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Chemistry · Ch 4 — The d- and f-Block Elements

Variation in Atomic and Ionic Sizes of Transition Metals

4.3.2

Variation in Atomic and Ionic Sizes of Transition Metals

The General Trend Within a Series

For ions of a given charge within one transition series, radius decreases steadily as atomic number increases. The reason is the same poor-shielding argument that recurs throughout this chapter: each time the nuclear charge goes up by one unit, the new electron being added enters a dd orbital, and dd electrons are not very effective at shielding one another from the nucleus. Because the shielding added is smaller than the increase in nuclear charge, the net electrostatic pull that the nucleus exerts on the outermost electron keeps increasing, and so ionic radius contracts. Atomic radii within a series follow the same downward trend, though here the change is comparatively small.

Comparing the 3dd, 4dd and 5dd Series — Lanthanoid Contraction

A more striking comparison emerges when the sizes of corresponding elements are set side by side across the three series (fig-4-3). Going from the first (3dd) series to the second (4dd) series, radius clearly increases, exactly as would be expected on descending a group. But the third (5dd) series does not continue that increase — its radii come out almost identical to those of the second (4dd) series.

The explanation is that the 4ff orbitals must be filled (across the lanthanoids) before the 5dd series can begin. Filling the 4ff subshell produces its own steady contraction in atomic radius, called the lanthanoid contraction, and this contraction is large enough to essentially cancel out the increase in size that would otherwise have been expected on going from the 4dd to the 5dd row. The net outcome is that the second and third dd-series elements of a given group end up with very similar radii — for example, r(Zr)≈160 pmr(\text{Zr}) \approx 160\ \text{pm} against r(Hf)≈159 pmr(\text{Hf}) \approx 159\ \text{pm} — and, as a consequence, much more similar physical and chemical properties than a simple family relationship would predict.

Figure 4.3Trends in atomic radii of transition elements
Fig. 4.3 — Trends in atomic radii of transition elements

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What the Graph Shows

The figure plots metallic radius (in pm) on the y‑axis against the elements of the three transition series on the x‑axis. Three separate curves are drawn:

  • First series (3d): Sc → Zn
  • Second series (4d): Y → Cd
  • Third series (5d): La, then Hf → Hg

Each curve shows how the atomic size changes as you move from left to right across a transition series.

What Each Axis and Curve Represents

  • Y‑axis: Metallic radius (in pm) – the half‑distance between nuclei in a metallic crystal.
  • X‑axis: Elements arranged by increasing atomic number within each series.
  • Curves:
    • All three curves first decrease (radius shrinks as nuclear charge increases).
    • In the middle of each series, the radius stays nearly constant.
    • Near the end, the radius rises slightly (due to electron‑electron repulsion in filled or nearly‑filled d‑orbitals).
  • Key visual feature: The 4d and 5d curves almost coincide – they lie close together and well above the 3d curve. This overlap is the graphical signature of the lanthanoid contraction.

The Physical Idea

The graph teaches two central concepts:

  1. General trend across a transition series: As you add protons, the nuclear charge increases. Electrons are added to inner (n–1)d orbitals, which shield the outer electrons poorly. So the effective nuclear charge felt by the outermost electrons rises, pulling them inward – hence the initial decrease in radius.

  2. Lanthanoid contraction: In the 5d series, the 4f orbitals (filled before the 5d orbitals) provide even poorer shielding than d‑orbitals. As a result, the 5d elements experience a stronger pull from the nucleus, making their radii almost identical to those of the 4d elements. This is why the 4d and 5d curves nearly overlap – a phenomenon called the lanthanoid contraction.

Key Formula the Textbook Develops

The textbook uses this figure to explain why the second and third transition series have nearly identical radii – a direct consequence of the lanthanoid contraction. The underlying reason is the poor shielding of one electron by another in the same set of orbitals, especially for f‑electrons.

The effective nuclear charge (ZeffZ_{\text{eff}}) is the key concept:

Zeff=Z−SZ_{\text{eff}} = Z - S

  • ZZ = atomic number (number of protons)
  • SS = shielding constant (accounts for electron‑electron repulsion) …

…

Table 4.2Electronic Configurations and some other Properties of the First Series of Transition Elements
ScTiVCrMnFeCoNiCuZn
Atomic number21222324252627282930
Config. M3d14s23d^14s^23d24s23d^24s^23d34s23d^34s^23d54s13d^54s^13d54s23d^54s^23d64s23d^64s^23d74s23d^74s^23d84s23d^84s^23d104s13d^{10}4s^13d104s23d^{10}4s^2
Config. M+M^+3d14s13d^14s^13d24s13d^24s^13d34s13d^34s^13d53d^53d54s13d^54s^13d64s13d^64s^13d74s13d^74s^13d84s13d^84s^13d103d^{10}3d104s13d^{10}4s^1
Config. M2+M^{2+}3d13d^13d23d^23d33d^33d43d^43d53d^53d63d^63d73d^73d83d^83d93d^93d103d^{10}
Config. M3+M^{3+}[Ar]3d13d^13d23d^23d33d^33d43d^43d53d^53d63d^63d73d^7——
ΔaH⊖\Delta_aH^\ominus/kJ mol⁻¹326473515397281416425430339126
ΔiH⊖\Delta_iH^\ominus I631656650653717762758736745906
ΔiH⊖\Delta_iH^\ominus II1235130914141592150915611644175219581734
ΔiH⊖\Delta_iH^\ominus III2393265728332990326029623243340235563837
Radius M/pm164147135129137126125125128137
Radius M2+M^{2+}/pm——7982827774707375
Radius M3+M^{3+}/pm7367646265656160——
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