Who are the lanthanoids
The f-block consists of two series — the lanthanoids (the fourteen elements following lanthanum) and the actinoids (the fourteen elements following actinium). Because lanthanum (Z = 57) so closely resembles the elements that follow it, it is conventionally discussed alongside them, and the general symbol Ln is used for the whole family. The 4f orbitals are filled across cerium (Z = 58) to lutetium (Z = 71).
What sets the lanthanoids apart from the ordinary transition metals is their uniformity. They resemble one another far more closely than the members of any single 3d, 4d or 5d series do, because the differentiating electron enters the deeply buried 4f subshell rather than the valence shell. Their chemistry therefore offers a clean window onto the effect of small, steady changes in size and nuclear charge across a row of otherwise near-identical elements.
| Feature | What NCERT §4.5 says |
|---|---|
| Members | Ce (58) to Lu (71); La (57) included by convention |
| Differentiating orbital | 4f (buried inside the [Xe] core) |
| General symbol | Ln |
| Stable oxidation state | +3 for all (Ln³⁺ = 4fn) |
| Mutual resemblance | Greater than within any d-series |
Electronic configurations
Every lanthanoid atom carries the common $\ce{6s^2}$ outer pair, with variable occupancy of the 4f level beneath it. The general atomic configuration is [Xe] 4f1–14 5d0–1 6s2. Two members, lanthanum and lutetium (and cerium and gadolinium), keep a single 5d electron, while the rest place all their extra electrons in 4f. The 5d1 appears at La (4f0), Ce, Gd (because 4f7 is a stable half-filled set) and Lu (4f14).
The crucial NEET point is the configuration of the tripositive ion. Once a lanthanoid loses three electrons to give Ln³⁺ — the dominant species — the configuration collapses to the simple regular form $\ce{4f^n}$, with n running from 1 (Ce³⁺) to 14 (Lu³⁺). This is why the Ln³⁺ radii decrease so smoothly, while neutral-atom radii are slightly irregular.
| Element | Z | Atom config (outside [Xe]) | Ln³⁺ config |
|---|---|---|---|
| Lanthanum (La) | 57 | 5d¹ 6s² | 4f⁰ |
| Cerium (Ce) | 58 | 4f¹ 5d¹ 6s² | 4f¹ |
| Europium (Eu) | 63 | 4f⁷ 6s² | 4f⁶ |
| Gadolinium (Gd) | 64 | 4f⁷ 5d¹ 6s² | 4f⁷ |
| Terbium (Tb) | 65 | 4f⁹ 6s² | 4f⁸ |
| Ytterbium (Yb) | 70 | 4f¹⁴ 6s² | 4f¹³ |
| Lutetium (Lu) | 71 | 4f¹⁴ 5d¹ 6s² | 4f¹⁴ |
Eu, Gd and Tb configurations
NEET 2016 asked the exact configurations of Eu, Gd and Tb. The half-filled-stability rule decides them: Eu stops at $\ce{4f^7 6s^2}$ (no 5d), Gd promotes one electron to give $\ce{4f^7 5d^1 6s^2}$ (keeping 4f⁷), and Tb is $\ce{4f^9 6s^2}$. Aspirants who blindly fill 4f without applying the half-filled rule choose the wrong option.
Half-filled (4f⁷) and filled (4f¹⁴) sets earn a 5d¹ at Gd and Lu — never memorise the row without this rule.
Oxidation states & the +2/+4 exceptions
In the lanthanoids, La(III) and Ln(III) compounds are the predominant species. The +3 state is so dominant because the energy needed to remove the third electron is repaid by lattice or hydration energy, and the resulting 4fn ions are well shielded. Occasionally, however, +2 and +4 ions appear in solution or in solid compounds. This irregularity — mirrored in the third ionisation enthalpies — arises mainly from the extra stability of empty, half-filled or completely-filled f subshells.
Cerium provides the classic +4 case: $\ce{Ce^4+}$ has an empty $\ce{4f^0}$ noble-gas configuration, so its formation is favoured. But Ce(IV) is a strong oxidant that readily reverts to Ce(III); the standard potential $E^\circ$ for $\ce{Ce^4+/Ce^3+}$ is +1.74 V, large enough that it could in principle oxidise water — though the reaction is so slow that Ce(IV) survives as a useful analytical reagent. Pr, Nd, Tb and Dy also show +4, but only in their oxides $\ce{MO2}$.
