The complex which has no d-electron in the central metal atom is .

Options

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

Explanation

To solve the question, "The complex which has no d-electron in the central metal atom is," we will analyze the given options one by one to determine which complex has a central metal atom with a d-electron count of zero (3D0).

### Step-by-Step Solution:

1. **Identify the Complexes and Their Central Metal Atoms:**
- We have four complexes to analyze. Let's denote them as A, B, C, and D for simplicity.

2. **Analyze Option A: MnO4⁻ (Manganate Ion)**
- The central metal atom is Manganese (Mn).
- Atomic number of Mn = 25.
- Electronic configuration of Mn = [Ar] 3D5 4S2.
- In MnO4⁻, Mn is in the +7 oxidation state.
- Therefore, the electronic configuration in this state is:
- 3D5 → 0 (all d-electrons are removed)
- 4S2 → 0
- Thus, the configuration becomes 3D0 4S0.
- **Conclusion:** MnO4⁻ has no d-electrons.

3. **Analyze Option B: CoCl4²⁻ (Cobalt Complex)**
- The central metal atom is Cobalt (Co).
- Atomic number of Co = 27.
- Electronic configuration of Co = [Ar] 3D7 4S2.
- In CoCl4²⁻, Co is in the +2 oxidation state.
- Therefore, the electronic configuration in this state is:
- 3D7 → 5 (removing 2 electrons from 4S)
- 4S2 → 0
- Thus, the configuration becomes 3D6 4S0.
- **Conclusion:** CoCl4²⁻ has d-electrons.

4. **Analyze Option C: FeCl3 (Iron Complex)**
- The central metal atom is Iron (Fe).
- Atomic number of Fe = 26.
- Electronic configuration of Fe = [Ar] 3D6 4S2.
- In FeCl3, Fe is in the +3 oxidation state.
- Therefore, the electronic configuration in this state is:
- 3D6 → 5 (removing 3 electrons from 4S and 3D)
- 4S2 → 0
- Thus, the configuration becomes 3D5 4S0.
- **Conclusion:** FeCl3 has d-electrons.

5. **Analyze Option D: CrCl3 (Chromium Complex)**
- The central metal atom is Chromium (Cr).
- Atomic number of Cr = 24.
- Electronic configuration of Cr = [Ar] 3D5 4S1.
- In CrCl3, Cr is in the +3 oxidation state.
- Therefore, the electronic configuration in this state is:
- 3D5 → 3 (removing 1 electron from 4S and 1 from 3D)
- 4S1 → 0
- Thus, the configuration becomes 3D4 4S0.
- **Conclusion:** CrCl3 has d-electrons.

6. **Final Conclusion:**
- Among the options analyzed, only **MnO4⁻** has a central metal atom with no d-electrons (3D0). Therefore, the correct answer is **Option A: MnO4⁻**.