The lanthanoids

What are the lanthanoids?

In plain words: across the lanthanoids each new electron goes deep inside the atom, into the 4f orbitals, where it hardly changes how the atom looks from outside. So the fourteen elements are near-twins, and the only steady change is that the atoms and ions shrink a little at each step.

They form the first row of the f-block, printed in a separate panel at the foot of the periodic table.

Electronic configurations

All the lanthanoid atoms have 6s^² in common, with a varying number of 4f electrons, and every Ln³⁺ ion, the most stable state, is 4fⁿ, with n rising from 1 to 14 (NCERT Section 4.5.1, page 109). Outside the [Xe] core (NCERT Table 4.9, page 110):

• Where 5d appears. Lanthanum, cerium, gadolinium and lutetium keep one electron in 5d. For gadolinium that leaves a half-filled 4f⁷, and for lutetium a full 4f¹⁴ (reasoned from the table).
• Other ions in NCERT Table 4.9: Ce⁴⁺ is 4f⁰, Pr⁴⁺ 4f¹, Nd⁴⁺ 4f², Tb⁴⁺ 4f⁷ and Dy⁴⁺ 4f⁸; Eu²⁺ is 4f⁷ and Yb²⁺ 4f¹⁴. Table 4.9 also lists configurations for Ln²⁺: most are the atom less its two 6s electrons, such as Gd²⁺ 4f⁷ 5d¹ and Lu²⁺ 4f¹⁴ 5d¹, but Ce²⁺ is 4f² (NCERT page 110). A configuration entry does not mean every such ion is a common stable aqueous species (reasoned).

Atomic and ionic sizes

• Both shrink from La to Lu. Compare radii on the same coordination and bonding convention. The fall in atomic radii, derived from the structures of the metals, is not quite regular, while the fall in the radii of the M³⁺ ions is (NCERT Section 4.5.2, page 109; the ions are plotted in NCERT Fig. 4.6). In Table 4.9 the atomic radius falls from 187 pm (La) to 173 pm (Yb), apart from europium’s 199 pm; the table gives no lutetium values, and the Ln³⁺ radius falls from 106 pm (La³⁺) to 86 pm (Yb³⁺) (NCERT page 110).
• NCERT slip (page 110): Table 4.9 gives ytterbium an atomic radius of 173 pm and lutetium none. Beyond the NCERT text, ytterbium’s metallic radius is about 193 pm, large like europium’s; europium metal is thought to hold the larger Eu²⁺ ion, and a similar reason, Yb²⁺ (4f¹⁴), is suggested for ytterbium, while about 174 pm is lutetium’s (Wikipedia, “Lanthanide”). NCERT’s own text names Eu and Yb as the exceptions to the smooth trends (page 110). If a question quotes Table 4.9, use its figures.

Lanthanoid contraction

• What it is. The steady decrease in size from lanthanum to lutetium is the lanthanoid contraction (NCERT page 109).
• Why it happens. As in an ordinary transition series, each added electron shields the others imperfectly from the nucleus. But one 4f electron shields another even less well than one d electron shields another, so as the nuclear charge rises along the series the size falls fairly regularly (NCERT page 109).
• Its consequence for the 5d series. The contraction of the lanthanoid series cancels the increase in size expected from the 4d to the 5d series, so the third transition series has almost the same radii as the second: zirconium 160 pm and hafnium 159 pm. That is why zirconium and hafnium occur together in nature and are hard to separate (NCERT page 109).
• Separating the lanthanoids. Beyond the NCERT text: because the ionic radius falls smoothly and predictably, the lanthanoid ions can be separated by chromatography, since the stability of their complexes with anions such as EDTA⁴⁻ rises as the radius falls (Wikipedia, “Lanthanide contraction”).

Oxidation states

• +3 dominates. La(III) and Ln(III) compounds predominate; +2 and +4 ions are occasionally found in solution or in solids. The irregularity comes mainly from the extra stability of empty, half-filled or filled f subshells (NCERT Section 4.5.3, page 109).
• NCERT slip (page 109): the sentence opens “In the lanthanoids, La(II) and Ln(III) compounds are predominant species”, confirmed on the page image. Lanthanum is +3 (La³⁺, 4f⁰, in Table 4.9 on page 110); read it as La(III).
• +4. Ce⁴⁺ is favoured by its noble gas configuration, 4f⁰, but it is a strong oxidant that returns to +3. Its E^⊖(Ce⁴⁺/Ce³⁺) of +1.74 V means it could oxidise water, but the reaction is very slow, so Ce(IV) is a good analytical reagent. NCERT says Pr, Nd, Tb and Dy “also exhibit +4 state but only in oxides, MO₂” (page 109); give that in an exam. Tb(IV), with half-filled f orbitals, is an oxidant (NCERT page 109). Beyond the NCERT text: “only in oxides” is too narrow, since terbium(IV) fluoride, TbF₄, is also known, a white solid and a strong oxidiser (Wikipedia, “Terbium(IV) fluoride”).
• +2. Eu²⁺ forms by losing the two s electrons, and its f⁷ configuration explains it; it is a strong reducing agent and returns to +3. Yb²⁺, f¹⁴, is a reductant too, and samarium, like europium, shows +2 and +3 (NCERT page 109).

