shielding ==> (effective nuclear charge) < (full nuclear charge)

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Tracey Greene
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1 Pultz Polyelectronic atoms When you have a nucleus with a +Z charge and only one electron outside the nucleus, as in H and He + and Li 2+ and Be 3+ and..., the Schrödinger equation can be solved exactly--this is a two-body problem according to physicists. When you have more than one electron outside the nucleus, you have a many-body problem which cannot be solved exactly. This occurs even in the apparently simple case of the He atom which has a +2 nucleus and 2 negative electrons outside the nucleus--this is a three-body problem. The fact that we cannot exactly account for the effect one electron has on the motions of the other electrons in an atom is called the electron correlation problem. Electron-electron repulsions appear to reduce the nuclear charge Z that a particular electron feels. In the case of He consider the following extreme arrangements: +2 e - e - and e - +2 e - The charge that an electron sees is somewhere between +1 and +2 ==> effective nuclear charge shielding ==> (effective nuclear charge) < (full nuclear charge) Penetration: an outer electron has some significant probability of being close to the nucleus and hence not shielded as much as expected by inner electron cloud

Note that the 3s orbital shows greater penetration than the 3p orbital which in turn shows greater penetration than the 3d orbital.

2 Pultz 2 Figure 12.33: Radial distribution Copyright by Houghton Mifflin Company. All rights reserved. Radial distribution of electron density for Na atom: The shaded area represents the 10 core electrons. Note that the 3s orbital shows greater penetration than the 3p orbital which in turn shows greater penetration than the 3d orbital. Zumdahl, Chemical Principles, 4th Figure 12.34: Radial probability Copyright by Houghton Mifflin Company. All rights reserved. Explain 3s < 3p < 4s 3d Compare to Figures 8-34 and 8-35 in PHHM9 (slides 42 & 43) E = E(n,l)

3 Pultz 3 Energy for atoms other than H: 1s < 2s < 2p < 3s < 3p < 4s 3d energy level diagram for H & some other elements Figure 8-36 (slide 44) Energy levels U:\_SC Student File Area\Pultz\EnergyLevelsAOs-f(Z)_Moore663.pdf

4 ground state vs. excited states: for H ground state is 1s 1 quicker to write electron configurations rather than n=1, l=0, m l =0, m s = +½ or -½ Pultz Electron configurations Assume all atoms have orbitals similar to those of a hydrogen atom. Bohr model of H atom had electrons in orbits labelled by n=1,2,3, QM model of atom has electrons in shells labelled by n=1,2,3, Within shells are one or more subshells, & each subshell has one or more orbitals. orbital box diagrams for H and He Pauli exclusion principle: no 2 electrons in an atom can have the same set of 4 quantum numbers (n, l, m l, m s ). Since electrons in the same orbital have the same values of n, l, & m l, this postulate says they must have different values of m s. Then, since only 2 values of m s are allowed, an orbital can only hold 2 electrons, and they must have opposite spins. help explain Periodic Table Remember possible values of: n, l, m l, m s Hund's rule: "The lowest energy configuration is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals."[zumdahl, 3rd, p308] or When putting electrons into orbitals with the same energy, put one electron pointing the same direction in each orbital before pairing electrons in order to obtain the ground state electron configuration. Orbital box diagrams for Li, Be, B, C, N, O, Na, K, Ca, Sc, V, Cr, Cu Electron configurations: 1s 2 2s 2 or [He]2s 2 Know electron configuration of H thru Zr (at. # 1-40) and other s and p block elements

Pultz 5 Electron configurations for all elements Figure 12.29: Periodic table Zumdahl 4th Copyright by Houghton Mifflin Company. All rights reserved.

5 Pultz 5 Electron configurations for all elements Figure 12.29: Periodic table Zumdahl 4th Copyright by Houghton Mifflin Company. All rights reserved. Electron configuration of C is 1s 2 2s 2 2p 2 n l m l m s label 1st electron ½ 1s 2nd electron ½ 1s 3rd electron ½ 2s 4th electron ½ 2s 5th electron 2 1 2p 6th electron 2 1 2p

6 History of the Periodic Table Dobereiner triads such as Cl, Br, and I Newlands law of octaves: properties seemed to repeat every 8th element Meyer Mendeleev: developed periodic table based on chemical properties arrange according atomic weight in periodic fashion predicted existence and properties of unknown elements Sc, Ga, Ge (Zumdahl4Table 12.4) Property of Ge Predicted in 1871 Observed in 1886 Atomic mass Density (g/cm 3 ) Specific heat (J o C -1 g -1 ) Melting point Very high 960 o C Oxide formula RO 2 GeO 2 Oxide density (g/cm 3 ) Chloride formula RCl 4 GeCl 4 Boiling point of chloride ( o C) corrected values of atomic weights for In, Be, U Pultz 6 But these properties correlate to electron configurations, so you can use the periodic table to write electron configurations, remembering exceptions for some transition metals. Figure 8-38 (slide 50) valence vs. core electrons Elements in the same group have the same valence electron configuration ==> similar chemical behavior Caution: Electron configurations may vary within a group of transition metals. Subshell energies help explain order in which electrons fill subshells. Self-Consistent Field method is often used to solve Schrödinger equation for polyelectronic atoms and for molecules. positive point charge for nucleus and many electrons Obtain hydrogenlike orbitals! Meaning/significance of each of the 4 quantum numbers Why does the wave function psi have no physical meaning? The wave function itself has no easily visualized meaning. "Although our attempts to attach physical significance to mathematical descriptions are quite useful to us as we try to understand how nature operates, they must be viewed with caution. Simple pictorial models of a particular natural phenomenon always oversimplify the phenomenon and should not be taken too literally." [Zumdahl, Chemical Principles, 4th, p533]

The Quantum Mechanical Model

Recall The Quantum Mechanical Model Quantum Numbers Four numbers, called quantum numbers, describe the characteristics of electrons and their orbitals Quantum Numbers Quantum Numbers The Case of Hydrogen