On the reducing side, $\ce{Eu^2+}$ forms by losing only the two 6s electrons, leaving the half-filled $\ce{4f^7}$ set; it is a strong reducing agent that changes back to the common +3 state. Similarly $\ce{Yb^2+}$ ($\ce{4f^14}$) is a reductant, and samarium behaves much like europium, showing both +2 and +3. Terbium, with a half-filled $\ce{4f^7}$ in its +4 state, is an oxidant.
| Ion | Config | Driving stability | Redox role |
|---|---|---|---|
| $\ce{Ce^4+}$ | 4f⁰ | Empty f (noble gas) | Strong oxidant → Ce³⁺ |
| $\ce{Tb^4+}$ | 4f⁷ | Half-filled f | Oxidant |
| $\ce{Eu^2+}$ | 4f⁷ | Half-filled f | Strong reductant → Eu³⁺ |
| $\ce{Yb^2+}$ | 4f¹⁴ | Filled f | Reductant |
The same exchange-energy stability explains an ionisation-enthalpy quirk that NEET loves: lanthanum, gadolinium and lutetium show abnormally low third ionisation enthalpies, because removing the third electron from each leaves a stable 4f0, 4f7 or 4f14 core respectively. Gadolinium's case (NEET 2022) is purely an exchange-enthalpy effect, not a size or electronegativity effect.
The lanthanoid contraction
The single most examined idea in this subtopic is the lanthanoid contraction: the overall, steady decrease in atomic and ionic radii on moving from lanthanum to lutetium with increasing atomic number. The decrease in the Ln³⁺ ionic radii is remarkably regular; the metallic-atom radii decrease too, but slightly less smoothly because of variable 5d/4f occupancies.
Why the contraction happens
The cause is the same one that drives the ordinary contraction across a transition series — the imperfect shielding of one electron by another in the same subshell — but it is more pronounced here. As we cross the series, each successive electron is added to the 4f subshell while the nuclear charge rises by one unit at every step. The 4f orbitals are diffuse and poorly directed, so one 4f electron shields another even less effectively than one d electron shields another.
The consequence is that the effective nuclear charge experienced by the outer 5s, 5p and 6s electrons creeps up steadily across the row. The whole electron cloud is pulled inward, and the size of the entire 4fn shell shrinks in a fairly regular fashion with increasing atomic number. Because the change at each step is small, the cumulative effect over fourteen elements is what matters — and it is exactly enough to undo the size increase that would otherwise be expected on going from one principal shell to the next.
It is worth being precise about the comparison NCERT draws. The contraction across the lanthanoids is "of the same kind" as the ordinary contraction seen across a normal transition series — both stem from imperfect intra-subshell shielding — but the 4f orbitals are far poorer screeners than d orbitals because of their shape and their deep penetration toward the nucleus. That is why the contraction in the 4f series, though gentle at each step, accumulates into a size reduction large enough to leave a lasting imprint on the elements that follow. The trend in the regular Ln³⁺ ions is therefore smooth, whereas the metallic (neutral-atom) radii show small humps at Eu and Yb, where the half-filled and filled 4f sets allow only the two 6s electrons into the metallic bonding, slightly enlarging those atoms.
The same poor-shielding logic underlies size, density and ionisation trends across the d-series. Revisit general properties of the transition elements to see where the contraction fits.
Consequences of the contraction
The lanthanoid contraction has consequences that reach well beyond the 4f block itself. The 4f orbitals are filled before the 5d transition series begins, so the contraction is "stored up" and then delivered to the third transition series. This is the most important examinable consequence.
1. Near-identical radii of the 4d and 5d series
On descending a transition group, the radius normally increases from the 3d to the 4d member. The expected further increase from 4d to 5d is cancelled by the intervening lanthanoid contraction. The result is that second-row and third-row transition metals have almost identical sizes — for example Zr (160 pm) and Hf (159 pm), and likewise the pairs Nb/Ta and Mo/W.
2. Similar physical and chemical properties of 4d/5d pairs
Because their radii match so closely, members of the second and third transition series in the same group show much greater similarity in physical and chemical behaviour than ordinary family relationships would predict. This is why Zr and Hf occur together in nature and are notoriously difficult to separate — their compounds behave almost identically.
3. Difficulty of separating the lanthanoids themselves
Within the 4f series, the radii change so gradually that adjacent Ln³⁺ ions differ only minutely in size. Their salts have nearly identical solubilities and complexation behaviour, which makes separation of individual lanthanoids by classical fractional methods extremely tedious — modern separation relies on ion-exchange and solvent-extraction techniques exploiting these tiny radius differences.
