Gadolinium (Gd) — its atomic orbitalsGadolinium is element 64: period 6, lanthanoid of the f block. Its ground-state configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 4f⁷ 5s² 5p⁶ 5d¹ 6s², so its outermost occupied shell is n = 6 and holds 2 electrons.Madelung order predicts 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 4f⁸ 5s² 5p⁶ 6s²; the atom fills 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 4f⁷ 5s² 5p⁶ 5d¹ 6s² instead. The filling rule is an approximation, and gadolinium is one of the twenty elements where the atom disagrees with it.Each orbital below is the hydrogen-like solution at the effective nuclear charge Slater's rules give its subshell, so its radial nodes and its angular nodes fall where the wavefunction changes sign rather than where a drawing puts them. Slater screening gives the effective charge; the energy is the hydrogen-like −13.606 Z_eff²/n², and ⟨r⟩ the mean radius of one orbital of the subshell.

Subshell

Electrons

Z_eff

Energy (eV)

Radial nodes

Angular nodes

⟨r⟩ (Å)

63.70

-55207.68

0.012

59.85

-12183.97

0.053

59.85

-12183.97

0.044

52.75

-4206.52

0.135

52.75

-4206.52

0.125

36.25

-1117.42

0.350

42.85

-2775.75

0.130

36.25

-1117.42

0.336

12.30

-82.34

1.613

24.85

-525.11

0.447

12.30

-82.34

1.570

3.00

-3.40

9.525

15.90

-214.98

0.599

3.00

-4.90

6.086

Atomic orbitals, hybridisation and molecular orbitals, computed and drawn in your browser. The tool needs JavaScript and WebGL2; these are the pages it offers: