F Block — Concepts, Formulas & Examples

The f-block elements are the two rows at the bottom of the periodic table. Lanthanides (4f) and actinides (5f). CBSE Class 12 and NEET test properties, the lanthanoid contraction and key uses.

Core Concepts

Lanthanides

14 elements from Ce to Lu. Commonly known as rare earths (though not actually rare). All show +3 oxidation state. Used in magnets (neodymium), phosphors (europium in screens) and catalysts.

Electronic configuration: The general configuration is $[\text{Xe}] 4f^{1-14} 5d^{0-1} 6s^2$ . The 4f orbitals are being progressively filled. Some irregularities occur because of the extra stability of half-filled ( $f^7$ ) and completely filled ( $f^{14}$ ) configurations.

Element	Symbol	Atomic No.	Config (beyond Xe)	Common OS
Cerium	Ce	58	$4f^1 5d^1 6s^2$	+3, +4
Europium	Eu	63	$4f^7 6s^2$	+3, +2
Gadolinium	Gd	64	$4f^7 5d^1 6s^2$	+3
Terbium	Tb	65	$4f^9 6s^2$	+3, +4
Ytterbium	Yb	70	$4f^{14} 6s^2$	+3, +2
Lutetium	Lu	71	$4f^{14} 5d^1 6s^2$	+3

Why +2 for Eu and Yb: Eu ( $4f^7$ ) and Yb ( $4f^{14}$ ) achieve extra-stable half-filled and fully-filled f configurations by losing only 2 electrons instead of 3. Ce and Tb show +4 because losing one extra electron gives them $4f^0$ and $4f^7$ respectively.

Colour: Most Ln $^{3+}$ ions are coloured due to f-f electronic transitions. These transitions are Laporte-forbidden (weak), so the colours are pale. Ce $^{3+}$ is colourless ( $4f^1$ — no f-f transition possible in the same way); La $^{3+}$ and Lu $^{3+}$ are also colourless ( $4f^0$ and $4f^{14}$ ).

Actinides

14 elements from Th to Lr. All radioactive. Natural only up to uranium; transuranium elements are synthetic. Used in nuclear reactors (U, Pu), smoke detectors (Am) and weapons.

Electronic configuration: $[\text{Rn}] 5f^{0-14} 6d^{0-2} 7s^2$ . The energy gap between 5f, 6d, and 7s orbitals is much smaller than the corresponding gap in lanthanides. This leads to more irregularities in configuration and a wider range of oxidation states.

Key actinides:

Thorium (Th): Most stable actinide, potential nuclear fuel. Half-life of Th-232: $1.4 \times 10^{10}$ years.
Uranium (U): Natural nuclear fuel. U-235 undergoes fission; only 0.7% of natural uranium is U-235 (rest is U-238). Enrichment is needed for reactors.
Plutonium (Pu): Synthetic, made in reactors from U-238. Pu-239 is used in nuclear weapons and fast breeder reactors.
Americium (Am): Am-241 is used in smoke detectors — it emits alpha particles that ionise air and allow current flow; smoke disrupts this current.

Lanthanoid contraction

Gradual decrease in atomic and ionic size across the lanthanide series. Caused by poor shielding by 4f electrons. Consequences — similar sizes of Zr and Hf (hard to separate), similar properties of 4d and 5d transition metals.

The ionic radius of Ln $^{3+}$ decreases steadily from Ce $^{3+}$ (103.4 pm) to Lu $^{3+}$ (86.1 pm).

Cause: 4f electrons have poor shielding efficiency. As each new proton is added to the nucleus, the 4f electron added does not fully shield the outer electrons. The effective nuclear charge ( $Z_{eff}$ ) felt by outer electrons increases, pulling them closer.

Consequences of lanthanoid contraction:

Zr and Hf have nearly identical radii: Zr $^{4+}$ = 79 pm, Hf $^{4+}$ = 78 pm. Hf comes after the lanthanides, so the contraction compensates for the expected size increase down the group. Separating Zr and Hf was one of the hardest problems in analytical chemistry.
Similar chemistry of 4d and 5d metals: Because of lanthanoid contraction, pairs like Zr/Hf, Nb/Ta, Mo/W have remarkably similar properties. This is why tungsten (5d) can substitute for molybdenum (4d) in many alloys.
Basicity decreases across the series: Smaller Ln $^{3+}$ ions have higher charge density and hold the OH $^-$ more tightly. Ce(OH) $_3$ is the most basic; Lu(OH) $_3$ is the least. This basicity difference is used to separate lanthanides by selective precipitation or ion exchange.

Oxidation states

Lanthanides mostly +3; a few show +2 or +4. Actinides show a wider range, +3 to +6 or higher (U shows +3, +4, +5, +6). Greater variability in actinides due to similar energies of 5f, 6d and 7s orbitals.

