Class 12 Chemistry Chapter 4 The d- and f-Block Elements — Formulas & Key Points

The electronic configuration of d-block elements follows the Aufbau principle with (n-1)d and ns orbitals. Transition elements have incompletely filled d-orbitals in their ground state or common oxidation states. The general configuration for first transition series (3d series) is [Ar] 3d¹⁻¹⁰ 4s¹⁻². Exceptions arise due to extra stability of half-filled and fully filled d-orbitals: Cr is [Ar] 3d⁵ 4s¹ (not 3d⁴ 4s²) and Cu is [Ar] 3d¹⁰ 4s¹ (not 3d⁹ 4s²). For lanthanoids, the general configuration is [Xe] 4f¹⁻¹⁴ 5d⁰⁻¹ 6s². Actinoids follow [Rn] 5f¹⁻¹⁴ 6d⁰⁻¹ 7s². These configurations determine oxidation states, magnetic properties, and chemical behaviour. Always write the ns electrons before (n-1)d in ground state configuration, but remember electrons are lost first from ns orbital during ionization.

The magnetic moment (μ) of a transition metal ion is calculated using the spin-only formula: μ = √(n(n+2)) BM (Bohr Magneton), where n is the number of unpaired electrons. This formula works well for first transition series compounds. Substances with unpaired electrons are paramagnetic (attracted to magnetic field), while those with all paired electrons are diamagnetic (repelled). To find n, write the electronic configuration of the ion and count unpaired electrons in d-orbitals. For example, Cu²⁺ has configuration [Ar] 3d⁹ with one unpaired electron, so μ = √(1×3) = 1.73 BM. This calculation appears frequently in CBSE board exams worth 2-3 marks. Remember to express your final answer in Bohr Magneton (BM) units. Higher values indicate stronger paramagnetism.

Transition elements exhibit multiple oxidation states because the energies of (n-1)d and ns orbitals are comparable, allowing variable electron participation in bonding. For first transition series (Sc to Zn), common oxidation states range from +2 to +7. Manganese shows maximum oxidation states from +2 to +7 due to availability of five 3d electrons plus two 4s electrons. Higher oxidation states are stabilized by small, highly electronegative atoms like O and F (e.g., MnO₄⁻ has Mn in +7 state). Lower oxidation states are found with electropositive elements. The +2 oxidation state is common across the series as it results from loss of two 4s electrons. Stability of higher oxidation states decreases across the period: for example, Fe³⁺ is more stable than Fe²⁺, but Cu²⁺ is more stable than Cu⁺. In the second and third transition series, higher oxidation states become more stable due to larger size and better orbital overlap.

Most transition metal compounds are coloured due to d-d electronic transitions. When white light falls on a compound with partially filled d-orbitals, electrons absorb specific wavelengths to jump from lower to higher energy d-orbitals. The complementary colour (wavelength not absorbed) is observed. This phenomenon occurs only when d-orbitals are partially filled (d¹ to d⁹). Compounds with d⁰ (Sc³⁺, Ti⁴⁺) or d¹⁰ (Zn²⁺, Cu⁺) configurations are colourless or white because no d-d transition is possible. The specific colour depends on the crystal field splitting energy (Δ) which varies with ligand and metal oxidation state. For example, Cu²⁺ solutions appear blue, Cr³⁺ compounds are green, and KMnO₄ is purple. In lanthanoids, colour arises from f-f transitions (weaker, hence paler colours). Charge transfer transitions (like in KMnO₄) produce intense colours as electrons move between metal and ligand orbitals.

Lanthanoid contraction refers to the steady decrease in atomic and ionic radii of lanthanoid elements from lanthanum (La) to lutetium (Lu) as we move across the 4f series. This occurs because the addition of each electron to 4f orbital does not effectively shield the increasing nuclear charge. 4f electrons have poor shielding ability compared to s, p, or d electrons due to their diffused shape. As a result, the effective nuclear charge experienced by outer electrons increases, pulling them closer to the nucleus and reducing the radius. The magnitude of contraction is approximately 10-12 pm across the series. Consequences include: (i) similar radii of second and third transition series elements (Zr and Hf have nearly identical radii), (ii) lanthanoids show similar chemical properties making separation difficult, (iii) basic strength decreases from La(OH)₃ to Lu(OH)₃, and (iv) higher ionization energies across the series.

Transition metals and their compounds act as excellent catalysts in industrial and biological processes due to: (i) ability to show variable oxidation states, allowing them to form intermediate compounds and provide alternate reaction pathways with lower activation energy, (ii) large surface area when finely divided, providing more active sites for reactant adsorption, and (iii) ability to form complexes with reactants, bringing them into close proximity. Examples include: Fe in Haber process (N₂ + 3H₂ → 2NH₃), V₂O₅ in Contact process (2SO₂ + O₂ → 2SO₃), Ni in vegetable oil hydrogenation, Pt in catalytic converters, and MnO₂ in decomposition of KClO₃. The metal provides a surface where bonds in reactant molecules weaken, facilitating reaction. Transition metal ions in enzymes (like Fe in cytochromes, Co in vitamin B₁₂) catalyze biological redox reactions. The catalyst itself remains unchanged at the end of the reaction.

