MHT-CET Chemistry · Transition and Inner Transition Elements

Lanthanoids and Actinoids: Membership, 4f Configurations and the Lanthanoid Contraction

The inner transition elements fill the 4f subshell (lanthanoids, La to Lu) or the 5f subshell (actinoids, Ac to Lr); their stable state is +3, the empty, half-filled and filled 4f subshells explain the extra +2 and +4 states, and the steady shrinking of the Ln³⁺ ion from La to Lu — the lanthanoid contraction — makes the hydroxides less basic along the series.

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Why this matters

41 PYQs, 2 HARD. Of the twenty-seven set from 2021 to 2025, eight ask which element is or is NOT a lanthanoid, an actinoid or a rare earth, the last lanthanoid, or the one used in fibre amplifiers; seven are 4f configurations — Ce⁴⁺ f⁰, Tb⁴⁺ f⁷, Lu³⁺ with no unpaired electrons, the filled 4f of Yb and Lu, the half-filled 4f of Gd, and La³⁺ with no moment; seven are the lanthanoid contraction — the largest and smallest Ln³⁺, the weakest base, and the two HARD ionisation enthalpies (Yb); five are compounds and properties — Ln(OH)₃ twice, LnC₂, and two 'NOT true' statements. Four cards.

Concept 1 of 4: Which Element Is a Lanthanoid, Which an Actinoid

Lanthanoids are the fifteen elements from lanthanum (57) to lutetium (71), in period 6; they and the actinoids are the rare earths. Actinoids run from actinium (89) to lawrencium (103), in period 7, and all are radioactive. A question gives four symbols and asks for one kind, so the fastest route is to know the two rows as lists and check which symbol sits in which.

Definition

Lanthanoids (4f, Z 57–71): La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu (the last). Also called rare earth elements.
Actinoids (5f, Z 89–103): Ac, Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr.
Lookalikes that are NOT f-block: Mo, Co, Hg, Zn, W, Cd (d-block).
Erbium is doped into optical fibres to make fibre amplifiers (erbium-doped fibre amplifiers).

Series	Z	Members to recognise
Lanthanoids (4f)	57–71	La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
Actinoids (5f)	89–103	Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr All actinoids are radioactive.

Tm, Pm, Sm are lanthanoids; Cm, Am, Np are actinoids — the look-alike pairs the options use.

Practise this conceptself-check · 4 quick reps

The same idea in a real exam question:

MHT-CET · 2023 · 9th May Shift 1 · Q56Easy

Example 1 · Transition and Inner Transition Elements · Inner Transition Elements, Lanthanoids and Actinoids

Which from following elements belongs to the actinoids?

Matching by the ending of the name

Promethium, thulium and samarium are lanthanoids; americium, curium and neptunium are actinoids. The names do not sort them — the lists do.

Drill 7 more on which element is a lanthanoid, which an actinoid

Concept 2 of 4: 4f Configurations and the +2 and +4 States

The stable state is +3. An extra state appears where it reaches an empty (f⁰), half-filled (f⁷) or filled (f¹⁴) 4f subshell. Cerium is 4f¹ 5d¹ 6s²; losing four electrons gives Ce⁴⁺ with f⁰. Terbium is 4f⁹ 6s²; losing four gives Tb⁴⁺ with f⁷. Europium (f⁷) and ytterbium (f¹⁴) show +2 for the same reason. For Ln³⁺, count f electrons as Z − 57: La³⁺ f⁰ and Lu³⁺ f¹⁴ have no unpaired electrons and no magnetic moment, Gd³⁺ f⁷ has seven.

Definition

+4 state: $\text{Ce}^{4+}$ f⁰; $\text{Tb}^{4+}$ f⁷. +2 state: $\text{Eu}^{2+}$ f⁷, $\text{Yb}^{2+}$ f¹⁴.
Filled 4f: Yb [Xe]4f¹⁴ 6s² (expected ground state); Lu [Xe]4f¹⁴ 5d¹ 6s² (expected AND observed).
Half-filled 4f: Gd [Xe]4f⁷ 5d¹ 6s² (observed); Eu 4f⁷ 6s².
$\text{Ln}^{3+}$ f electrons = Z − 57. $\text{La}^{3+}$ f⁰ and $\text{Lu}^{3+}$ f¹⁴ → 0 unpaired, no magnetic moment.

f electrons in Ln³⁺

n_f(\text{Ln}^{3+}) = Z - 57;\quad \text{unpaired} = \begin{cases} n_f & n_f \le 7 \\ 14 - n_f & n_f > 7 \end{cases}

Worked example

How many unpaired electrons does Dy³⁺ have (Z = 66)?

Practise this conceptself-check · 4 quick reps

The same idea in a real exam question:

MHT-CET · 2025 · 26 April Shift I · Q73Moderate

Example 2 · Transition and Inner Transition Elements · Inner Transition Elements, Lanthanoids and Actinoids

Which lanthanoid from following may exhibit +4 oxidation state with

f^{0}

configuration?

Expecting f⁷ at +3 for europium

Eu is already 4f⁷ as an atom, so Eu³⁺ is f⁶; it is Eu²⁺ that keeps the half-filled shell. The f⁷ ion at +3 is Gd³⁺, and the f⁷ ion at +4 is Tb⁴⁺.

