d and f Block Elements: Exam-Pattern Drill (4)

easy • 3 min read
Tags D And F Block Elements

Question

Among Sc3+Sc^{3+}, Ti3+Ti^{3+}, V3+V^{3+}, and Mn2+Mn^{2+}, identify the most paramagnetic and the diamagnetic species. Justify with electronic configuration.

Solution — Step by Step

Atomic numbers: Sc=21Sc = 21, Ti=22Ti = 22, V=23V = 23, Mn=25Mn = 25.

For transition-metal ions, remove 4s4s electrons FIRST, then 3d3d:

  • Sc3+Sc^{3+}: [Ar][Ar] → 00 unpaired electrons
  • Ti3+Ti^{3+}: [Ar]3d1[Ar]3d^1 → 11 unpaired
  • V3+V^{3+}: [Ar]3d2[Ar]3d^2 → 22 unpaired
  • Mn2+Mn^{2+}: [Ar]3d5[Ar]3d^5 → 55 unpaired (half-filled, all parallel by Hund’s rule)

μ=n(n+2) BM\mu = \sqrt{n(n+2)} \, \text{BM}

where nn is the number of unpaired electrons.
  • Sc3+Sc^{3+}: μ=0\mu = 0 (diamagnetic)
  • Ti3+Ti^{3+}: μ=3≈1.73\mu = \sqrt{3} \approx 1.73 BM
  • V3+V^{3+}: μ=8≈2.83\mu = \sqrt{8} \approx 2.83 BM
  • Mn2+Mn^{2+}: μ=35≈5.92\mu = \sqrt{35} \approx 5.92 BM
  • Most paramagnetic: Mn2+Mn^{2+} with μ≈5.92\mu \approx 5.92 BM (5 unpaired electrons).
  • Diamagnetic: Sc3+Sc^{3+} (no unpaired electrons).

Why This Works

Magnetic behaviour depends entirely on unpaired electrons. The spin-only formula gives the magnetic moment in Bohr Magnetons (BM), and a higher value means more paramagnetic.

For 3d transition ions, Mn2+Mn^{2+} (d5d^5) and Fe3+Fe^{3+} (d5d^5) are the magnetic champions in the first row — half-filled dd shell with all five spins parallel.

Speed shortcut: Memorise unpaired electron counts for common ions:

  • d0,d10d^0, d^{10} → 0 unpaired (diamagnetic)
  • d1,d9d^1, d^9 → 1 unpaired
  • d2,d8d^2, d^8 → 2 unpaired
  • d3,d7d^3, d^7 → 3 unpaired
  • d4,d6d^4, d^6 → 4 unpaired (assume high-spin for simple cases)
  • d5d^5 → 5 unpaired

Alternative Method — Direct Counting

Just count unpaired electrons in 3d3d. The ion with most unpaired = most paramagnetic. Skip the formula if the question only asks for ranking.

Common Mistake

Students often forget to remove 4s4s electrons FIRST when forming transition-metal cations. This leads to wrong configurations:

Mn2+Mn^{2+} is [Ar]3d5[Ar]3d^5, NOT [Ar]3d34s2[Ar]3d^3 4s^2 (which would be neutral Mn) or [Ar]3d44s1[Ar]3d^4 4s^1 (which is also wrong for the cation).

Another classic: confusing high-spin and low-spin states for d4−d7d^4-d^7 ions in octahedral complexes. For free ions or weak-field complexes, use high-spin (max unpaired). For strong-field ligands like CN⁻, use low-spin.

JEE Main consistently asks one magnetic moment problem per shift. NEET 2023 and 2024 both asked for the ion with maximum magnetic moment. The d5d^5 ions (Mn2+Mn^{2+}, Fe3+Fe^{3+}) are the go-to answer when the option list includes them.

For coordination chemistry (Class 12), this same logic extends — but ligand field theory determines high-spin vs low-spin.

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