d and f Block Elements — Practice Questions with Answers

Transition elements are defined as those having a partially filled d-subshell in either the neutral atom's ground state or in at least one of their commonly observed ions.

Zinc, cadmium, and mercury (Group 12) all have a completely filled $d^{10}$ configuration in both their elemental state and in their common (+2) oxidation state — since they never actually display a partially filled d-subshell in practice, they are generally excluded from strict classification as true transition elements, despite being located within the d-block region of the periodic table.

Across a transition series, additional electrons are added to the inner (n-1)d subshell, rather than directly to the outermost ns valence shell.

Since these newly added d-electrons are relatively effective at shielding the outermost ns electrons from the increasing nuclear charge (compared to how outer-shell electrons shield each other in s/p-block elements), the increase in effective nuclear charge experienced by the outermost electrons across a transition series is comparatively modest — this partial shielding by d-electrons is precisely why the decrease in atomic radius across a transition metal period is comparatively small and gradual, unlike the much more pronounced decrease seen across typical s/p-block periods.

In an isolated, free transition metal ion, all five d-orbitals have equal energy (degenerate). However, when surrounded by ligands (as in a complex ion or coordination compound), these d-orbitals split into groups of slightly different energies.

If the metal ion has partially filled d-orbitals (neither completely empty nor completely full), an electron can absorb a specific, precise amount of energy (corresponding to visible light of a particular wavelength) to transition from a lower-energy d-orbital to a higher-energy one — this selective absorption of specific visible wavelengths (with the complementary, non-absorbed wavelengths being transmitted or reflected) is precisely why many transition metal compounds/ions display characteristic colours.

Transition metals form strong metallic bonds involving not just their outer ns electrons, but also their (n-1)d electrons — this greater number of electrons available for delocalised metallic bonding results in a stronger overall "electron sea" holding the metal atoms together.

This additional d-electron involvement in metallic bonding (beyond just the s-electrons used in typical s-block metallic bonding) results in significantly stronger interatomic attraction throughout the metal lattice, requiring considerably more thermal energy to overcome — this is precisely why transition metals generally have notably higher melting and boiling points compared to s-block metals.

Lanthanide contraction refers to the steady, gradual (though cumulatively significant) decrease in atomic/ionic radii observed across the lanthanide series, caused by the poor shielding ability of the 4f electrons being progressively added across the series.

Consequence: This contraction results in the atomic radii of the third-row transition metals (period 6, immediately following the lanthanides, e.g., Hf, Ta, W) being remarkably similar to their corresponding second-row transition metal counterparts (period 5, e.g., Zr, Nb, Mo) — this similarity in size causes these paired elements to exhibit very similar chemical properties, making their separation and purification notably challenging.

Transition metals' ability to show multiple, readily interconvertible oxidation states allows them to form temporary intermediate complexes with reactant molecules, providing an alternative reaction pathway with lower activation energy compared to the uncatalysed reaction.

Example: Iron (as a catalyst, with molybdenum as a promoter) is used in the Haber process for industrial ammonia synthesis ($N_2+3H_2 \rightleftharpoons 2NH_3$) — the iron catalyst provides a surface where nitrogen and hydrogen molecules can adsorb, weakening their strong bonds and facilitating easier reaction, significantly speeding up the industrially important ammonia production process.

Paramagnetism occurs in species with one or more unpaired electrons — these unpaired electrons possess a net magnetic moment, causing weak attraction towards an externally applied magnetic field.

Diamagnetism occurs in species with all electrons completely paired (no unpaired electrons) — the paired electrons' magnetic moments cancel each other out, resulting in overall zero net magnetic moment, causing weak repulsion from an externally applied magnetic field. The specific electron configuration of a transition metal ion (determined by its identity and oxidation state) directly determines whether it displays paramagnetic or diamagnetic behaviour.

Transition metal ions typically have a relatively small ionic size combined with a high effective nuclear charge and readily available, empty (or partially filled) d-orbitals — this combination gives them significant polarising power and an accessible set of orbitals well-suited for accepting electron pairs donated by surrounding ligands.

