Why is hafnium no bigger than zirconium?

Atomic radii of the 3d, 4d and 5d series side by side, with Ln³⁺ radii shrinking from 106 to 86 pm; a toggle 'no 4f filling' shows where Hf would have been without the contraction.

Find the 4d/5d pair whose radii differ by only 1 pm (Zr 160, Hf 159) and switch the contraction off to see the gap it erased.

Hf should be clearly larger than Zr because it is one period lower.

• They behave as metals should: they are strong in tension, can be drawn into wires and beaten into sheets, carry heat and electricity well and shine. All of them except Zn, Cd, Hg and Mn adopt one or more of the usual metallic crystal structures at room temperature.
• Except Zn, Cd and Hg they are very hard, of low volatility, and have high melting and boiling points, because (n−1)d electrons join the ns electrons in metallic bonding.
• Along each row the melting point rises to a maximum near d⁵ and then falls steadily, with Mn and Tc as anomalies.
• Enthalpies of atomisation are high and peak near the middle of each series, where one unpaired electron per d orbital gives the strongest interatomic bonding. First-row values run from 326 (Sc) up to 515 kJ mol⁻¹ (V) and fall to 126 kJ mol⁻¹ for Zn, whose 3d electrons take no part in metallic bonding.
• A metal with a very high enthalpy of atomisation tends to be noble in its reactions. The 4d and 5d metals have higher enthalpies of atomisation than the 3d metals, which is one reason metal-metal bonds are common in compounds of the heavy transition metals.
• Ions of the same charge shrink across a series, and atomic radii shrink too, though only slightly: each added d electron shields the growing nuclear charge poorly.
• Radii grow from the 3d to the 4d series, but the 5d radii are almost the same as the 4d ones. The 4f orbitals fill between them, and the steady shrinkage this causes (the lanthanoid contraction) cancels the expected increase. Zr (160 pm) and Hf (159 pm) are the classic pair.
• Smaller radii with rising atomic mass mean density increases across the row: 4.1 g cm⁻³ for Ti up to 8.9 g cm⁻³ for Cu.

Teaching this idea? Put the simulation on your own page or LMS with this code.