Magnetic moment of which of the following is zero

Options

A. `Zn^(2+)`
B. `Cu^(2+)`
C. `Ni^(2+)`
D. `Cr^(2+)`

Answer

To determine which of the given ions has a magnetic moment of zero, we need to analyze the electronic configurations of each ion and count the number of unpaired electrons. The magnetic moment is zero for species that have no unpaired electrons.

### Step-by-Step Solution:

1. **Identify the Ions**: The ions given in the question are:
- Zn²⁺
- Cu²⁺
- Ni²⁺
- Cr²⁺

2. **Determine the Electronic Configuration of Each Ion**:
- **Zn²⁺**:
- Atomic number of Zn = 30
- Neutral Zn: [Ar] 3d¹⁰ 4s²
- Zn²⁺: Loses 2 electrons from 4s, so configuration is [Ar] 3d¹⁰.
- **Cu²⁺**:
- Atomic number of Cu = 29
- Neutral Cu: [Ar] 3d¹⁰ 4s¹
- Cu²⁺: Loses 2 electrons (1 from 4s and 1 from 3d), so configuration is [Ar] 3d⁹.
- **Ni²⁺**:
- Atomic number of Ni = 28
- Neutral Ni: [Ar] 3d⁸ 4s²
- Ni²⁺: Loses 2 electrons from 4s, so configuration is [Ar] 3d⁸.
- **Cr²⁺**:
- Atomic number of Cr = 24
- Neutral Cr: [Ar] 3d⁵ 4s¹
- Cr²⁺: Loses 2 electrons (1 from 4s and 1 from 3d), so configuration is [Ar] 3d⁴.

3. **Count the Unpaired Electrons**:
- **Zn²⁺**: [Ar] 3d¹⁰ → 0 unpaired electrons.
- **Cu²⁺**: [Ar] 3d⁹ → 1 unpaired electron.
- **Ni²⁺**: [Ar] 3d⁸ → 2 unpaired electrons.
- **Cr²⁺**: [Ar] 3d⁴ → 4 unpaired electrons.

4. **Determine the Magnetic Moment**:
- Magnetic moment is zero for ions with no unpaired electrons.
- Zn²⁺ has 0 unpaired electrons, so its magnetic moment is zero.
- Cu²⁺, Ni²⁺, and Cr²⁺ all have unpaired electrons, so their magnetic moments are not zero.

5. **Conclusion**: The ion with zero magnetic moment is **Zn²⁺**.

### Final Answer:
The magnetic moment of **Zn²⁺** is zero.