Which of the following species has no `'d'` electrons in the central metal atom is ?

Explanation

To determine which of the given species has no 'd' electrons in the central metal atom, we will analyze each option step by step.

### Step 1: Analyze MnO4⁻
1. **Determine the oxidation state of Manganese (Mn)**:
- Let the oxidation state of Mn be \( x \).
- The formula is: \( x + 4(-2) = -1 \) (since there are 4 oxygen atoms each with a -2 charge).
- This simplifies to: \( x - 8 = -1 \) → \( x = +7 \).

2. **Find the electronic configuration of Mn**:
- The atomic number of Mn is 25, so its electronic configuration is:
\[ \text{Mn: } 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5 \]

3. **Determine the electronic configuration of Mn in the +7 oxidation state**:
- Remove 2 electrons from 4s and 5 electrons from 3d:
\[ \text{Mn}^{+7}: \text{Argon configuration (18 electrons)} \]
- Thus, Mn in MnO4⁻ has **no d electrons**.

### Step 2: Analyze [Co(NH3)6]³⁺
1. **Determine the oxidation state of Cobalt (Co)**:
- Let the oxidation state of Co be \( x \).
- The formula is: \( x + 6(0) = +3 \) (NH3 is a neutral ligand).
- This implies \( x = +3 \).

2. **Find the electronic configuration of Co**:
- The atomic number of Co is 27, so its electronic configuration is:
\[ \text{Co: } 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7 \]

3. **Determine the electronic configuration of Co in the +3 oxidation state**:
- Remove 2 electrons from 4s and 2 from 3d:
\[ \text{Co}^{+3}: \text{Argon configuration} + 3d^6 \]
- Thus, Co in [Co(NH3)6]³⁺ has **d electrons**.

### Step 3: Analyze [Fe(CN)6]³⁻
1. **Determine the oxidation state of Iron (Fe)**:
- Let the oxidation state of Fe be \( x \).
- The formula is: \( x + 6(-1) = -3 \) (CN has a -1 charge).
- This implies \( x = +3 \).

2. **Find the electronic configuration of Fe**:
- The atomic number of Fe is 26, so its electronic configuration is:
\[ \text{Fe: } 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6 \]

3. **Determine the electronic configuration of Fe in the +3 oxidation state**:
- Remove 2 electrons from 4s and 1 from 3d:
\[ \text{Fe}^{+3}: \text{Argon configuration} + 3d^5 \]
- Thus, Fe in [Fe(CN)6]³⁻ has **d electrons**.

### Step 4: Analyze [Cr(H2O)6]³⁺
1. **Determine the oxidation state of Chromium (Cr)**:
- Let the oxidation state of Cr be \( x \).
- The formula is: \( x + 6(0) = +3 \) (H2O is a neutral ligand).
- This implies \( x = +3 \).

2. **Find the electronic configuration of Cr**:
- The atomic number of Cr is 24, so its electronic configuration is:
\[ \text{Cr: } 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5 \]

3. **Determine the electronic configuration of Cr in the +3 oxidation state**:
- Remove 1 electron from 4s and 3 from 3d:
\[ \text{Cr}^{+3}: \text{Argon configuration} + 3d^3 \]
- Thus, Cr in [Cr(H2O)6]³⁺ has **d electrons**.

### Conclusion
From the analysis:
- **MnO4⁻** has no d electrons.
- **[Co(NH3)6]³⁺**, **[Fe(CN)6]³⁻**, and **[Cr(H2O)6]³⁺** all have d electrons.

Therefore, the species that has no 'd' electrons in the central metal atom is **MnO4⁻**.