General characteristics

• The metals. Silvery white, soft, and quick to tarnish in air; hardness rises with atomic number, samarium being steel hard. They have typical metallic structures and conduct heat and electricity well. Density and other properties change smoothly except for Eu and Yb, and sometimes Sm and Tm (NCERT Section 4.5.4, page 110).
• Melting points. NCERT gives them as 1000 to 1200 K, with samarium at 1623 K (NCERT page 110).
• NCERT slip (page 110): beyond the NCERT text, the Wikipedia “Melting points of the elements (data page)” shows that only three lanthanoids melt between 1000 and 1200 K, cerium (1068 K), ytterbium (1097 K) and europium (1099 K), as does lanthanum (1193 K); the remaining values extend much higher. The Royal Society of Chemistry lists samarium at 1345 K and lutetium at 1936 K, so samarium is not the highest-melting member. If a question quotes NCERT’s figures, use them.
• Colour. Many Ln³⁺ ions are coloured, in solids and in solution, which NCERT attributes to their f electrons; neither La³⁺ nor Lu³⁺ shows any colour, but the rest do so. The absorption bands are narrow, probably because the excitation is within the f level (NCERT page 110).
• NCERT slip (page 110): NCERT says every Ln³⁺ ion except La³⁺ and Lu³⁺ is coloured. Beyond the NCERT text: in aqueous solution Ce³⁺, Eu³⁺, Gd³⁺ and Yb³⁺ are colourless too (Wikipedia, “Lanthanide”, table of ion colours, after Cotton). In an exam, give NCERT’s La³⁺ and Lu³⁺; add the others only if the options require it.
• Magnetism. The lanthanoid ions other than the f⁰ type (La³⁺ and Ce⁴⁺) and the f¹⁴ type (Yb²⁺ and Lu³⁺) are all paramagnetic (NCERT page 110); give that in an exam. Strictly, their moments cannot be found by counting unpaired electrons alone: spin–orbit coupling and thermally populated levels matter, especially for Eu(III) and Sm(III) (reasoned).
• Ionisation enthalpies. The first is about 600 kJ mol⁻¹ and the second about 1200 kJ mol⁻¹, comparable with calcium’s. Abnormally low third ionisation enthalpies for lanthanum, gadolinium and lutetium point to the extra stability of empty, half-filled and full f levels, as with exchange energy in the 3d series (NCERT page 110).
• Reactivity. The early lanthanoids are reactive, like calcium; the later ones behave more like aluminium. E^⊖(Ln³⁺/Ln) lies between −2.2 and −2.4 V, except −2.0 V for europium (NCERT pages 110–111).
• Reactions (NCERT page 111, Fig. 4.7): with hydrogen on gentle heating; with carbon at 2773 K, giving the carbides Ln₃C, Ln₂C₃ and LnC₂; with dilute acids, liberating hydrogen; with halogens, burning to LnX₃; with oxygen to Ln₂O₃; with water to Ln(OH)₃ and H₂; with nitrogen to LnN and with sulphur to Ln₂S₃. The hydroxides are definite compounds, not just hydrated oxides, and basic like the alkaline earth hydroxides.
• Uses named by NCERT. NCERT calls the production of alloy steels for plates and pipes “the best single use of the lanthanoids” (page 111); give that in an exam. Mischmetall, about 95% lanthanoid metal and 5% iron with traces of S, C, Ca and Al, goes into magnesium-based alloys for bullets, shells and lighter flints. Mixed lanthanoid oxides catalyse petroleum cracking, and some oxides are phosphors in television screens (NCERT page 111).

Solved examples

Common mistakes to avoid

Quick revision summary

• Lanthanoids: Ce to Lu (Z = 58–71), 4f filling; with La they are written Ln; atoms 6s^² with varying 4f; Ln^³⁺ = 4f^ⁿ, n = 1 to 14.
• Lanthanoid contraction: steady fall in size La → Lu, from the poor shielding of one 4f electron by another; Zr 160 pm ≈ Hf 159 pm.
• +3 dominant; Ce^⁴⁺ (f^⁰) and Tb^⁴⁺ (f^⁷) oxidants; Eu^²⁺ (f^⁷) and Yb^²⁺ (f^¹⁴) reductants.
• Soft, silvery, reactive metals: early ones like calcium, later like aluminium; many Ln^³⁺ ions are coloured, NCERT excepting La^³⁺ and Lu^³⁺ (Ce^³⁺, Eu^³⁺, Gd^³⁺ and Yb^³⁺ are colourless too). All ions except the f^⁰ and f^¹⁴ types are paramagnetic (NCERT).
• Uses: alloy steels, mischmetall (about 95% Ln, 5% Fe) in lighter flints, cracking catalysts, phosphors.