Drill 6 more on 4f configurations and the +2 and +4 states

Concept 3 of 4: The Lanthanoid Contraction: Size, Basicity and Ionisation Enthalpy

Across the lanthanoids each step adds a proton and a 4f electron, and 4f electrons shield each other poorly. The effective nuclear charge rises, so the Ln³⁺ ion shrinks steadily from La³⁺ (largest) to Lu³⁺ (smallest). A smaller cation holds OH⁻ more tightly and gives it up less, so the hydroxides grow LESS basic: La(OH)₃ is the strongest base and Lu(OH)₃ the weakest. First ionisation enthalpies are low and close together, but a filled 4f¹⁴ subshell stands out: ytterbium has the highest of the options it appears with.

Definition

Ionic radius of $\text{Ln}^{3+}$ decreases La → Lu: largest La³⁺, smallest Lu³⁺.
Basicity of $\text{Ln(OH)}_3$ decreases La → Lu: weakest base $\text{Lu(OH)}_3$ .
First ionisation enthalpy (kJ mol⁻¹): Nd 533, Ce 534, La 538, Dy 573, Gd 593, Tm 597, Yb 603 — Yb (4f¹⁴ 6s²) is highest of these.
Consequence: 4d and 5d elements of the same group are almost the same size (Zr and Hf).

Trends along the lanthanoids

r(\text{La}^{3+}) > \ldots > r(\text{Lu}^{3+});\quad \text{La(OH)}_3 > \ldots > \text{Lu(OH)}_3\ \text{(basicity)}

Worked example

Arrange Sm³⁺, La³⁺ and Er³⁺ in decreasing ionic radius, and name the weakest base among their hydroxides.

Practise this conceptself-check · 4 quick reps

The same idea in a real exam question:

MHT-CET · 2025 · 22 April Shift I · Q78Moderate

Example 3 · Transition and Inner Transition Elements · Inner Transition Elements, Lanthanoids and Actinoids

Identify a weakest base from following

Picking Yb as the smallest ion

Yb is near the end but Lu is after it: when both appear, the smallest Ln³⁺ is Lu³⁺. Yb wins only the ionisation-enthalpy question.

Drill 6 more on the lanthanoid contraction: size, basicity and ionisation enthalpy

Concept 4 of 4: Lanthanoid Compounds and General Properties

Because the common state is +3, lanthanoid compounds follow the Ln³⁺ formula: the hydroxide is Ln(OH)₃, the oxide Ln₂O₃, the halide LnX₃. Heated with carbon at about 2773 K they give carbides LnC₂. The metals are soft, silvery and good conductors; their compounds are strongly paramagnetic (except f⁰ and f¹⁴); their large ions take coordination numbers above six. Not all are stable nuclei: promethium is radioactive.

Definition

Formulas: hydroxide $\text{Ln(OH)}_3$ ; oxide $\text{Ln}_2\text{O}_3$ ; halide $\text{LnX}_3$ ; carbide (with C at high temperature) $\text{LnC}_2$ ; with water → $\text{Ln(OH)}_3 + \text{H}_2$ ; with $\text{N}_2$ → LnN.
True: soft metals; good conductors of heat and electricity; coordination number usually greater than six; strongly paramagnetic.
NOT true: 'bad conductors'; 'all are non-radioactive' (promethium, Pm, is radioactive).

Common lanthanoid compounds

\text{Ln}^{3+}:\ \text{Ln(OH)}_3,\ \text{Ln}_2\text{O}_3,\ \text{LnX}_3;\quad \text{Ln} + 2\text{C} \xrightarrow{\Delta} \text{LnC}_2

Worked example

Write the formulas of the oxide and the chloride of gadolinium.

Practise this conceptself-check · 3 quick reps

The same idea in a real exam question:

MHT-CET · 2023 · 4th May Shift 2 · Q67Easy

Example 4 · Transition and Inner Transition Elements · Inner Transition Elements, Lanthanoids and Actinoids

Which from following properties of lanthanoids is NOT true?

Assuming every lanthanoid is stable

Promethium (Z = 61) has no stable isotope. 'All lanthanoids are non-radioactive' is the false statement the paper keys.

Drill 4 more on lanthanoid compounds and general properties

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

4f Configurations and the +2 and +4 States
f electrons in Ln³⁺
$n_f(\text{Ln}^{3+}) = Z - 57;\quad \text{unpaired} = \begin{cases} n_f & n_f \le 7 \\ 14 - n_f & n_f > 7 \end{cases}$
The Lanthanoid Contraction: Size, Basicity and Ionisation Enthalpy
Trends along the lanthanoids
$r(\text{La}^{3+}) > \ldots > r(\text{Lu}^{3+});\quad \text{La(OH)}_3 > \ldots > \text{Lu(OH)}_3\ \text{(basicity)}$
Lanthanoid Compounds and General Properties
Common lanthanoid compounds
$\text{Ln}^{3+}:\ \text{Ln(OH)}_3,\ \text{Ln}_2\text{O}_3,\ \text{LnX}_3;\quad \text{Ln} + 2\text{C} \xrightarrow{\Delta} \text{LnC}_2$

Reference tables (1)

Which Element Is a Lanthanoid, Which an Actinoid2 rows

Series	Z	Members to recognise
Lanthanoids (4f)	57–71	La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
Actinoids (5f)	89–103	Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr All actinoids are radioactive.

Tm, Pm, Sm are lanthanoids; Cm, Am, Np are actinoids — the look-alike pairs the options use.

Watch out for (4)

Matching by the ending of the name
→ Which Element Is a Lanthanoid, Which an Actinoid
Expecting f⁷ at +3 for europium
→ 4f Configurations and the +2 and +4 States
Picking Yb as the smallest ion
→ The Lanthanoid Contraction: Size, Basicity and Ionisation Enthalpy
Assuming every lanthanoid is stable
→ Lanthanoid Compounds and General Properties

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