Comparison:

Property	Lanthanides	Actinides
Dominant OS	+3	+3 to +6
Variable OS elements	Ce(+4), Eu(+2), Yb(+2)	U(+3 to +6), Np, Pu (wide range)
Reason for variability	4f electrons are buried deep	5f, 6d, 7s are close in energy
Ionisation energy trend	Relatively uniform	More irregular

Magnetic properties

Most Ln $^{3+}$ ions are paramagnetic because they have unpaired f electrons. The magnetic moment for lanthanides is calculated using:

\mu = g\sqrt{J(J+1)}\;\mu_B

Where $g$ is the Lande g-factor and $J$ is the total angular momentum quantum number. This is different from the spin-only formula used for d-block elements because orbital contribution is significant in f-block (unlike quenched orbital moments in d-block).

Gd $^{3+}$ ( $4f^7$ ) has 7 unpaired electrons and the highest magnetic moment among Ln $^{3+}$ ions — used in MRI contrast agents (gadolinium-DTPA).

Uses

Lanthanides in magnets, lasers, alloys and phosphors. Actinides mainly in nuclear applications — U and Pu as fuel, Am in detectors, Th as potential thorium reactor fuel.

Lanthanide applications:

Nd: Nd $_2$ Fe $_{14}$ B magnets — strongest permanent magnets known. Used in headphones, hard drives, electric motors.
Eu: Red phosphor in TV screens, LED lights, and fluorescent lamps.
Ce: Catalytic converters in cars (CeO $_2$ stores and releases oxygen). Also used as a polishing agent for glass.
La: La-Ni alloy in rechargeable batteries (NiMH batteries in hybrid cars).
Er: Erbium-doped fibre amplifiers — the backbone of internet optical fibre networks.
Mischmetal (alloy of mixed lanthanides): Used in lighter flints and as an additive in steel.

India has significant thorium reserves (especially in Kerala beach sand). Thorium-based nuclear reactors are a part of India’s three-stage nuclear programme. This India-specific detail occasionally appears in competitive exams.

Separation of lanthanides

All lanthanides are similar in size and chemistry, making separation extremely difficult. Methods used:

Ion exchange chromatography: The most effective modern method. Ln $^{3+}$ ions are loaded on a cation exchange resin and eluted with a complexing agent (EDTA or citrate). Smaller ions (heavier lanthanides) are eluted first because they form stronger complexes.
Selective oxidation/reduction: Ce can be oxidised to Ce $^{4+}$ and separated from the +3 lanthanides. Eu can be reduced to Eu $^{2+}$ and precipitated as EuSO $_4$ (insoluble, like BaSO $_4$ ).

Worked Examples

Lanthanoid contraction makes Hf (which follows the lanthanides) almost the same size as Zr (which is a period earlier). Their chemistries are nearly identical.

Losing two 6s electrons and one 5d or 4f electron gives +3 — the most stable configuration. The 4f electrons are too tightly held to be easily removed beyond that.

Eu has electronic configuration $[\text{Xe}] 4f^7 6s^2$ . By losing only 2 electrons (the two 6s), it achieves the extra-stable half-filled $4f^7$ configuration. The stability of this configuration compensates for the energy cost of being in a lower oxidation state than usual.

In actinides, the 5f, 6d, and 7s orbitals are very close in energy. Electrons can be removed from any of these levels without a huge energy penalty. In lanthanides, the 4f orbitals are much lower in energy than 5d, so removing more than one 4f electron is very costly.

Solved Problems (Exam Style)

Problem 1 (NEET pattern): Which lanthanide ion is colourless — La $^{3+}$ , Ce $^{3+}$ , Nd $^{3+}$ , or Gd $^{3+}$ ?

La $^{3+}$ : $4f^0$ — no f electrons, no f-f transitions. Colourless. Gd $^{3+}$ : $4f^7$ — all f electrons are in different orbitals (half-filled). f-f transitions are possible but forbidden. Very pale. La $^{3+}$ is the clearly colourless one. Answer: La $^{3+}$

(Lu $^{3+}$ with $4f^{14}$ is also colourless — fully filled, no f-f transitions.)

Problem 2 (JEE Main pattern): Arrange in order of decreasing ionic radius: La $^{3+}$ , Nd $^{3+}$ , Gd $^{3+}$ , Lu $^{3+}$ .

Ionic radius decreases steadily across the lanthanide series due to poor shielding by 4f electrons.

La $^{3+}$ > Nd $^{3+}$ > Gd $^{3+}$ > Lu $^{3+}$

(La $^{3+}$ = 103.4 pm, Lu $^{3+}$ = 86.1 pm — a decrease of about 17 pm across 14 elements.)

