The complex ion which has no d electrons in the central metal atom is (Atomic number Cr = 24, Mn = 25, Fe = 26, Co = 27)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → [MnO4]−
The number of d electrons on the central atom comes from its oxidation state: find the oxidation state by charge balance, write the configuration of the neutral atom from Z, and remove that many electrons (4s first, then 3d).
Oxidation state of Mn: in \( \ce{[MnO4]^-} \), x + 4(−2) = −1, so x = +7.
Configuration: Mn (Z = 25) is [Ar]3d54s2, with 7 electrons outside [Ar].
Electrons removed: +7 removes both 4s electrons and all five 3d electrons, so Mn(VII) is [Ar]3d0 — no d electrons.
Why the other options are incorrect
Option (2) [Co(NH3)6]3+ — Incorrect. \( \ce{NH3} \) is neutral, so x = +3. Co (Z = 27) is [Ar]3d74s2; removing the two 4s electrons and one 3d electron leaves \( \ce{Co^3+} \): 3d6.
Option (3) [Fe(CN)6]3− — Incorrect. x + 6(−1) = −3, so x = +3. Fe (Z = 26) is [Ar]3d64s2; removing the two 4s electrons and one 3d electron leaves \( \ce{Fe^3+} \): 3d5.
Option (4) [Cr(H2O)6]3+ — Incorrect. \( \ce{H2O} \) is neutral, so x = +3. Cr (Z = 24) is [Ar]3d54s1; removing the 4s electron and two 3d electrons leaves \( \ce{Cr^3+} \): 3d3.