Which two stable ions of the first transition series have the largest…

The correct answer is Option (3) → Fe³⁺ and Mn²⁺

The magnetic moment rises with the number of unpaired electrons, \( \mu=\sqrt{n(n+2)} \) BM. In the five 3d orbitals the electrons go in singly first, so the largest number of unpaired electrons, five, belongs to a 3d⁵ ion. The 4s electrons are lost first when the ion forms.

\( \ce{Fe^3+} \) (Z = 26, [Ar]3d⁶4s² minus three electrons) is 3d⁵, 5 unpaired; \( \ce{Mn^2+} \) (Z = 25, [Ar]3d⁵4s² minus two electrons) is 3d⁵, 5 unpaired. Only Fe³⁺ and Mn²⁺ both have five unpaired electrons.

Magnetic moment of a d⁵ ion: \( \mu=\sqrt{5(5+2)}=\sqrt{35}=5.92 \) BM, the highest value in the series.

Why the other options are incorrect

Option (1) Ni²⁺ and Co²⁺ — Incorrect. \( \ce{Ni^2+} \) (Z = 28) is 3d⁸, 2 unpaired; \( \ce{Co^2+} \) (Z = 27) is 3d⁷, 3 unpaired.

Option (2) Cr²⁺ and Fe²⁺ — Incorrect. \( \ce{Cr^2+} \) (Z = 24) is 3d⁴, 4 unpaired; \( \ce{Fe^2+} \) (Z = 26) is 3d⁶, 4 unpaired.

Option (4) Ti⁴⁺ and Mn²⁺ — Incorrect. \( \ce{Ti^4+} \) (Z = 22) is 3d⁰, 0 unpaired; \( \ce{Mn^2+} \) is 3d⁵, 5 unpaired.

NCERT (2026-27 edition):
4.3.3 Ionisation Enthalpies – “… However, the trend of steady increase in second and third ionisation enthalpy breaks for the formation of Mn²⁺ and Fe³⁺ respectively. In both the cases, ions have d⁵ configuration.”

4.3.9 Magnetic Properties – “The magnetic moment increases with the increasing number of unpaired electrons. … The magnetic moments calculated from the ‘spin-only’ formula and those derived experimentally for some ions of the first row transition elements are given in Table 4.7.”

Table 4.7: Calculated and Observed Magnetic Moments (BM)