The complex ion which has no d electrons in the central metal atom is (Atomic number Cr = 24, Mn = 25, Fe = 26, Co = 27)

\([MnO_4]^–\)

The correct answer is option 1. \([MnO_4]^–\)

To determine which complex ion has no d electrons in the central metal atom, we need to examine the electronic configuration of the central metal ions in each complex after accounting for their oxidation states.

1. [MnO₄]⁻:

Central Metal Ion: Mn (Manganese)

Oxidation State: +7

Electronic Configuration of Mn: [Ar] 3d⁵ 4s²

Electronic Configuration of Mn⁷⁺: [Ar] (removal of 7 electrons from the 3d and 4s orbitals)

Resulting Configuration: [Ar]

d Electrons: 0 (no d electrons)

2. [Co(NH₃)₆]³⁺:

Central Metal Ion: Co (Cobalt)

Oxidation State: +3

Electronic Configuration of Co: [Ar] 3d⁷ 4s²

Electronic Configuration of Co³⁺: [Ar] 3d⁶ (removal of 3 electrons)

d Electrons: 6

3. [Fe(CN)₆]³⁻:

Central Metal Ion: Fe (Iron)

Oxidation State: +3

Electronic Configuration of Fe: [Ar] 3d⁶ 4s²

Electronic Configuration of Fe³⁺: [Ar] 3d⁵ (removal of 3 electrons)

4. [Cr(H₂O)₆]³⁺:

Central Metal Ion: Cr (Chromium)

Oxidation State: +3

Electronic Configuration of Cr: [Ar] 3d⁵ 4s¹

Electronic Configuration of Cr³⁺: [Ar] 3d³ (removal of 3 electrons)

d Electrons: 3

Conclusion: The complex ion that has no d electrons in the central metal atom is: [MnO₄]⁻