f-Block

🟢 Lite — Quick Review (1h–1d)

Rapid summary of lanthanides and actinides for quick revision.

The f-block elements comprise the lanthanides (elements 57–71, filling 4f orbitals) and actinides (elements 89–103, filling 5f orbitals). The lanthanides follow lanthanum (La, Z = 57) and include cerium (Ce), praseodymium (Pr), neodymium (Nd), promethium (Pm), samarium (Sm), europium (Eu), gadolinium (Gd), terbium (Tb), dysprosium (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb), and lutetium (Lu). The general electronic configuration is [Xe]4f¹⁻¹⁴5d¹⁰6s², where the 4f subshell is being filled.

Lanthanide Contraction: The steady decrease in atomic and ionic radii across the lanthanide series (from La³⁺ to Lu³⁺, ionic radius ~1.16 Å to ~0.85 Å) is called lanthanide contraction. This occurs because the 4f electrons are poorly shielding.

Key consequences of lanthanide contraction:

• Second and third transition series elements have similar atomic/ionic radii (e.g., Zr/Hf; Nb/Ta)
• Complex formation increases across the series — Lu³⁺ forms more stable complexes than La³⁺
• Basicity decreases: La³⁺ is most basic, Lu³⁺ is least basic

Oxidation states: Lanthanides exhibit +3 oxidation state almost exclusively. Ce and Eu also show +4 and +2 respectively due to half-filled/filled f-subshell stability. Yb shows +2.

Actinides: Thorium (Th, Z = 90) through Lawrencium (Lr, Z = 103). They show variable oxidation states (+3 to +7) because 5f electrons are more readily involved in bonding. The actinide contraction is analogous to lanthanide contraction.

⚡ Exam tip: In JEE Advanced, questions on lanthanides focus on contraction consequences, separation methods, and electronic configuration anomalies. Remember Ce³⁺/Ce⁴⁺ and Eu²⁺/Eu³⁺ as the most common redox couples.

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding of f-block chemistry.

Electronic Configuration of Lanthanides

The 14 lanthanides fill the 4f subshell. Cerium begins with [Xe]4f¹5d¹6s², not [Xe]4f²6s² as might be predicted by simple aufbau. The actual configurations arise from subtle energy differences between 4f, 5d, and 6s orbitals. Key points:

• Gd (Z = 64): [Xe]4f⁷5d¹6s² — half-filled 4f shell provides extra stability
• Lu (Z = 71): [Xe]4f¹⁴5d¹6s² — completely filled 4f shell
• Some lanthanides (Sm, Eu, Yb, Tm) retain the configuration [Xe]4fⁿ6s² rather than adopting 5d¹, due to the extra stability of half-filled and fully filled f-subshells

Magnetic Properties: Paramagnetism in lanthanides arises from unpaired f-electrons. The magnetic moment can be calculated using the spin-only formula: μ = √[n(n+2)] BM, where n = number of unpaired electrons. However, lanthanides show deviations from spin-only values because orbital angular momentum is not fully quenched (L ≠ 0). The effective magnetic moment is μ_eff = √[4S(S+1) + L(L+1)] BM. Gd³⁺ (4f⁷, S = 7/2) is the most paramagnetic ion in the series with μ ≈ 7.94 BM.

Separation of Lanthanides — Ion Exchange Method: Individual lanthanides have very similar chemical properties, making separation extremely difficult. The ion exchange method exploits the slight differences in stability of lanthanide complexes with complexing agents like ammonium citrate or EDTA. The process:

1. Lanthanide ions are passed through a cation exchange resin (e.g., Dowex 50)
2. All Ln³⁺ ions are retained on the resin due to similar charge density
3. An eluting solution (e.g., ammonium citrate buffer, pH ~6) is passed through
4. Slightly more stable complexes (heavier lanthanides with smaller ionic radii form stronger complexes) move faster and elute first
5. Fractions are collected and analysed by spectroscopy

This method can achieve >99.99% purity for individual lanthanides. Solvent extraction is an alternative based on partition coefficients between two immiscible solvents.

Comparison Table of Lanthanide Properties:

Element	Symbol	Z	Electronic Config	Ionic Radius Ln³⁺ (pm)	Common Oxidation State
Lanthanum	La	57	[Xe]5d¹6s²	116	+3
Cerium	Ce	58	[Xe]4f¹5d¹6s²	111	+3, +4
Praseodymium	Pr	59	[Xe]4f³6s²	113	+3, +4
Neodymium	Nd	60	[Xe]4f⁴6s²	109	+3
Samarium	Sm	62	[Xe]4f⁶6s²	107	+2, +3
Gadolinium	Gd	64	[Xe]4f⁷5d¹6s²	105	+3
Terbium	Tb	65	[Xe]4f⁹6s²	103	+3, +4
Ytterbium	Yb	70	[Xe]4f¹⁴6s²	86	+2, +3
Lutetium	Lu	71	[Xe]4f¹⁴5d¹6s²	85	+3

Actinide Series: The actinides fill the 5f subshell. Unlike lanthanides, actinides show extensive oxidation state variation. Thorium shows +4 (most stable), Protactinium +4/+5, Uranium +3 to +6 (most stable +6), Neptunium +3 to +7, Plutonium +3 to +7 (most stable +4). The 5f electrons participate more in bonding, making actinide chemistry richer but more complex.