S-block metal ions, by contrast, generally have larger ionic size, lower charge density, and lack readily available d-orbitals in their valence shell for this specific purpose — this combination makes s-block metal ions considerably less effective at forming strong, stable coordination bonds with ligands compared to transition metal ions, explaining why complex/coordination compound formation is so much more prevalent and important among transition metals.

Interstitial compounds are formed when small non-metal atoms (such as hydrogen, carbon, boron, or nitrogen) become trapped within the empty spaces (interstices) present in the crystal lattice structure of a transition metal, without significantly altering the metal's original crystal structure.

Characteristic property: Interstitial compounds are typically extremely hard and possess very high melting points (often even higher than the pure metal itself) — this occurs because the trapped interstitial atoms effectively reinforce and rigidify the surrounding metallic lattice, considerably enhancing its mechanical strength and thermal stability.

In actinides, the energy levels of the 5f, 6d, and 7s orbitals are much closer to each other (more comparable in energy) than the corresponding 4f, 5d, and 6s orbitals are in lanthanides.

This closer energy proximity among the relevant actinide orbitals means electrons from more than one of these subshells can participate relatively easily in bonding, giving actinides access to a considerably wider variety of stable oxidation states (e.g., uranium showing +3, +4, +5, and +6 states) — lanthanides, with their more energetically separated 4f orbitals (which participate in bonding far less readily than actinide 5f orbitals), are comparatively restricted, predominantly showing just the single, characteristic +3 oxidation state throughout most of the series.

Fe (Z=26): $[Ar]3d^64s^2$

$Fe^{3+}$: When forming $Fe^{3+}$, three electrons are removed — first the two 4s electrons, then one 3d electron: $[Ar]3d^5$

$Fe^{3+}$ ($3d^5$) is particularly stable because this represents an exactly half-filled d-subshell — each of the five 3d orbitals contains exactly one electron, all with parallel spin, giving maximum exchange energy and a symmetric, especially stable electron distribution, consistent with the general extra-stability associated with half-filled subshells.

$Cu^{2+}$ has electronic configuration $3d^9$ — a partially filled d-subshell (9 out of a possible 10 electrons), meaning there is at least one vacancy available for an electron to transition into upon absorbing an appropriate amount of visible light energy — this d-d transition is precisely what gives $Cu^{2+}$ (and its aqueous solutions/compounds) their characteristic blue colour.

$Cu^+$ has electronic configuration $3d^{10}$ — a completely filled d-subshell, with no available vacant d-orbital positions for an electron to transition into. Since no d-d transition is possible in a completely filled subshell, $Cu^+$ compounds/solutions are typically colourless (or very pale), directly illustrating the fundamental principle that colour in transition metal species specifically requires a partially (not completely) filled d-subshell.

For $Fe^{2+}$ ($3d^6$), following Hund's rule, the electron distribution across the five 3d orbitals gives 4 unpaired electrons (one orbital has a pair, the remaining 4 orbitals each have one unpaired electron).

$\mu = \sqrt{n(n+2)} = \sqrt{4(4+2)} = \sqrt{4\times6} = \sqrt{24}$

$\mu \approx \mathbf{4.90\text{ BM (Bohr Magnetons)}}$

Manganese has 7 valence electrons available for bonding (5 in 3d + 2 in 4s), and since the energy difference between 3d and 4s orbitals in transition metals is very small, varying numbers of these 7 electrons can participate in bonding under different chemical conditions.

This allows manganese to display oxidation states ranging from +2 all the way up to +7 (its maximum possible, corresponding to the loss/use of all 7 valence electrons, as seen in the permanganate ion, $MnO_4^-$) — manganese, positioned in the middle of the first transition series with exactly 7 available valence electrons, is uniquely positioned to show this maximum range of oxidation states, more extensive than elements to either side of it in the series (which have either fewer valence electrons available, or increasingly favour lower oxidation states due to a smaller pool of easily removable electrons).

Actual configuration: $Cr: [Ar]3d^54s^1$

A half-filled d-subshell ($3d^5$) provides extra stability due to symmetric electron distribution across all five d-orbitals (each singly occupied with parallel spin) and maximum favourable exchange energy between these parallel-spin electrons.

