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Lecture 19: The Aufbau Principle
• Reading: Zumdahl 12.11-12.13
• Outline:– Spin– The Aufbau Principle– Filling up orbitals and the Periodic Table
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Spin
• Further experimentsdemonstrated the needfor one more quantumnumber.
• Specifically, someparticles (electrons inparticular)demonstrated inherentangular momentum.
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Spin (cont.)
• The new quantumnumber is ms(analagous to ml).
• For the electron, mshas two values:
+1/2 and -1/2
ms = 1/2
ms = -1/2
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The Aufbau Principal• For polyelectronic atoms, a direct solution of the
Schrodinger Eq. is not possible.
• When we construct polyelectronic atoms, we usethe hydrogen-atom orbital nomenclature to discussin which orbitals the electrons reside.
• This is an approximation (and it is surprising howwell it actually works).
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The Aufbau Principal (cont.)• When placing electrons into orbitals in the
construction of polyelectronic atoms, we use theAufbau Principle.
• This principle states that in addition to addingprotons and neutrons to the nucleus, one simplyadds electrons to the hydrogen-like atomic orbitals
• Pauli exclusion principle: No two electrons mayhave the same quantum numbers. Therefore, onlytwo electrons can reside in an orbital(differentiated by ms).
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The Aufbau Principal (cont.)• Finally, orbitals are filled starting from the lowest
energy.
• Example: Hydrogen
1s 2s 2p• Example: Helium (Z = 2)
1s 2s 2p
1s1
1s2
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The Aufbau Principal (cont.)• Lithium (Z = 3)
1s 2s 2p
1s 2s 2p
• Berillium (Z = 4)
• Boron (Z = 5)
1s 2s 2p
1s22s1
1s22s2
1s22s22p1
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The Aufbau Principal (cont.)• Carbon (Z = 6)
1s 2s 2p
1s 2s 2p
• Nitrogen (Z = 7)
Hund’s Rule: Lowest energy configuration is the one in which the maximum number of unpaired electronsare distributed amongst a set of degenerate orbitals.
1s22s22p2
1s22s22p3
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The Aufbau Principal (cont.)• Oxygen (Z = 8)
1s 2s 2p
1s 2s 2p
• Fluorine (Z = 9)
1s22s22p4
1s22s22p5
1s 2s 2p
• Neon (Z = 10)1s22s22p6
full
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The Aufbau Principal (cont.)• Sodium (Z = 11)
3s
1s22s22p63s1
3s 3p
• Argon (Z = 18)[Ne] 3s23p6
Ne [Ne]3s1
Ne
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The Aufbau Principal (cont.)• We now have the orbital configurations for the first 18 elements.
• Elements in same column have the same # of valence electrons!
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The Aufbau Principal (cont.)• Similar to Sodium, we begin the next row of the periodic table by adding electrons to the 4s orbital.
• Why not 3d before 4s?
• 3d is closer to the nucleus
• 4s allows for closer approach; therefore, is energetically preferred.
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The Aufbau Principal (cont.)• Elements Z=19 and Z= 20:
Z= 19, Potassium: 1s22s22p63s23p64s1 = [Ar]4s1
Z= 20, Calcuim: 1s22s22p63s23p64s2 = [Ar]4s2
• Elements Z=21to Z=30 have occupied d orbitals:
Z= 21, Scandium: 1s22s22p63s23p64s23d1 = [Ar] 4s23d1
Z= 30, Zinc: 1s22s22p63s23p64s23d10 = [Ar] 4s23d10
Z = 24, Chromium: [Ar] 4s13d5 exception
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The Aufbau Principal (cont.)
• This orbital filling scheme gives rise to the modernperiodic table.
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The Aufbau Principal (cont.)
• After Lanthanum ([Xe]6s25d1), we start filling 4f.
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The Aufbau Principal (cont.)
• After Actinium ([Rn]7s26d1), we start filling 5f.
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The Aufbau Principal (cont.)
• Heading on column given total number of valenceelectrons.
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The Aufbau Principal (cont.)
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Summary
• Electrons go intohydrogen-like orbitalsto constructpolyelectronic atoms.
• Remember theadjacent “trick” forremembering how tofill orbitals.