Questions students ask

What is the difference between lanthanides, lanthanoids and rare earth elements?

Lanthanides and lanthanoids are two names for the same elements: IUPAC recommends lanthanoid, keeping the ending -ide for anions such as chloride, though lanthanide is still common (beyond the NCERT text; IUPAC Recommendations 2005, IR-3.5). NCERT counts 14 lanthanoids, cerium to lutetium, and discusses lanthanum with them (NCERT page 108), while the IUPAC periodic table labels all 15 elements from 57 to 71 lanthanoids (IUPAC Recommendations 2005). The rare earth elements are a wider set of 17, the 15 lanthanoids with scandium and yttrium, which share their ores and much of their chemistry (Wikipedia, “Rare-earth element”); actinide and actinoid pair the same way.

Why is europium’s atomic radius so much larger than its neighbours’?

Europium’s atomic radius, 199 pm against 180 pm for both samarium and gadolinium (NCERT Table 4.9, page 110), is large because in the metal each europium atom keeps its half-filled 4f⁷ set and gives only its two 6s electrons to the metallic bonding, as Eu²⁺, where most of the others give three (beyond the NCERT text; Wikipedia, “Lanthanide”). With fewer bonding electrons the atoms sit farther apart, and europium has the lowest density of the series; ytterbium, 4f¹⁴, behaves the same way, with a metallic radius near 193 pm (same source), though Table 4.9 prints 173 pm. NCERT names Eu and Yb as the elements whose density breaks the smooth trend (page 110).

Does the spin-only formula give the magnetic moments of lanthanoid ions?

No, the spin-only formula, μ = √(n(n + 2)) BM, fits few lanthanoid ions: 4f electrons lie inside the filled 5s and 5p shells and, unlike 3d electrons, whose orbital contribution is quenched (NCERT page 102), keep their orbital motion, strongly coupled to spin (beyond the NCERT text; Wikipedia, “Lanthanide”, “Lanthanide contraction”). So Dy³⁺ and Ho³⁺, with five and four unpaired electrons, show the largest moments, about 10.4–10.7 BM (Wikipedia, “Lanthanide”). If a question asks for the spin-only value, as NCERT Exercise 4.31 does, use the formula.

Why are the lanthanoids so difficult to separate from one another?

The lanthanoids are hard to separate because their ions are nearly identical: all are mainly +3 (NCERT page 109), and neighbouring Ln³⁺ ions differ in radius by only 1–3 pm (NCERT Table 4.9, page 110), so their salts dissolve, crystallise and form complexes almost alike (reasoned). Beyond the NCERT text, industry uses solvent extraction over many stages: tributyl phosphate dissolved in kerosene, shaken with a water solution of the nitrates, takes up some lanthanoids a little more readily than others, so each pass enriches the two layers slightly (Wikipedia, “Lanthanide”; reasoned).

Is the lanthanoid contraction in the JEE Main and NEET syllabus?

Yes, the lanthanoid contraction is named in Unit 11 of both the JEE Main 2027 and the NEET (UG) 2026 syllabus, in the line “Lanthanoids - Electronic configuration, oxidation states and Lanthanoid contraction” (JEE Main; NEET prints “oxidation states, and lanthanoid contraction”). The actinoids line names only their “Electronic configuration and oxidation states”, so the actinoid contraction (NCERT page 112) is not named in either.

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. Use Hund’s rule to derive the electronic configuration of the Ce³⁺ ion, and calculate its spin-only magnetic moment. (NCERT Exercise 4.31.)

   Show answerHide answer

   Ce is [Xe] 4f¹ 5d¹ 6s²; losing the two 6s electrons and the 5d electron leaves Ce³⁺ [Xe] 4f¹, one unpaired electron. μ = √(1 × 3) = 1.73 BM.

2. Q2. What are inner transition elements? Decide which of these atomic numbers belong to them: 29, 59, 74, 95, 102, 104. (NCERT Exercise 4.28.)

   Show answerHide answer

   Inner transition elements are the f-block elements, in which the 4f or 5f orbitals fill: the lanthanoids and the actinoids (NCERT page 89). 59 (praseodymium) is a lanthanoid, and 95 (americium) and 102 (nobelium) are actinoids. 29 (copper), 74 (tungsten) and 104 (rutherfordium) are d-block elements; rutherfordium belongs to the 6d series, which is actinium plus rutherfordium to copernicium (NCERT page 89).

3. Q3. What is mischmetall, and what is it used for? (Based on NCERT Exercise 4.27.)

   Show answerHide answer

   An alloy of about 95% lanthanoid metal and 5% iron, with traces of S, C, Ca and Al. Much of it goes into magnesium-based alloys for bullets, shells and lighter flints (NCERT page 111).