How many of the following lanthanoid ions are paramagnetic?La3+, Ce3+…

The correct answer is Option (2) → 4

An ion is paramagnetic when it has unpaired electrons. Lanthanoid ions lose the 6s electrons first, then the 5d electron if there is one, and then 4f electrons. An ion with an empty (f⁰) or completely filled (f¹⁴) 4f subshell has no unpaired electron and is diamagnetic; every other lanthanoid ion is paramagnetic.

Paramagnetic:

• Ce³⁺ (Ce is [Xe]4f¹5d¹6s²; Ce³⁺ is 4f¹, one unpaired electron)

• Nd³⁺ (Nd is [Xe]4f⁴6s²; Nd³⁺ is 4f³, three unpaired electrons)

• Eu²⁺ (Eu is [Xe]4f⁷6s²; Eu²⁺ is 4f⁷, seven unpaired electrons)

• Gd³⁺ (Gd is [Xe]4f⁷5d¹6s²; Gd³⁺ is 4f⁷, seven unpaired electrons)

Diamagnetic (not counted):

• La³⁺ — La is [Xe]5d¹6s², so La³⁺ is 4f⁰.

• Ce⁴⁺ — 4f⁰.

• Yb²⁺ — Yb is [Xe]4f¹⁴6s², so Yb²⁺ is 4f¹⁴.

• Lu³⁺ — Lu is [Xe]4f¹⁴5d¹6s², so Lu³⁺ is 4f¹⁴.

Paramagnetic ions: Ce³⁺, Nd³⁺, Eu²⁺ and Gd³⁺ = 4.

NCERT (2026-27 edition):
4.5.4 General Characteristics – “…The lanthanoid ions other than the f⁰ type (La³⁺ and Ce⁴⁺) and the f¹⁴ type (Yb²⁺ and Lu³⁺) are all paramagnetic.”