Which of the following sets of elements shows an abnormally low value…

The correct answer is Option (1) → La, Gd and Lu

The third ionisation enthalpy is the energy needed to change Ln²⁺ into Ln³⁺. As in the 3d series, exchange enthalpy gives extra stability to an empty, half-filled or completely filled f level. When the third electron removed leaves such a stable f level behind, the third ionisation enthalpy is abnormally low.

• Lanthanum: La²⁺ 5d¹ → La³⁺ 4f⁰ (empty f level).

• Gadolinium: Gd²⁺ 4f⁷5d¹ → Gd³⁺ 4f⁷ (half-filled f level).

• Lutetium: Lu²⁺ 4f¹⁴5d¹ → Lu³⁺ 4f¹⁴ (completely filled f level).

In each case the electron lost is the 5d electron, and a stable f configuration is left.

Why the other options are incorrect

Option (2) Ce, Eu and Yb — Incorrect.

• For Eu (Eu²⁺ 4f⁷ → Eu³⁺ 4f⁶) and Yb (Yb²⁺ 4f¹⁴ → Yb³⁺ 4f¹³) the third electron has to come out of a half-filled or filled f level, which breaks a stable configuration instead of reaching one.

• Ce²⁺ (4f²) → Ce³⁺ (4f¹) gives no special configuration.

Option (3) Pr, Nd and Sm — Incorrect. Their Ln³⁺ ions are 4f², 4f³ and 4f⁵, none of which is an empty, half-filled or filled f level.

Option (4) Ce, Gd and Yb — Incorrect. Gd fits, but Ce does not, and for Yb the third electron comes out of the filled 4f¹⁴ level, breaking a stable configuration.

NCERT (2026-27 edition):
4.5.4 General Characteristics – “…A detailed discussion of the variation of the third ionisation enthalpies indicates that the exchange enthalpy considerations (as in 3d orbitals of the first transition series), appear to impart a certain degree of stability to empty, half-filled and completely filled orbitals f level. This is indicated from the abnormally low value of the third ionisation enthalpy of lanthanum, gadolinium and lutetium.”

Table 4.9: Electronic Configurations and Radii of Lanthanum and Lanthanoids (rows and columns needed here; only electrons outside the [Xe] core are shown)