The lowest value of paramagnetism is shown by

Options

A. `[Co(CN)_(6)]^(3-)`
B. `[Fe(CN)_(6)]^(3-)`
C. `[Cr(CN)_(6)]^(3-)`
D. `[Mn(CN)_(6)]^(3-)`

Answer

To determine which coordination compound exhibits the lowest value of paramagnetism, we need to analyze the electronic configurations of the metal ions in their respective oxidation states and identify the number of unpaired electrons.

### Step-by-Step Solution:

1. **Understanding Paramagnetism**:
- Paramagnetism arises from the presence of unpaired electrons in an atom or ion. The more unpaired electrons, the stronger the paramagnetic behavior.

2. **Identify the Metal Ions and Their Oxidation States**:
- The question mentions cobalt (Co), iron (Fe), chromium (Cr), and manganese (Mn) in the +3 oxidation state.

3. **Determine the Electronic Configurations**:
- **Cobalt (Co)**: Atomic number = 27
- Electronic configuration = [Ar] 4s² 3d⁷
- In +3 oxidation state: Co³⁺ = [Ar] 3d⁶ (loses 2 electrons from 4s and 1 from 3d)
- **Iron (Fe)**: Atomic number = 26
- Electronic configuration = [Ar] 4s² 3d⁶
- In +3 oxidation state: Fe³⁺ = [Ar] 3d⁵ (loses 2 electrons from 4s and 1 from 3d)
- **Chromium (Cr)**: Atomic number = 24
- Electronic configuration = [Ar] 4s² 3d⁵
- In +3 oxidation state: Cr³⁺ = [Ar] 3d³ (loses 2 electrons from 4s and 1 from 3d)
- **Manganese (Mn)**: Atomic number = 25
- Electronic configuration = [Ar] 4s² 3d⁵
- In +3 oxidation state: Mn³⁺ = [Ar] 3d⁴ (loses 2 electrons from 4s and 1 from 3d)

4. **Count the Unpaired Electrons**:
- **Co³⁺ (3d⁶)**:
- Configuration: ↑↓ ↑ ↑ ↑ ↑ (4 unpaired electrons)
- **Fe³⁺ (3d⁵)**:
- Configuration: ↑ ↑ ↑ ↑ ↑ (5 unpaired electrons)
- **Cr³⁺ (3d³)**:
- Configuration: ↑ ↑ ↑ (3 unpaired electrons)
- **Mn³⁺ (3d⁴)**:
- Configuration: ↑ ↑ ↑ ↑ (4 unpaired electrons)

5. **Compare the Number of Unpaired Electrons**:
- Co³⁺: 4 unpaired electrons
- Fe³⁺: 5 unpaired electrons
- Cr³⁺: 3 unpaired electrons
- Mn³⁺: 4 unpaired electrons

6. **Conclusion**:
- The ion with the lowest number of unpaired electrons is Cr³⁺, which has 3 unpaired electrons. Therefore, it exhibits the lowest value of paramagnetism.

### Final Answer:
The lowest value of paramagnetism is shown by **Cr³⁺ (Chromium in +3 oxidation state)**.