Though both belong to f-block, actinoids (5f series, Th to Lr) differ from lanthanoids (4f series, Ce to Lu) in several aspects. All actinoids are radioactive due to unstable nuclei, while lanthanoids (except promethium) are non-radioactive. Actinoids exhibit a wider range of oxidation states (+3 to +7), whereas lanthanoids predominantly show +3 state. This is because 5f, 6d, and 7s orbitals have comparable energies in actinoids. Actinoid contraction is greater than lanthanoid contraction due to poorer shielding by 5f electrons. Actinoids form more stable complexes than lanthanoids because 5f orbitals are less shielded and can participate more in bonding. Examples: U shows +3, +4, +5, +6 states; Pu shows +3 to +7. Lanthanoids like Ce, Tb can show +4, but +3 dominates. Uranium and plutonium are important for nuclear energy applications.

Transition elements are d-block elements that have partially filled d-orbitals in their ground state or in any stable oxidation state. Note: Zn, Cd, Hg are NOT transition elements as they have completely filled d¹⁰ configuration. Inner transition elements are f-block elements (lanthanoids and actinoids) in which the last electron enters f-orbitals. Interstitial compounds are non-stoichiometric compounds formed when small atoms (H, C, N) occupy interstitial voids in the crystal lattice of transition metals (examples: TiH, VH₀.₅₆, Fe₃C). These retain metallic properties like conductivity but are harder and less malleable. Alloys are homogeneous mixtures of two or more metals (or metals with non-metals) with enhanced properties: steel (Fe + C), bronze (Cu + Sn), brass (Cu + Zn). Crystal field splitting energy (Δ) is the energy difference between split d-orbitals in the presence of ligands. Spectrochemical series ranks ligands by their splitting ability: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO.

Students often make avoidable errors in d- and f-block element questions. When writing electronic configurations, never write 4s electrons after 3d in ground state atoms (wrong: 3d⁶ 4s², correct: [Ar] 3d⁶ 4s² or better [Ar] 4s² 3d⁶ in filling order). However, during ionization, remove 4s electrons first, not 3d. For magnetic moment, always express the answer in Bohr Magneton (BM) units; writing just the number without BM loses marks. Do not confuse lanthanoid contraction (within lanthanoids) with the consequence that affects Zr-Hf pair. When calculating oxidation state of metals in compounds, remember oxygen is usually -2 (except in peroxides -1 and superoxides -½) and hydrogen is +1 (except in metal hydrides -1). For K₂Cr₂O₇, the oxidation state of Cr is +6, not +12 (common mistake of counting two Cr atoms). In formula writing, check charge balance: potassium dichromate is K₂Cr₂O₇, not KCr₂O₇. Always write lanthanoids and actinoids, not lanthanides/actinides in CBSE board exams.

For electronic configuration exceptions in 3d series, remember the phrase 'Copper and Chromium are half-full and full happy' — Cr prefers [Ar] 3d⁵ 4s¹ (half-filled d-orbital) and Cu prefers [Ar] 3d¹⁰ 4s¹ (fully filled d-orbital) over expected configurations. To recall which transition metal ions are colourless, use 'Scooter Tightens Zinc': Sc³⁺ (d⁰), Ti⁴⁺ (d⁰), Zn²⁺ (d¹⁰) are colourless. For lanthanoid contraction consequences, remember 'Z-H twins': Zr and Hf are like twins with similar size and properties. For catalytic reactions, 'FVNP Metals': Fe (Haber), V₂O₅ (Contact), Ni (Hydrogenation), Pt (Catalytic converter). Oxidation state stability: 'Iron prefers three, Copper prefers two' — Fe³⁺ is more stable than Fe²⁺ in aqueous solution, while Cu²⁺ is more stable than Cu⁺. For f-block, remember 'Lanthanoids are Lazy with +3' (predominantly show +3), while 'Actinoids Are Ambitious' (show multiple oxidation states from +3 to +7).

Transition elements: (n-1)d¹⁻⁹ ns¹⁻² || Exceptions: Cr [Ar]3d⁵4s¹, Cu [Ar]3d¹⁰4s¹ || Magnetic moment: μ = √(n(n+2)) BM where n = unpaired e⁻ || Colourless ions: Sc³⁺(d⁰), Ti⁴⁺(d⁰), Zn²⁺(d¹⁰) || Variable oxidation states: due to comparable (n-1)d and ns energies || Mn shows max states: +2 to +7 || Colour: d-d transition in d¹ to d⁹ ions || Lanthanoid contraction: decrease in radii La→Lu due to poor 4f shielding (10-12 pm) || Consequence: Zr ≈ Hf in size || Catalysts: Fe(Haber), V₂O₅(Contact), Ni(Hydrogenation), Pt(Converters) || Interstitial compounds: TiH, VH, Fe₃C (small atoms in metal voids) || Actinoids: radioactive, +3 to +7 states, 5f filling || Lanthanoids: mostly +3 state, 4f filling, non-radioactive (except Pm) || Stability: Fe³⁺>Fe²⁺, Cu²⁺>Cu⁺ || KMnO₄: Mn is +7 || K₂Cr₂O₇: Cr is +6 || Always ionize ns before (n-1)d.

Use these quick-lookup tables during numerical problem-solving and last-minute revision. The first table lists all key formulas with when to apply them. The second table summarizes important properties across the first transition series (Sc to Zn). The third table contrasts lanthanoids and actinoids on multiple parameters. Keep these tables bookmarked for rapid reference during mock tests and actual board exam preparation. CBSETUTOR.ai offers a 24×7 AI tutor where you can upload a photo of any numerical problem from this chapter (like calculating magnetic moment or oxidation states) and get instant step-by-step solutions, explanations of concepts, and tips for board exam marking schemes — all at a flat ₹999/month covering every subject for Classes 6-12, with a 3-day free trial so you can test it during your Chapter 4 revision itself.