d-Block & f-Block Elements – Chemistry Study Notes

General Characteristics and Electronic Configurations of d-Block Elements

Transition elements are strictly defined as elements that have incompletely filled d-subshells either in their ground state or in one of their common oxidation states. According to this definition, zinc, cadmium, and mercury (Group 12) have full d¹⁰ configurations in both their atomic and common ionic states, and therefore are not true transition elements, although they are studied alongside d-block chemistry due to similar physical and chemical behaviors. The general outer electronic configuration of d-block elements is represented as (n-1)d^1-10 ns^1-2.

The d-block is divided into four distinct series based on the principal quantum number of the filling d-orbitals: the 3d-series (Sc to Zn, Period 4), the 4d-series (Y to Cd, Period 5), the 5d-series (La, Hf to Hg, Period 6), and the incomplete 6d-series (Ac, Rf to Cn, Period 7). Exceptional electronic configurations, such as those seen in Chromium (Cr: 3d⁵4s¹) and Copper (Cu: 3d¹⁰4s¹), arise due to the extra stability associated with exactly half-filled and completely filled subshells, paired with small inter-electronic repulsion and exchange energy stabilization.

Metallic radii across a transition series show a distinct trend. As we move across a period from left to right, atomic and ionic radii initially decrease because the effective nuclear charge increases while the added electrons enter the inner (n-1)d orbitals, providing imperfect shielding. However, near the middle of the series, the radii remain nearly constant (zero-slope region), and towards the end, they expand slightly due to electron-electron repulsions overpowering nuclear attraction. In heavier transition series (4d and 5d), the lanthanoid contraction—the progressive decrease in atomic and ionic radii along the lanthanoid series—leads to the 5d series elements having nearly identical radii to their 4d period counterparts.

Oxidation States and Standard Electrode Potentials

Unlike s-block elements, transition metals exhibit a wide array of variable oxidation states because the energy gap between the outermost ns and penultimate (n-1)d orbitals is exceptionally small, allowing electrons from both subshells to participate in chemical bonding. The minimum oxidation state is equal to the number of valence ns electrons, while the maximum oxidation state corresponds to the sum of the ns and unpaired (n-1)d electrons.

For example, Manganese (Mn) exhibits oxidation states ranging from +2 to +7 in compounds like $\text{MnO}_4^-$, displaying a maximum of 7 corresponding to its $3d^54s^2$ configuration. Higher oxidation states are most commonly stabilized by highly electronegative and small-sized atoms such as fluorine and oxygen, yielding species like $\text{OsO}_4$ and $\text{VF}_5$. Conversely, lower oxidation states are stabilized by $\pi$-acid ligands like carbon monoxide ($\text{CO}$), forming metal carbonyls through synergic bonding.

Standard Electrode Potentials ($E^\circ$): The trends in $M^{2+}/M$ standard reduction potentials do not follow a smooth monotonic curve across a transition series. The irregularity is governed by the net sum of enthalpy changes including sublimation enthalpy, ionization enthalpy, and hydration enthalpy. Notably, the high negative value for Mn, Ni, and positive or less negative values for elements like Cu ($E^\circ = +0.34\text{ V}$) reflect the unique hydration energies and stability of particular d-electron counts, such as the stability of half-filled ($d^5$) and fully-filled ($d^{10}$) configurations.

Magnetic Properties, Colored Ions, and Complex Formation

Most transition metal ions and their compounds are distinctly colored in solid and solution states. This coloration arises primarily due to d-d electronic transitions. When ligands approach a transition metal ion in a coordination sphere, the degeneracy of the five d-orbitals is lifted (crystal field splitting, $\Delta_0$). Photons in the visible region of the spectrum are absorbed, promoting an electron from a lower-energy d-orbital to a higher-energy d-orbital. The observed color is complementary to the color of the light absorbed. Ions with $d^0$ or $d^{10}$ configurations, such as $\text{Sc}^{3+}$ and $\text{Zn}^{2+}$, are colorless due to the absence of d-d transitions.

Transition metal compounds are generally paramagnetic, meaning they are attracted by an external magnetic field, due to the presence of one or more unpaired electrons in their d-orbitals. The magnetic moment can be calculated using the spin-only formula:

$$\mu = \sqrt{n(n+2)} \text{ Bohr Magnetons (BM)}$$

where $n$ represents the number of unpaired electrons. As the number of unpaired electrons increases, the magnetic moment increases linearly up to $d^5$, after which it decreases for $d^6$ to $d^{10}$ configurations.

