Identify the Colorless Ion
From the analysis:
- Mn²⁺: Colored (5 unpaired electrons)
- Cu⁺: Colorless (0 unpaired electrons)
- Cr³⁺: Colored (3 unpaired electrons)
- Fe²⁺: Colored (4 unpaired electrons)

### Final Answer
The ion that is colorless is **Cu⁺**.

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