The correct statement about 4f-series elements is:

The correct answer is Option (3) → Promethium is artificially synthesised 4f series element.

Promethium (Pm, Z = 61) has no stable isotope; it is practically absent from the earth’s crust and is obtained artificially (as a product of nuclear reactions). It is the only lanthanoid made in this way.

Why the other options are incorrect

• Option (1) Paramagnetism falls to minimum in Nd. — Incorrect. The reverse is true; the paramagnetism of the Ln³⁺ ions rises to a maximum in neodymium.

• Option (2) \(Lu^{3+}\) ions are bright green in aqueous solution. — Incorrect. Lu (Z = 71) is [Xe]4f¹⁴5d¹6s²; removing the two 6s electrons and the 5d electron gives \( \ce{Lu^{3+}} \): [Xe]4f¹⁴. All seven 4f orbitals are full (no unpaired electron), so no f–f transition is possible and Lu³⁺ is colourless.

• Option (4) Absorption bands of Lanthanoids are broad. — Incorrect. The colour comes from excitation within the inner 4f level, which is shielded from the surroundings, so the absorption bands are narrow.

NCERT (2026-27 edition):
General Characteristics – …