Common Mistakes

Saying all f-block elements are rare. They are not — cerium is more abundant than lead.

Confusing lanthanide and actinide. Lanthanides are 4f; actinides are 5f.

Writing that actinides are all natural. Most are synthetic.

Assuming all Ln $^{3+}$ ions are coloured. La $^{3+}$ ( $4f^0$ ) and Lu $^{3+}$ ( $4f^{14}$ ) are colourless because no f-f transitions are possible.

Using the spin-only formula for lanthanide magnetic moments. Unlike d-block elements, the orbital contribution is not quenched in lanthanides. The full $\mu = g\sqrt{J(J+1)}$ formula must be used.

Exam Weightage and Revision

This topic is a repeat performer in board papers and entrance exams. NEET typically asks one to two questions on the core mechanisms, CBSE boards give three to six marks, and state PMT papers often include a diagram-based long answer. The PYQs cluster around a small set of facts — lock those and you clear the topic.

JEE Main 2023 asked about lanthanoid contraction consequences. NEET 2022 tested +2 oxidation state of Eu. CBSE boards regularly ask about properties and uses of lanthanides. This is a relatively small chapter — 2-3 hours of focused study can lock it completely.

When a question gives a scenario, identify the core mechanism first, then match it to the concepts above. Most wrong answers come from reading the scenario too quickly.

Three facts to lock — lanthanoid contraction, +3 is common, actinides are radioactive.

Practice Questions

Q1. What causes lanthanoid contraction?

Poor shielding by 4f electrons. As we move across the lanthanide series, each additional proton increases the nuclear charge, but the added 4f electron does not effectively shield the outer electrons from this increased charge. The result is a steady increase in effective nuclear charge ( $Z_{eff}$ ), pulling the outer electron cloud inward and decreasing ionic radius.

Q2. Why does cerium show a +4 oxidation state?

Ce has configuration $[\text{Xe}] 4f^1 5d^1 6s^2$ . Losing 4 electrons (2 from 6s, 1 from 5d, 1 from 4f) gives Ce $^{4+}$ with a noble gas-like configuration $[\text{Xe}] 4f^0$ . The completely empty 4f shell is very stable, making +4 a favourable state for cerium. CeO $_2$ and Ce(SO $_4$ ) $_2$ are common Ce(IV) compounds.

Q3. Name the lanthanide used in MRI contrast agents and explain why.

Gadolinium (as Gd-DTPA complex). Gd $^{3+}$ has 7 unpaired electrons ( $4f^7$ ), giving it the highest magnetic moment among lanthanide ions. This strong paramagnetism enhances the relaxation of nearby water protons, improving MRI image contrast. The DTPA chelate is needed to prevent free Gd $^{3+}$ toxicity.

Q4. Why are transuranium elements synthetic?

Elements beyond uranium (Z > 92) are unstable — their nuclei are too large to be held together by the strong nuclear force against the electromagnetic repulsion of so many protons. They undergo radioactive decay with increasingly short half-lives. They must be created artificially by bombarding lighter elements with neutrons or other nuclei in reactors or particle accelerators.

Q5. How are lanthanides separated from each other?

By ion exchange chromatography. Ln $^{3+}$ ions are adsorbed on a cation exchange resin and eluted with a complexing agent like EDTA. Heavier (smaller) lanthanide ions form stronger complexes with EDTA and are eluted first. The slight difference in ionic radii due to lanthanoid contraction is enough to achieve separation.

FAQs

Why are they called rare earth elements if they are not rare? The name dates to the 18th century when these elements were first isolated from rare minerals. They were hard to separate, so people assumed they were scarce. In reality, cerium is about as abundant as copper, and even the least abundant lanthanide (thulium) is more common than gold.

What is the difference between lanthanide and lanthanoid? IUPAC recommends “lanthanoid” (meaning “lanthanide-like”) because the “-ide” suffix usually refers to a negative ion (like chloride). In practice, “lanthanide” is far more commonly used and is acceptable in exams.

Why is thorium considered a future nuclear fuel? Thorium-232 is 3-4 times more abundant than uranium. It can be converted to fissile U-233 in a reactor. Thorium reactors produce less long-lived radioactive waste and are harder to weaponise. India has one of the world’s largest thorium reserves and has a three-stage nuclear programme built around thorium.

Why do actinides have more radioactive isotopes than lanthanides? Actinide nuclei are very large (Z = 89-103). The electrostatic repulsion between protons becomes overwhelming, and the strong nuclear force cannot hold the nucleus together indefinitely. This makes all actinides radioactive, with increasingly short half-lives as atomic number increases.

The f-block is where the periodic table gets interesting. Similar sizes, many uses, and a chemistry worth knowing for modern technology.