The pair in which both species have the same spin-only magnetic moment is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → [Cr(H2O)6]2+ and [Fe(H2O)6]2+
The spin-only magnetic moment depends only on the number of unpaired electrons n: \( \mu=\sqrt{n(n+2)} \) BM. Two species have the same moment when they have the same n.
\( \ce{[Cr(H2O)6]^2+} \): Cr (Z = 24) is [Ar]3d54s1; \( \ce{Cr^2+} \) is 3d4; water is a weak field ligand for these hydrated ions (high spin: Table 4.7 gives 4 unpaired electrons for hydrated \( \ce{Cr^2+} \)), so the four d electrons stay unpaired, n = 4 and μ = √24 = 4.90 BM.
\( \ce{[Fe(H2O)6]^2+} \): Fe (Z = 26) is [Ar]3d64s2; \( \ce{Fe^2+} \) is 3d6; with water it is also high spin, so one d orbital holds a pair and four hold single electrons, so n = 4 and μ = 4.90 BM.
\( \ce{[Mn(H2O)6]^2+} \): Mn (Z = 25) is [Ar]3d54s2; \( \ce{Mn^2+} \) is 3d5; n = 5 and μ = √35 = 5.92 BM.
\( \ce{[CoCl4]^2-} \): x + 4(−1) = −2, so Co is +2; Co (Z = 27) is [Ar]3d74s2, so \( \ce{Co^2+} \) is 3d7. In a tetrahedral complex the splitting is too small to force pairing, so n = 3 and μ = √15 = 3.87 BM.
Only \( \ce{[Cr(H2O)6]^2+} \) and \( \ce{[Fe(H2O)6]^2+} \) both have 4 unpaired electrons and the same moment, 4.90 BM.
NCERT (2026-27 edition):
4.3.9 Magnetic Properties – “Paramagnetism arises from the presence of unpaired electrons, each such electron having a magnetic moment associated with its spin angular momentum and orbital angular momentum. … For these, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the ‘spin-only’ formula, i.e., \( \mu=\sqrt{n(n+2)} \) where n is the number of unpaired electrons and μ is the magnetic moment in units of Bohr magneton (BM).”
“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. The experimental data are mainly for hydrated ions in solution or in the solid state.”
Table 4.7: Calculated and Observed Magnetic Moments (BM)