JEE Advanced Problem-Solving Tip: When asked about separation of lanthanides, ion exchange is the most common method tested. For contraction consequences, focus on the Zr/Hf pair and Nb/Ta pair as classic examples where similarity in properties makes separation difficult.

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🔴 Extended — Deep Study (3mo+)

Comprehensive theory for complete mastery of f-block chemistry.

Detailed Treatment of Lanthanide Contraction

The lanthanide contraction has three measurable consequences that JEE Advanced examiners frequently probe:

1. Similar radii in transition series: Zr (atomic radius 160 pm) and Hf (159 pm) are nearly identical in size. This occurs because the reduction in atomic size from the lanthanide contraction (+4f electrons have very poor shielding, 0.35 of d-electron shielding) exactly compensates for the normal periodic decrease. The same applies to Nb/Ta and Mo/W pairs.

2. Basicity of Ln³⁺ ions: Basicity is inversely related to charge density. La³⁺ has the largest ionic radius (103 pm, coordination number 6) and therefore the lowest charge density, making it the most basic. As ionic radius decreases across the series, charge density increases, making cations more acidic (harder Lewis acids). This affects their behaviour in complexes: heavier lanthanides form more stable complexes with ligands like EDTA.

3. Progressive change in properties: Colour, magnetic moment, and standard electrode potentials all vary systematically. For example, La³⁺ is colourless (4f⁰), while many Ln³⁺ ions are coloured due to f-f transitions. Gd³⁺ (4f⁷) is colourless; Tb³⁺ (4f⁸) is greenish; Tm³⁺ (4f¹²) is green; Yb³⁺ (4f¹³) is colourless.

Derivation of Ionic Radii Contraction:

The contraction arises from inadequate shielding by 4f electrons. As nuclear charge increases by +1 across the series, the added electron enters a 4f orbital that provides only 0.35 units of shielding per electron (compared to 1.0 for s-electrons). The net effect: Z_eff increases, and electrons are drawn closer.

Ionic radius of Ln³⁺ can be estimated: r(Ln³⁺) ≈ r(La³⁺) − k(n − 1), where n is the position in series and k ≈ 1.5–1.8 pm per element. For example: r(La³⁺) = 116 pm, r(Lu³⁺) = 85 pm, giving a total contraction of ~31 pm across 14 elements.

Actinide Contraction and Transactinide Elements: The actinide contraction parallels the lanthanide contraction: successive addition of protons draws 5f electrons inward, reducing ionic radii from Ac³⁺ (~111 pm) to Lr³⁺ (~97 pm). Beyond the actinides, the 6d and 7s shells are affected. The Rutherfordium (Rf, Z = 104) through Copernicium (Cn, Z = 112) elements belong to periods 7, showing properties dominated by relativistic effects.

Standard Electrode Potentials:

E°(Ln³⁺/Ln) becomes increasingly negative across the series (La³⁺: −2.52 V to Lu³⁺: −2.25 V), meaning La is the most electropositive. This has practical consequences for extraction: lanthanides are obtained by reduction of their oxides with calcium or aluminium.

Contraction Consequences — Worked JEE Problem: Q: Why is the separation of Zr and Hf difficult? A: Due to lanthanide contraction, Zr (Z = 40) and Hf (Z = 72) have nearly identical ionic radii (Zr⁴⁺ = 74 pm, Hf⁴⁺ = 71 pm). They have identical coordination geometry and form complexes of similar stability, making separation by fractional crystallisation or precipitation extremely difficult. Instead, ion exchange or solvent extraction is employed.

Applications in JEE Context:

• Lanthanide oxides (La₂O₃, Nd₂O₃) used in ceramics and lasers
• Gadolinium compounds as MRI contrast agents
• Uranium and thorium in nuclear reactors
• Cerium(IV) sulphate as an oxidising agent in redox titrations

Previous Year JEE Advanced Patterns: Topics that appear repeatedly in JEE Advanced (2015–2024):

1. Lanthanide contraction: consequences on second/third transition series (~2 questions per 3 years)
2. Ion exchange separation: procedure and principle (~1 question per 2 years)
3. Actinide oxidation states: especially uranium chemistry (~1 question per 3 years)
4. Magnetic moments: calculation of unpaired electrons and μ values (~1 question per 4 years)

Numerical problems often involve calculation of magnetic moment: for Gd³⁺ (4f⁷), n = 7, μ = √[7×9] = √63 = 7.94 BM, which matches the experimental value of 7.9–8.0 BM.

Key Differences — Lanthanides vs Actinides:

Property	Lanthanides	Actinides
f-subshell	4f (filled gradually)	5f (filled gradually)
Common oxidation state	+3 only	+3, +4, +5, +6, +7
f-electron involvement	Largely core-like	Actively participate in bonding
Magnetic properties	Simple paramagnetism	Complex (both orbital + spin)
Radioactivity	Only Pm is radioactive	All are radioactive
Separation difficulty	Moderate	Very high (especially Pa)

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