Which one of the following has lowest value of paramagnetic behaviour?

Options

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

Answer

To determine which of the given coordination compounds has the lowest value of paramagnetic behavior, we will follow these steps:

### Step 1: Identify the Coordination Compounds
We need to identify the coordination compounds provided in the question. Let's assume we have the following complexes:
1. [Cr(CN)6]³⁻
2. [Mn(CN)6]³⁻
3. [Co(CN)6]³⁻
4. [Fe(CN)6]³⁻

### Step 2: Determine the Oxidation States
Next, we will calculate the oxidation states of the central metal ions in each complex:
- For [Cr(CN)6]³⁻: CN is a -1 ligand, so the oxidation state of Cr is +3.
- For [Mn(CN)6]³⁻: CN is a -1 ligand, so the oxidation state of Mn is +3.
- For [Co(CN)6]³⁻: CN is a -1 ligand, so the oxidation state of Co is +3.
- For [Fe(CN)6]³⁻: CN is a -1 ligand, so the oxidation state of Fe is +3.

### Step 3: Write the Electronic Configurations
Now we will write the electronic configurations for the metals in their +3 oxidation states:
- Chromium (Cr): Atomic number 24 → [Ar] 4s² 3d⁴ → In +3 state: [Ar] 3d³ (3 unpaired electrons)
- Manganese (Mn): Atomic number 25 → [Ar] 4s² 3d⁵ → In +3 state: [Ar] 3d⁴ (4 unpaired electrons)
- Cobalt (Co): Atomic number 27 → [Ar] 4s² 3d⁷ → In +3 state: [Ar] 3d⁶ (4 unpaired electrons)
- Iron (Fe): Atomic number 26 → [Ar] 4s² 3d⁶ → In +3 state: [Ar] 3d⁵ (5 unpaired electrons)

### Step 4: Determine the Number of Unpaired Electrons
Now we will determine the number of unpaired electrons in each case:
- [Cr(CN)6]³⁻: 3 unpaired electrons
- [Mn(CN)6]³⁻: 4 unpaired electrons
- [Co(CN)6]³⁻: 4 unpaired electrons
- [Fe(CN)6]³⁻: 5 unpaired electrons

### Step 5: Analyze the Ligand Field Strength
Since CN⁻ is a strong field ligand, it causes pairing of electrons. Thus, we need to consider that:
- In the case of [Cr(CN)6]³⁻, the 3 unpaired electrons can pair up due to the strong field nature of CN⁻.
- The same applies to the other complexes, but the extent of pairing will depend on the number of unpaired electrons.

### Step 6: Conclusion
After analyzing the number of unpaired electrons:
- [Cr(CN)6]³⁻: can become diamagnetic (0 unpaired electrons)
- [Mn(CN)6]³⁻: 4 unpaired electrons
- [Co(CN)6]³⁻: 4 unpaired electrons
- [Fe(CN)6]³⁻: 5 unpaired electrons

The complex with the lowest value of paramagnetic behavior is [Cr(CN)6]³⁻, which can become diamagnetic due to the strong field ligand CN⁻.

### Final Answer
The coordination compound with the lowest value of paramagnetic behavior is **[Cr(CN)6]³⁻**.