Lesson 1 · 30 min

Trends across the d-block

Why do chromium and copper break the filling rules? Why are zirconium and hafnium the same size? Why can manganese reach +7 while zinc stops at +2? Radii, melting points and oxidation states across the d-block, starting from electron configurations.

In this lesson

Write configurations of first-row transition-metal atoms and ions, including the Cr and Cu exceptions, and explain why ions lose 4s electrons first
Describe the trends in metallic radius, melting point and density across the three series, and use the lanthanide contraction to explain why period-5 and period-6 partners are almost the same size
Read the oxidation-state chart of the first series: why the highest state rises and then falls, and which state is most stable
Work out the d-electron count of an ion from its group number and oxidation state

In 1923 Coster and von Hevesy, working in Copenhagen, found a new element in zirconium ore: hafnium. It had been hiding in every zirconium mineral all along, chemically almost indistinguishable from zirconium, until X-ray spectra gave it away. Separating zirconium from hafnium is still one of the hardest separations in metallurgy — for one reason: the two atoms are the same size.

Predict first

Which pair of atoms from the same group is closest in size?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Titanium and zirconium (Ti, Zr) Zirconium and hafnium (Zr, Hf) Chromium and molybdenum (Cr, Mo) Copper and silver (Cu, Ag)

Configurations: 4s fills first and empties first

From scandium to zinc, electrons go into the 3d orbitals: Sc [Ar]3d¹4s², Ti 3d²4s², … with two exceptions: chromium is [Ar]3d⁵4s¹ and copper [Ar]3d¹⁰4s¹ — the extra stability of a half-filled or full d shell beats keeping a second electron in 4s (see electron configurations).

When the atom forms an ion, the 4s electrons leave first: $\ce{Fe}$ [Ar]3d⁶4s² → $\ce{Fe^2+}$ [Ar]3d⁶ → $\ce{Fe^3+}$ [Ar]3d⁵. Once 3d is occupied it lies below 4s, so transition-metal ions have only 3d electrons outside the core. By the IUPAC definition a transition element has an incomplete d subshell in the atom or in a common ion — zinc and $\ce{Zn^2+}$ are both 3d¹⁰, so strictly zinc does not qualify.

Size, melting point and density

Along a transition series the metallic radius changes little (the first series shrinks from 164 to about 125 pm, then creeps up again): the added electrons enter the inner (n−1)d orbitals and partly shield the outer ones.

Metallic bonding involves both s and d electrons, and the more unpaired d electrons, the stronger it gets: melting points peak around groups 5 and 6 (vanadium 1910 °C; tungsten, at 3422 °C, has the highest of all metals) and collapse as the d shell fills — zinc melts at 420 °C and mercury is a liquid at room temperature (−39 °C). The band picture of metallic bonding is in metals and bands.

The lanthanide contraction has another striking consequence: period-6 atoms are the size of their period-5 partners but nearly twice as heavy, so osmium (22.6 g/cm³) and iridium (22.4 g/cm³) are the densest elements, and hafnium (13.3 g/cm³) is about twice as dense as zirconium (6.52 g/cm³).

Oxidation states

The 4s and 3d electrons of a transition metal are close in energy and can be lost one at a time, so these elements have many oxidation states. From scandium to manganese the highest state equals the group number: Sc +3, Ti +4, V +5, Cr +6 ( $\ce{Cr2O7^2-}$ ), Mn +7 ( $\ce{MnO4-}$ ) — every 4s and 3d electron is given up. Beyond manganese the growing nuclear charge holds the 3d electrons ever more tightly and the highest state falls again: iron usually reaches +3 (the rare ferrate $\ce{FeO4^2-}$ is +6), cobalt and nickel are mostly +2, copper +1 and +2, and zinc only +2.

n_d = G - N

The d-electron count of a transition-metal ion: group number minus oxidation state (the ion has lost all its 4s electrons).

$n_d$: number of d electrons in the ion
$G$: group number (3–12)
$N$: oxidation state

Known states, the most stable one, and d-electron counts

Oxidation states of the first transition series

+1+2+3+4+5+6+7

Most stable (in water, in air)
Common
Rare, a few compounds only
State equal to the group number

The highest state climbs from Sc (+3) to Mn (+7) — losing every 4s and 3d electron — and then falls, because after manganese the 3d electrons are held ever more tightly.

Manganese +7 [Ar] 3d⁵ 4s² Common

d electrons: d0 · Example: $\ce{MnO4-}$ — permanganate (purple, strong oxidant)

Click each oxidation state for its d count and an example (with its colour, where it can be computed). Follow the diagonal of highest states up to manganese; then switch to the potential trends and compare Mn³⁺/Mn²⁺ with Fe³⁺/Fe²⁺ — why are Mn²⁺ and Fe³⁺ (both d⁵) so common?

Worked example

From configuration to d count

Write the configurations of $\ce{Cr}$ , $\ce{Cr^3+}$ , $\ce{Mn^2+}$ and $\ce{Cu+}$ , and check them with $n_d = G - N$ .

Concept check

Which of these ions has the configuration [Ar]3d⁵?

\ce{Mn^2+}

\ce{Fe^2+}

\ce{Cr^3+}

\ce{Co^2+}

Try the calculation

Zirconium and hafnium have almost the same metallic radius (160 and 159 pm). Assuming equal atomic volumes, estimate the density of hafnium from zirconium’s 6.52 g/cm³ and the molar masses (Zr 91.22, Hf 178.49 g/mol).

Key takeaways

Cr and Cu are 3d⁵4s¹ and 3d¹⁰4s¹; ions lose 4s electrons first, and an ion’s d count is group number minus oxidation state.
Radii change little along a series; melting points peak near groups 5–6 (tungsten 3422 °C) and collapse at d¹⁰ (mercury is liquid).
The lanthanide contraction makes period-5 and period-6 partners almost the same size (Zr 160 pm, Hf 159 pm), so the period-6 metals are extremely dense.
The highest oxidation state rises from Sc (+3) to Mn (+7) and then falls; the d⁵ ions Mn²⁺ and Fe³⁺ are especially common.

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Data and references

N. N. Greenwood, A. Earnshaw, Chemistry of the Elements, 2nd ed. (1997), ch. 19–29.
C. E. Housecroft, A. G. Sharpe, Inorganic Chemistry, 5th ed. (2018), ch. 19–22 and Appendix 6 (metallic radii).
A. F. Wells, Structural Inorganic Chemistry, 5th ed., Clarendon Press (1984) (metallic radii, 12-coordination).
IUPAC, Compendium of Chemical Terminology (Gold Book), “transition element”.
PubChem Periodic Table of Elements (melting points, densities), via the site’s element table.