Shifting one electron from the 4s orbital into the 3d subshell (achieving this extra-stable $3d^5$ configuration, at the cost of a less-stable, singly-occupied $4s^1$, rather than a filled $4s^2$) results in an overall lower-energy, more thermodynamically stable configuration than the naively "expected" $3d^44s^2$ arrangement — this specific extra stability of the half-filled configuration is precisely why chromium adopts this exceptional electronic configuration.

$Zn^{2+}$ has a completely filled $3d^{10}$ configuration — with no available vacant d-orbital for an electron to transition into upon absorbing visible light, no d-d transition can occur, and $Zn^{2+}$ compounds are consequently colourless.

$Ti^{3+}$ has only 1 electron in its d-subshell ($3d^1$) — this single electron can readily absorb an appropriate amount of visible light energy and transition to a higher-energy d-orbital (once split by surrounding ligands in a complex) — this available d-d transition pathway (present because the d-subshell is neither empty nor completely full) is precisely why $Ti^{3+}$ compounds/solutions display a characteristic (typically violet/purple) colour, contrasting directly with the colourless $Zn^{2+}$.

Normally, moving down a group (from period 5 to period 6) would be expected to result in a significant increase in atomic radius, due to the addition of an entire extra electron shell.

However, hafnium immediately follows the entire lanthanide series in the periodic table — the cumulative "lanthanide contraction" occurring across these 14 intervening lanthanide elements (due to poor shielding by the progressively added 4f electrons) causes a substantial decrease in atomic radius that almost exactly offsets/cancels the expected radius increase from adding the new electron shell.

This near-perfect cancellation between the expected group-based radius increase and the lanthanide contraction's radius decrease is precisely why zirconium and hafnium end up with almost identical atomic radii, despite hafnium's substantially higher atomic number — this remarkable similarity also explains why these two elements show such closely comparable chemical properties, historically making their separation notably difficult.

$Mn^{2+}$ has configuration $3d^5$ — following Hund's rule, all five electrons occupy the five separate 3d orbitals singly, with parallel spins (a half-filled subshell), giving 5 unpaired electrons.

Spin-only magnetic moment: $\mu = \sqrt{n(n+2)} = \sqrt{5(5+2)} = \sqrt{5\times7} = \sqrt{35}$

$\mu \approx \mathbf{5.92\text{ BM}}$ — this is actually the maximum possible spin-only magnetic moment among the common first-row transition metal ions, directly reflecting its maximum possible number (5) of unpaired electrons.

Enthalpy of atomisation (the energy required to convert one mole of solid metal into isolated gaseous atoms) is generally high for transition metals because they form strong metallic bonds involving both their ns and (n-1)d electrons — this greater number of bonding electrons (compared to typical s-block metals) results in stronger interatomic metallic bonding throughout the solid lattice.

Highest atomisation enthalpy: Among the first-row transition series, elements positioned roughly in the middle of the series (with the maximum number of unpaired d-electrons available for strong metallic bonding, before significant electron pairing occurs later in the series) — such as vanadium (V), tend to show particularly high atomisation enthalpies, since a greater number of unpaired d-electrons directly correlates with stronger metallic bonding within the solid.

$Sc^{3+}$ forms by removing all three of scandium's valence electrons (2 from 4s, 1 from 3d), leaving it with a completely empty d-subshell configuration ($3d^0$) — identical in electron count to the preceding noble gas, argon.

Since $Sc^{3+}$ has no d-electrons at all, no d-d electronic transition is possible upon absorption of visible light — this is precisely why $Sc^{3+}$ compounds are consistently colourless, unlike most other transition metal ions with partially filled d-subshells.

Furthermore, since $Sc^{3+}$ has no partially filled d-subshell in its only commonly observed oxidation state (+3), it technically fails the strict definition of a transition element (requiring a partially filled d-subshell in the element or at least one of its common ions) — this is precisely why scandium, despite its position within the d-block of the periodic table, is sometimes noted as not displaying fully typical transition metal characteristics in its most common (+3) oxidation state.