aims for lectures 5-6: many electron atoms Chemistry 1B lectures 5-6 Chapter 12 pp. 557-569 th 7 *(569-571) 7th electron spin, the 4 th quantum number and the Pauli exclusion principle effective nuclear charge, Z eff the net attraction for an electron in a many-electron atom knowledge of the principal quantum number (n) and Z eff for and atom s valence electrons leads to an understanding of: E 2s < E 2p E 3p < E 3d E 3d vs E 4s Hund s Rule and electron configuration in many-electron atoms the Aufbau Principle 4 7 2012 Nobel in QUANTUM physics new considerations for many-electron atoms (somewhat different order of presentation than Zumdahl how does increased atomic number (Z) and the presence of other electrons affect orbital energies? how does one fill up the available orbitals in many-electron atoms 5 8 many-electron atoms and Schrödinger Equation (ppn557-558) the spin quantum number Although the Schrödinger equation for polyelectronic atoms (and molecules) cannot be solved exactly (mathematically), numerical computer calculations give solutions that agree perfectly with experiment but are very complex. Stern-Gerlach experiment (fig. 8-1 Silberberg) We can (and will!!) use the hydrogen-like orbitals as a very good approximation to the exact solutions of the Schrödinger equation for many-electron atoms. 6 9 1
Pauli exclusion principle (PEP) (sec 12.10) voila no two electrons can have the same four quantum numbers: n=1 =0 m = 0 m s =½ n=1 =0 m = 0 m s =½ n=1 =0 m = 0 m s =½ n=1 =0 m = 0 m s =½ VOILA!!! 10 13 many-electron atoms what we will need to figure out He, Li, Be, B, C, N, O, F, Ne greater nuclear charge (Z) than hydrogen (Z=1) more electrons than hydrogen (one-electron) How do the energies of the various hydrogenlike orbitals change when we take into account the effects of increased Z and the other electrons present????? in hydrogen E 2s = E 2p in boron why E 2s < E 2p????? 11 14 where we are heading!!! chapter 12 configurations (for and 2s levels) ground states (preview) Quantum mechanics describes many-electron atoms by filling hydrogen-like orbitals with the atom s electrons in a manner consistent with the Pauli Exclusion Principle. E 2s 2s This description allows us to understand the energies of electrons in atoms and ions, the relative sizes of atoms and ions, and the chemical reactivity and other properties of various elements. H He 2 Li 2 2s Be 2 2s 2 12 15 2
orbital energies in many-electron atoms Energy of H vs He vs Li 2 (still 1 electron) Energy dependence on n and Z all electrons (n=1) Z=1 Z=2 Z=3 Holds EXACTLY for 1-electon atoms and ions: H, He, Li 2,Be 3,... H (Z=1) He (Z=2) Li 2 (Z=3) Here Z is regular nuclear charge with Z=1, 2, 3, 4,... 16 increase Z more attraction lower (more negative) energy (ie higher IE) smaller r avg 19 remembering Silberberg Figure 8.3 Energy of H vs He vs Li 2 (still 1 electron) Energy and average radius of electron in a hydrogen orbital ionization energy (ionization potential) of an electron in an atom or molecule is energy required to (just) remove an electron from its stationary state (from n ) (HW2 #11). ionization energy Increase Z more attraction lower energy (ie higher IE) smaller average radius 17 20 ionization energy (section problem S3) Energy of H vs He (HO 12.1) ionization energy (IE) : the energy required to remove an electron from an atom, ion, or molecule in the gas phase Z and Ionization Energies X (g) IE ö X (g) e } (absorbs energy endothermic, sign for energetics) E Z=1 similar to the work function in the photoelectric effect, except IE refers to gas phase ionization where refers to removal of electron from the solid 18 Z=2 Z (He ) > Z (H) 21 3
what happens when other electrons are present: effective nuclear charge (p 546) Important Factoids in Understanding Effective Nuclear Charge Energy dependence on n and Z eff Energy of He 2 vs He ( HO fig 12.2) Z eff and Ionization Energies Z eff (He ) > Z eff (He 2 ) Z eff and shielding Z eff = Z (shielding of other electrons) Z eff = Z (effect of electron repulsions) electron feels full Z==2 nuclear attraction electrons in same shell: He vs He 2 E Z eff=z=2 IE=3.8 10-18 J Z eff ª1.34 (1.20) the two electrons shield one another from the Z=2 nuclear pull 22 this is approximate way to calculate Z eff ; other techniques give slightly different numbers 25 He vs He (what positive charge does a electron see?) energy of He 2 vs He (same shell shielding) Zumdahl (p. 558-9) less attraction (more shielded) 2 nd electron (e - ) Z=2 Z=2 He He 2 shielding by 2nd electron 1 < Z eff < 2 2 e He 23 26 He vs He (what net positive charge does a electron see?) Silberberg figure 8.4A: energy of He 2 vs He (same shell shielding) Zumdahl (p. 556-8) [558-559] 7th shielding of electron by 2nd electron 1 < Z eff < 2 2 e e Z eff e Z=2 Z=2 actual He atom Zumdahl s hypothetical He atom He He 2 2 He e 24 27 4
