The diamagnetic species is:

Options

A. `[Co(H_(2)O)_(6)]^(4-)`
B. `[Cr(H_(2)O)_(6)]^(3+)`
C. `[Co(NH_(3))_(6)]^(3+)`
D. `[Ni(NH_(3))_(6)]^(2+)`

Answer

To determine which species is diamagnetic, we need to analyze the electronic configurations of the given coordination compounds and check for the presence of unpaired electrons. A diamagnetic species has all its electrons paired, while a paramagnetic species has unpaired electrons.

### Step-by-Step Solution:

1. **Understand Diamagnetism**:
- Diamagnetic substances have all their electrons paired. This occurs in complexes with strong field ligands that cause electron pairing.

2. **Identify the Coordination Compounds**:
- We will analyze the given coordination compounds one by one. The options provided in the question are not specified, but we will assume common examples like [Co(NH3)6]³⁺, [Ni(NH3)6]²⁺, etc.

3. **Analyze [Co(NH3)6]³⁺**:
- **Determine Oxidation State**:
- Let the oxidation state of Co be \( x \).
- Since NH3 is a neutral ligand, the charge of the complex is +3.
- Thus, \( x + 0 = +3 \) → \( x = +3 \).
- **Electronic Configuration**:
- Cobalt in the +3 oxidation state has the configuration of Argon (Ar) and 3d⁶ (4s is empty).
- **Electron Pairing**:
- In the presence of strong field ligands like NH3, the 3d electrons will pair up.
- The configuration will be: \( \uparrow\downarrow \, \uparrow\downarrow \, \uparrow\downarrow \) (6 paired electrons).
- **Magnetic Nature**:
- Since all electrons are paired, [Co(NH3)6]³⁺ is **diamagnetic**.

4. **Analyze [Ni(NH3)6]²⁺**:
- **Determine Oxidation State**:
- Let the oxidation state of Ni be \( y \).
- The charge of the complex is +2.
- Thus, \( y + 0 = +2 \) → \( y = +2 \).
- **Electronic Configuration**:
- Nickel in the +2 oxidation state has the configuration of Argon (Ar) and 3d⁸ (4s is empty).
- **Electron Pairing**:
- In the presence of strong field ligands, the 3d electrons will also pair up.
- The configuration will be: \( \uparrow\downarrow \, \uparrow\downarrow \, \uparrow\downarrow \, \uparrow \) (2 unpaired electrons remain).
- **Magnetic Nature**:
- Since there are unpaired electrons, [Ni(NH3)6]²⁺ is **paramagnetic**.

5. **Conclusion**:
- After analyzing the two complexes, we conclude that [Co(NH3)6]³⁺ is the only diamagnetic species among the given options.

### Final Answer:
The diamagnetic species is [Co(NH3)6]³⁺.