4. Decreasing basicity of the hydroxides
As the ionic radius of Ln³⁺ shrinks across the series, the charge density on the cation rises, the $\ce{Ln-OH}$ bond becomes stronger and more covalent, and the hydroxide releases $\ce{OH-}$ less readily. Hence basic strength falls steadily: $\ce{La(OH)3}$ is the most basic and $\ce{Lu(OH)3}$ the least basic of the series.
| Consequence | Effect |
|---|---|
| 4d vs 5d radii | Nearly equal: Zr ≈ Hf, Nb ≈ Ta, Mo ≈ W |
| Properties of pairs | 5d metals resemble 4d congeners closely |
| Separation | Zr/Hf and adjacent lanthanoids hard to separate |
| Hydroxide basicity | Decreases La(OH)₃ → Lu(OH)₃ |
| Covalent character | Increases toward the heavier (smaller) ions |
Don't confuse cause with consequence
The cause of the lanthanoid contraction is poor 4f shielding of an increasing nuclear charge. The consequence is the Zr ≈ Hf radius coincidence. NEET 2021 asked why Zr and Hf have similar radii — the answer is "lanthanoid contraction," not "diagonal relationship" or "same group." Read the stem carefully to know whether it wants the reason for the contraction or its downstream effect.
Cause = poor 4f shielding · Consequence = identical 4d/5d radii (Zr ≈ Hf).
General characteristics
All lanthanoids are silvery-white soft metals that tarnish rapidly in air; hardness rises with atomic number, samarium being steel-hard. Melting points lie between 1000 and 1200 K (samarium is an outlier at 1623 K), and they are good conductors of heat and electricity. The decrease in metallic radius combined with rising atomic mass gives a general increase in density across the series, while properties change smoothly except for Eu and Yb (and occasionally Sm and Tm), whose anomalies trace back to the half-filled and filled f-sets.
Many trivalent ions are coloured in both solid and solution, the colour arising from f–f transitions; the absorption bands are narrow. The exceptions are the $\ce{4f^0}$ ions ($\ce{La^3+}$, $\ce{Ce^4+}$) and the $\ce{4f^14}$ ions ($\ce{Yb^2+}$, $\ce{Lu^3+}$), which are colourless and diamagnetic. All Ln ions other than these f⁰ and f¹⁴ types are paramagnetic. Chemically the earlier members behave like calcium and the later ones more like aluminium; the lanthanoids burn in oxygen, react with water to give $\ce{Ln(OH)3}$ and hydrogen, and combine with halogens to give $\ce{LnX3}$.
Which lanthanoid ions are diamagnetic, and why?
Diamagnetism requires no unpaired electrons. Among lanthanoid ions this is satisfied only by the empty-f and full-f configurations: $\ce{Ce^4+}$ and $\ce{La^3+}$ are $\ce{4f^0}$, while $\ce{Yb^2+}$ and $\ce{Lu^3+}$ are $\ce{4f^14}$ — all with zero unpaired electrons. Hence the pair $\ce{Ce^4+}$ and $\ce{Yb^2+}$ is diamagnetic (NEET 2024). Ions such as $\ce{Eu^2+}$ ($\ce{4f^7}$, seven unpaired) or $\ce{Gd^3+}$ ($\ce{4f^7}$) are strongly paramagnetic.
Lanthanoids & the contraction in one minute
- Lanthanoids = Ce–Lu (4f series); La included by convention; symbol Ln; differentiating electron enters 4f.
- General atom config [Xe] 4f1–14 5d0–1 6s²; all Ln³⁺ are simply $\ce{4f^n}$ — the dominant +3 state.
- Exceptions from f-stability: $\ce{Ce^4+}$ (4f⁰, oxidant), $\ce{Eu^2+}$ (4f⁷, reductant), $\ce{Yb^2+}$ (4f¹⁴), $\ce{Tb^4+}$ (4f⁷).
- Lanthanoid contraction = steady fall in atomic/ionic radii La → Lu, caused by poor 4f shielding of a rising nuclear charge.
- Consequences: Zr ≈ Hf (and Nb/Ta, Mo/W) radii equal; 4d/5d pairs hard to separate; lanthanoids hard to separate; basicity of Ln(OH)₃ falls La → Lu.
- Coloured/paramagnetic except f⁰ (La³⁺, Ce⁴⁺) and f¹⁴ (Yb²⁺, Lu³⁺), which are colourless and diamagnetic.