Z eff : effective nuclear charge Energy of Li 2 2s vs Li [ 2 ] 2s (HO Fig. 12.3) Energy dependence on n and Z eff Z eff (Li 2 2s) > Z eff (Li[ 2 ]2s) Z eff and shielding Z eff = Z - shielding of other electrons Z eff =Z (effect of electron repulsions) E IE=3.8 10-18 J Z eff ª 1.34 (1.20) IE=0.86 10-18 J Z eff ª 1.26 IE=4.9 10-18 J Z eff = Z = 3 electrons in different shells Li 2 2s vs Li [ 2 ] 2s shielding the 2s electron 28 this is approximate way to calculate Z eff ; other techniques give slightly different numbers 31 Z eff for 2s electron in Li 2 2s same shell shielding He 2 vs inner shell shielding Li 2 2S 2s electron Z=3 how would one expect the shielding of electron for another electron [same shell] to compare to the shielding of a electron for a 2s electron [different shells]?? shielding of same shell < > shielding of outer shell He 2 vs Li 2 2s How so? [Z eff =Z nucleus -shielding of other electrons] shielding by 2 electrons Z eff 1.26 Li 2 2s 29 32 figure 8.4 B (Silb) shielding by inner shell electrons how do the energies of the 2s and 2p orbitals compare in manyelectron atoms? In 1-electron atoms (H-atom) and 1-electron ions, the 2s and 2p orbitals have the. SAME energies Z eff and the effect of penetration of inner shell electron density by electrons in the same shell 30 33 5
Z eff for 2s vs 2p: 2p and 2s have SAME energy in 1-electon ion Energy of Li [ 2 ] 2s vs Li [ 2 ] 2p (HO Fig. 12.5): penetration penetration by 2s electron of 2 shielding GIVES INCREASED Zeff y2s radial probability Z eff (Li[ 2 ] 2s) > Z eff (Li[ 2 ]2p) 2s electron Z=3 IE=0.86 10-18 J Z eff ª1.26 IE=0.6 10-18 J Z eff ª 1.02 shielding by 2 Li 2 2s Z eff ª 1.26 actual 2s electron density (one radial node; one inner maximum in radial probability) 34 IE=4.8 10-18 J Z eff = Z= 3 37 Z eff for 2s vs 2p how do the energies of the 2s and 2p orbitals compare in manyelectron atoms? no (less) penetration of 2 shielding by 2p electron GIVES relatively smaller Z eff 2p electron Configurations and valence-level orbital diagrams Z=3 Hund s rule shielding by 2 Li 2 2p Z eff for 2s > Z eff for 2p E 2s < E 2p actual 2p electron density (no radial nodes; no inner maxima in radial probability) 35 2 nd row aufbau fig 8.8 (Sil) 38 Z eff for 2s vs 2p (handout fig. 12.4) 3s 3p 3d 4s orbital energy ordering Increasing Z eff due to increasing penetration effects (figure HO 12Z.6); (Z eff ) 3s > (Z eff ) 3p > (Z eff ) 3d (E) 3s < (E) 3p < (E) 3d 4s vs 3d (Z eff vs n) more penetration of inner shell electron density E 2s < E 2p Orbital energy ordering fig 8.6 (Silb) (figure 8.13, Silb) electron see s more Z and has greater Z eff 36 39 6
configurations Hund s rule Energy ordering Unambiguous (closed shell, 1e, (n-1)e s Ambiguous (e.g. p 2,p 3,p 4, d 2 d 8 ) end of lectures 5-6 Examples (periodic table) ground state excited state not allowed configuration transition metal cations exceptions 40 43 unpaired electrons and magnetic properties (Gouy balance) Z eff and ionization potentials Diamagnetic pushed out of magnet no unpaired electrons Paramagnetic pulled into magnet unpaired electrons Z eff = Z = 1. IE=0.86 10-18 J Z eff ª1.26 IE=0.6 10-18 J Z eff ª1.02 IE=0.86 10-18 J Z eff ª1.26 IE=3.8 10-18 J Z eff ª1.34 (1.20) IE=4.9 10-18 J Z eff = Z = 3. Gouy Balance Z eff = Z = 2. 41 44 the Periodic Table Silberberg figure 8.8 42 45 7
Silberberg figure 8.6 Figure HO 8.6: penetration of 3s vs 3p vs 3d; radial nodes = n-l-1 screening by n=2 electrons 3s: 2 radial nodes 2 inner electron density maxima 3p: 1 radial node 1 inner maxima 3d: 0 radial nodes 0 inner maxima 46 less penetration smaller Z eff higher energy more penetration larger Z eff lower Energy 49 Silberberg figure 8.13 Figure HO 8.6: penetration of 3s vs 3p vs 3d; radial nodes = n-l-1 screening by n=2 electrons more penetration larger Z 3s: 2 radial nodes eff 2 inner electron density lower maxima Energy 3p: 1 radial node 1 inner maxima 3d: 0 radial nodes 0 inner maxima less penetration 47 smaller Z eff higher energy 50 Zumdahl figure 12.29 Why B [He] 2s 2 2p 1 is unambiguous ground state configuration Experimental spectrum (states) of B E Only one energy state (ignore 3/2 vs 1/2) 48 51 8
Why C [He] 2s 2 2p 2 is ambiguous ground state configuration Experimental spectrum (states) of C Ø Ø E Ground energy state (ignore 0 vs 1 vs 2 ) Excited states with same [He] 2s 2 2p 2 configuration 52 Why B [He] 2s 2 2p 1 is unambiguous ground state configuration Experimental spectrum (states) of B E Only one energy state (ignore 3/2 vs 1/2) Excited states have excited [He] 2s 1 2p 2 configuration 53 9