3 Li (He) (2s) Sip 4 Be (He)(2s)? 1s) 5 B (He)(2s)?(2p) Pia 6 C (He)(2s)" (2p) 3 Py 7 oN (He)(2s)? (2p)? 4S 8 O (He)(2s)?(2p)* 3 Py 9 F (He)(2s)?(2p) > Pa2 10 Ne (He)(2s)2(2p) Sy 11 Na (Ne)(3s) Sin 12 Mg (Ne)(3s)? 1g 13 Al (Ne)(3s)(3p) Pip 14 Si (Ne)(3s)?(3p) 3P 1s P (Ne)(3s)?(3p)5 483 )2 16 S$ (Ne)(3s)?(3 py 3 Py 17 Cl (Ne)(35)?(3p) 2 Pay 18 Ar (Ne)(3s)?(3p) 'So 19 K (An(4s) 2819 20 Ca (Ar)(4s)? Sy 21. Sc (Ar)(4s)? (3d) > Dap 2 Ti (An)(4s)? (3d)? 3 23. O=~V (Ar)(4s)? (34)? 4 Fp 24 Cr (Arj(4s)d)> 7S, 25 Mn (Ar)(4s)? (3d) 8579 26 Fe (Ar)(4s)* (3d) 5 D4 27 Co (An(4s)? (3a)? 4 Foy 28 Ni Ary(4s)? 3d)8 3 Fy 29 Cu Ar)(4s)Gd)' S172 30. Zn Ar)(4s)? (3d)! sy 31 Ga Arj(4s)?(3d)!(4p) Piya 32 Ge (Ary(4s)?(3d)!9(4p)?_ 3 Py 33. As Ary(4s)?(3d)!(4p)3 4 83/5 34 Se Ar)(4s)?(3d)!(4p)4 3 Ph 35 sBr An(4sr Bd) (4p? Ps 360 Kr (Ary(4sy(3a) (4p) 1S

(c) Hunds first rule says that, all other things being equal, the state with the highest total spin will have the lowest energy. What would this predict in the case of the excited states of helium? Sec. 5.3: Solids 193 (d) Hunds second rule says that if a subshell (n, J) is no more than half filled, then the lowest energy level has J = |L S|; if it is more than half filled, then J = L +S has the lowest energy. Use this to resolve the boron ambiguity in (b). (e) Use Hunds rules and the fact that a symmetric spin state must go with an antisymmetric position state (and vice versa) to resolve the carbon ambiguity in (b). What can you say about nitrogen? Problem 5.12 The ground state of dysprosium (element 66, in the sixth row of the Periodic Table) is listed as *Jg. What are the total spin, total orbital, and grand total angular momentum quantum numbers? Suggest a likely electron configuration for dysprosium. 3.3 SOLIDS

In the solid state, a few of the loosely bound outermost valence electrons in each atom become detached and roam around throughout the material, no longer subject only to the Coulomb field of a specific parent nucleus, but rather to the combined potential of the entire crystal lattice. In this section we will examine two extremely primitive models: first, the electron gas theory of Sommerfeld, which ignores ail forces (except the confining boundaries), treating the wandering electrons as free particles in a box (the three-dimensional analog to an infinite square well); and second, Blochs theory, which introduces a periodic potential representing the electrical attraction of the regularly spaced, positively charged, nuclei (but still ignores electron-electron repulsion). These models are no more than the first halting steps toward a quantum theory of solids, but already they reveal the critical role of the Pauli exclusion principle in accounting for the solidity of solids, and provide i

5.3.1 The Free Electron Gas Suppose the object in question is a rectangular solid, with dimensions /,, /,, /,, and imagine that an electron inside experiences no forces at all, except at the impenetrable walls: 0, #fO<x<1,0<y<1,,0<2<!1,); co, otherwise. [5.35] VQ,y2= | The Schrdinger equation, nh? -V'y = Ey, 2m 194 Chap. 5 Identical Particles