Among the following complex ions, the species whose central metal atom does not have 'd' electron is :
`[MnO_(4)]^(-)`
`[CO(NH_(3))_(6)]^(3+)`
`[Fe(CN)_(6)]^(3-)`
`[Cr(H_(2)O)_(6)]^(3+)`

Options

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

Answer

To determine which complex ion has a central metal atom that does not have 'd' electrons, we need to analyze each complex ion provided in the question. We will find the oxidation state of the central metal in each complex and then check the electronic configuration to see if there are any 'd' electrons present.

### Step-by-Step Solution:

1. **Analyze `[MnO4]^(-)`**:
- Manganese (Mn) has an atomic number of 25, with an electronic configuration of Argon 18, 3d^5 4s^2.
- In the ion `[MnO4]^(-)`, let the oxidation state of Mn be \( X \).
- Oxygen has an oxidation state of -2. There are 4 oxygen atoms, so the total contribution from oxygen is \( 4 \times (-2) = -8 \).
- The overall charge of the ion is -1. Therefore, the equation becomes:
\[ X - 8 = -1 \implies X = +7 \]
- In the +7 oxidation state, Mn loses 7 electrons: 5 from 3d and 2 from 4s. Thus, its configuration becomes 3d^0 4s^0.
- **Conclusion**: Mn in `[MnO4]^(-)` has 0 d-electrons.

2. **Analyze `[Co(NH3)6]^(3+)`**:
- Cobalt (Co) has an atomic number of 27, with an electronic configuration of Argon 18, 3d^7 4s^2.
- Let the oxidation state of Co be \( X \).
- Ammonia (NH3) is a neutral ligand, contributing 0 to the charge. Therefore:
\[ X + 0 = +3 \implies X = +3 \]
- In the +3 oxidation state, Co loses 3 electrons: 2 from 4s and 1 from 3d, resulting in 3d^6.
- **Conclusion**: Co in `[Co(NH3)6]^(3+)` has 6 d-electrons.

3. **Analyze `[Fe(CN)6]^(3-)`**:
- Iron (Fe) has an atomic number of 26, with an electronic configuration of Argon 18, 3d^6 4s^2.
- Let the oxidation state of Fe be \( X \).
- Cyanide (CN) has a charge of -1, and there are 6 CN ligands, contributing \( 6 \times (-1) = -6 \) to the charge. Therefore:
\[ X - 6 = -3 \implies X = +3 \]
- In the +3 oxidation state, Fe loses 3 electrons: 2 from 4s and 1 from 3d, resulting in 3d^5.
- **Conclusion**: Fe in `[Fe(CN)6]^(3-)` has 5 d-electrons.

4. **Analyze `[Cr(H2O)6]^(3+)`**:
- Chromium (Cr) has an atomic number of 24, with an electronic configuration of Argon 18, 3d^5 4s^1.
- Let the oxidation state of Cr be \( X \).
- Water (H2O) is a neutral ligand, contributing 0 to the charge. Therefore:
\[ X + 0 = +3 \implies X = +3 \]
- In the +3 oxidation state, Cr loses 3 electrons: 1 from 4s and 2 from 3d, resulting in 3d^3.
- **Conclusion**: Cr in `[Cr(H2O)6]^(3+)` has 3 d-electrons.

### Final Conclusion:
The complex ion whose central metal atom does not have 'd' electrons is:
\[ \text{Answer: } [MnO4]^(-) \]