The correct order of the number of unpaired electrons in the ions `Cu^(2+), Ni^(2+), Fe^(3+)`, and `Cr^(3+)`is

Options

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

Explanation

To determine the correct order of the number of unpaired electrons in the ions \( \text{Cu}^{2+} \), \( \text{Ni}^{2+} \), \( \text{Fe}^{3+} \), and \( \text{Cr}^{3+} \), we will analyze the electronic configurations of each ion step by step.

### Step 1: Determine the electronic configuration of each ion.

1. **Copper (\( \text{Cu}^{2+} \))**:
- Atomic number of Cu = 29
- Ground state configuration: \( [\text{Ar}] 3d^{10} 4s^1 \)
- For \( \text{Cu}^{2+} \), we remove 2 electrons (1 from \( 4s \) and 1 from \( 3d \)):
- Configuration: \( [\text{Ar}] 3d^9 \)

2. **Nickel (\( \text{Ni}^{2+} \))**:
- Atomic number of Ni = 28
- Ground state configuration: \( [\text{Ar}] 3d^8 4s^2 \)
- For \( \text{Ni}^{2+} \), we remove 2 electrons from \( 4s \):
- Configuration: \( [\text{Ar}] 3d^8 \)

3. **Iron (\( \text{Fe}^{3+} \))**:
- Atomic number of Fe = 26
- Ground state configuration: \( [\text{Ar}] 3d^6 4s^2 \)
- For \( \text{Fe}^{3+} \), we remove 3 electrons (2 from \( 4s \) and 1 from \( 3d \)):
- Configuration: \( [\text{Ar}] 3d^5 \)

4. **Chromium (\( \text{Cr}^{3+} \))**:
- Atomic number of Cr = 24
- Ground state configuration: \( [\text{Ar}] 3d^5 4s^1 \)
- For \( \text{Cr}^{3+} \), we remove 3 electrons (1 from \( 4s \) and 2 from \( 3d \)):
- Configuration: \( [\text{Ar}] 3d^3 \)

### Step 2: Count the number of unpaired electrons in each ion.

1. **\( \text{Cu}^{2+} \) (3d\(^9\))**:
- Configuration: \( 3d^9 \)
- Unpaired electrons: 1 (since 9 electrons fill 4 orbitals and leave 1 unpaired).

2. **\( \text{Ni}^{2+} \) (3d\(^8\))**:
- Configuration: \( 3d^8 \)
- Unpaired electrons: 2 (8 electrons fill 4 orbitals, leaving 2 unpaired).

3. **\( \text{Fe}^{3+} \) (3d\(^5\))**:
- Configuration: \( 3d^5 \)
- Unpaired electrons: 5 (all 5 electrons are unpaired in separate orbitals).

4. **\( \text{Cr}^{3+} \) (3d\(^3\))**:
- Configuration: \( 3d^3 \)
- Unpaired electrons: 3 (3 electrons fill 3 orbitals, leaving all unpaired).

### Step 3: Arrange the ions in decreasing order of unpaired electrons.

- \( \text{Fe}^{3+} \): 5 unpaired electrons
- \( \text{Cr}^{3+} \): 3 unpaired electrons
- \( \text{Ni}^{2+} \): 2 unpaired electrons
- \( \text{Cu}^{2+} \): 1 unpaired electron

### Final Order:
The correct order of the number of unpaired electrons is:
\[ \text{Fe}^{3+} > \text{Cr}^{3+} > \text{Ni}^{2+} > \text{Cu}^{2+} \]