Match Ion given in List I with their Magnetic moment (Calculated) giv…

The correct answer is Option (1) → (A) - (IV), (B) - (II), (C) - (I), (D) - (III)

For ions of the first transition series, the magnetic moment comes from the unpaired electrons only (the orbital contribution is quenched). It is given by the spin-only formula, where n is the number of unpaired electrons:

    \( \displaystyle \mu=\sqrt{n(n+2)}\ \mathrm{BM} \)

To find n, write the configuration of the neutral atom, remove the 4s electrons first and then the 3d electrons, and place the d electrons singly in the five d orbitals (Hund’s rule).

• (A) Sc³⁺ — This matches (IV) 0. Sc (Z = 21) is [Ar]3d¹4s²; losing the two 4s electrons and the one 3d electron gives Sc³⁺: 3d⁰. With n = 0, μ = 0, so the ion is diamagnetic.

• (B) Ti³⁺ — This matches (II) 1.73. Ti (Z = 22) is [Ar]3d²4s²; losing the two 4s electrons and one 3d electron gives Ti³⁺: 3d¹. With n = 1:

      \( \displaystyle \mu=\sqrt{1(1+2)}=\sqrt{3}=1.73\ \mathrm{BM} \)

• (C) V²⁺ — This matches (I) 3.87. V (Z = 23) is [Ar]3d³4s²; losing the two 4s electrons gives V²⁺: 3d³. With n = 3:

      \( \displaystyle \mu=\sqrt{3(3+2)}=\sqrt{15}=3.87\ \mathrm{BM} \)

• (D) Mn²⁺ — This matches (III) 5.92. Mn (Z = 25) is [Ar]3d⁵4s²; losing the two 4s electrons gives Mn²⁺: 3d⁵, with all five d electrons unpaired. With n = 5:

      \( \displaystyle \mu=\sqrt{5(5+2)}=\sqrt{35}=5.92\ \mathrm{BM} \)

NCERT (2026-27 edition):
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 the compounds of the first series of transition metals, the contribution of the orbital angular momentum is effectively quenched and hence is of no significance. For these, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the ‘spin-only’ formula, i.e.,

    \( \displaystyle \mu=\sqrt{n(n+2)} \)

where n is the number of unpaired electrons and μ is the magnetic moment in units of Bohr magneton (BM). A single unpaired electron has a magnetic moment of 1.73 Bohr magnetons (BM).”

Table 4.7 (part):