Transition metals possess high tendencies to form coordination complexes because of three primary factors:

• Small size and high nuclear charge density of the metal ions.
• Availability of vacant d-orbitals of appropriate energy to accept lone pairs of electrons donated by ligands.
• Variable oxidation states that accommodate different types of donor atoms.

f-Block Elements: Lanthanoids and Actinoids

The f-block elements consist of two series corresponding to the filling of 4f and 5f orbitals: the lanthanoids (14 elements from Cerium, $\text{Ce}_{58}$, to Lutetium, $\text{Lu}_{71}$) and the actinoids (14 elements from Thorium, $\text{Th}_{90}$, to Lawrencium, $\text{Lr}_{103}$). They are frequently termed inner-transition elements because they form an inner transition series within the transition series.

The general electronic configuration for lanthanoids is [Xe] 4f^1-14 5d^0-1 6s², while for actinoids it is [Rn] 5f^1-14 6d^0-2 7s². Because 4f orbitals are deeply buried inside the atom and effectively shielded by outer 5s and 5p electrons, 4f electrons do not participate actively in bonding. Consequently, lanthanoids exhibit a dominant +3 oxidation state, with occasional +2 and +4 states occurring only when they lead to a stable empty ($f^0$), half-filled ($f^7$), or completely filled ($f^{14}$) configuration (e.g., $\text{Ce}^{4+}$, $\text{Eu}^{2+}$, $\text{Tb}^{4+}$).

The defining chemical and physical consequence of the lanthanoid series is the lanthanoid contraction—the steady decrease in atomic and ionic radii from La to Lu. Poor shielding of nuclear charge by the 4f electrons causes the effective nuclear charge to pull the outer shell inward. This contraction explains why the atomic radii of second and third-row transition elements (such as Zr and Hf) are nearly identical, making their separation chemically challenging.

Unlike lanthanoids, actinoids display a much wider range of oxidation states (+3, +4, +5, +6, and +7) because the 5f, 6d, and 7s orbitals are comparable in energy. Furthermore, all actinoids are strictly radioactive, and many of the heavier members (transuranic elements beyond uranium) are synthetically produced in laboratories via nuclear bombardment.

Key Points to Remember

• Zinc, Cadmium, and Mercury are not considered true transition elements as they possess completely filled $(n-1)d^{10}$ configurations in both elemental and common ionic states.
• Anomalous configurations like $\text{Cr}$ ($3d^5 4s^1$) and $\text{Cu}$ ($3d^{10} 4s^1$) maximize exchange energy and symmetry stability.
• Lanthanoid contraction results in the near-identical atomic radii of 4d and 5d transition series elements (e.g., Zirconium and Hafnium).
• Manganese exhibits the highest common oxidation state of +7 in the 3d series ($\text{MnO}_4^-$).
• Spin-only magnetic moment formula: $\mu = \sqrt{n(n+2)}$ BM, where $n$ is the number of unpaired electrons.
• Color of transition metal ions is attributed to d-d transitions facilitated by crystal field splitting in coordination complexes.
• Lanthanoids predominantly display a +3 oxidation state, whereas actinoids exhibit varied and higher oxidation states due to comparable 5f and 6d orbital energies.

Important Facts / Formulas

Previous Year Question Hints

1. Magnetic Moment Calculation: Expect numerical questions asking to compute the spin-only magnetic moment of ions like $\text{Fe}^{3+}$ ($d^5$) or $\text{Co}^{2+}$ ($d^7$). Remember to correctly count the unpaired electrons based on the electronic configuration.
2. Identification of Colorless Ions: Questions frequently test conceptual understanding of d-d transitions. Remember that ions with $d^0$ (e.g., $\text{Sc}^{3+}$, $\text{Ti}^{4+}$) or $d^{10}$ (e.g., $\text{Zn}^{2+}$, $\text{Cu}^+$) configurations are colorless.
3. Consequences of Lanthanoid Contraction: Be prepared for conceptual questions explaining why elements of the 4d and 5d series (such as Nb and Ta, or Zr and Hf) possess virtually identical chemical properties and atomic sizes.

Quick Revision Summary

• Transition elements require partially filled d-orbitals in their elemental or ionic states.
• Half-filled ($d^5$) and fully-filled ($d^{10}$) subshells impart extra stability, explaining electronic anomalies in Cr and Cu.
• Variable oxidation states arise due to the small energy difference between $(n-1)d$ and $ns$ orbitals.
• Standard electrode potentials show irregular trends across periods due to competing sublimation, ionization, and hydration energies.
• Colors in transition metal complexes are caused by d-d electron excitation driven by crystal field splitting.
• Paramagnetism is directly proportional to the number of unpaired d-electrons via the spin-only formula.
• Lanthanoids show a prominent +3 oxidation state and undergo lanthanoid contraction, affecting the periodic table down the groups.
• Actinoids are radioactive inner-transition elements with multiple accessible oxidation states due to close 5f and 6d energy levels.