The transition metal ion with the least magnetic moment is typically the one with the fewest unpaired electrons in its d-orbital configuration. Among common ions like Co³⁺, Fe³⁺, Cr²⁺, and V³⁺, V³⁺ (3d²) has the least number of unpaired electrons (two unpaired electrons), and hence the least magnetic moment. The magnetic moment (μ\mu μ) can be approximated by the spin-only formula:

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

where nnn is the number of unpaired electrons. For example:

• V³⁺ (3d²) has 2 unpaired electrons, magnetic moment ≈2.83\approx 2.83≈2.83 BM.
• Co³⁺ (3d⁶) typically has 4 unpaired electrons.
• Fe³⁺ (3d⁵) has 5 unpaired electrons.
• Cr²⁺ (3d⁴) has 4 unpaired electrons.

Therefore, V³⁺ has the least magnetic moment among these ions due to fewer unpaired electrons.