Protactinium (Pa) — its atomic orbitalsProtactinium is element 91: period 7, actinoid of the f block. Its ground-state configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 4f¹⁴ 5s² 5p⁶ 5d¹⁰ 5f² 6s² 6p⁶ 6d¹ 7s², so its outermost occupied shell is n = 7 and holds 2 electrons.Madelung order predicts 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 4f¹⁴ 5s² 5p⁶ 5d¹⁰ 5f³ 6s² 6p⁶ 7s²; the atom fills 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 4f¹⁴ 5s² 5p⁶ 5d¹⁰ 5f² 6s² 6p⁶ 6d¹ 7s² instead. The filling rule is an approximation, and protactinium 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)

90.70

-111927.10

0.009

86.85

-25656.67

0.037

86.85

-25656.67

0.030

79.75

-9614.78

0.090

79.75

-9614.78

0.083

63.25

-3401.90

0.201

69.85

-7375.83

0.080

63.25

-3401.90

0.192

33.35

-605.30

0.595

51.85

-2286.12

0.214

33.35

-605.30

0.579

11.55

-50.42

2.474

40.45

-1391.35

0.235

19.85

-214.44

0.920

11.55

-50.42

2.428

3.00

-2.50

12.965

12.65

-87.09

1.318

3.00

-3.40

8.996

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