Atom and Particle Physics

Term Schema of electron hulls (2002/06/19)

Dan (02/06/19): The term schema of the electron hull in an arbitrary atom is obtained by solving the Schrödinger equation for a sufficiently detailed Coulomb potential. For any electron state, we denote by n ... the principal quantum number (shells K,L,... with n = 1,2,...), l ... the orbital angular momentum (orbitals s,p,... with l = 0,...,n), m ... the magnetic quantum number (m = -l,...,l). Boldface state numbers denote closed hull shells and are called shell magic numbers. # of states K (n = 1) L (n = 2) M (n = 3) N (n = 4) O (n = 5) P (n = 6) Q (n = 7) R (n = 8) S (n = 9) Elements 172 ___8p(3/2)4 Bi''..Rn'' 168 ___9p(1/2)2 Tl'',Pb'' 166 ___9s2 Fr'',Ra'' 164 ___7d10 Lr'...Hg'' 154 ___6f14 Ac'...No' 140 ___5g18 Ubt...Uqn 122 ___8p(1/2)2 Ubu,Ubb 120 ___8s2 Fr',Ra' 118 ___7p6 Uut...Uuo 112 ___6d10 Lr...Uub 102 ___5f14 Ac...No 88 ___7s2 Fr,Ra 86 ___6p6 Tl...Rn 80 ___5d10 Lu...Hg 70 ___4f14 La...Yb 56 ___6s2 Cs,Ba 54 ___5p6 In...Xe 48 ___4d10 Y...Cd 38 ___5s2 Rb,Sr 36 ___4p6 Ga...Kr 30 ___3d10 Sc...Zn 20 ___4s2 K,Ca 18 ___3p6 Al...Ar 12 ___3s2 Na,Mg 10 ___2p6 B...Ne 4 ___2s2 Li,Be 2 ___1s2 H,He At Z = 121 the Term Schema becomes irregular, since not only the 8s-orbital but even a part of the 8p-orbital lies lower than the 5g- (a totally new feature), 6f-, and 7d-orbitals. The other part of the 8p-orbital, however, lies above the 9s- and 9p-orbitals. This is the reason why the 8th and 9th period do not show the Seaborg parallel alignment configuration which was characteristic for the 6th (lanthanides) and 7th (actinides) period.