lecture 18: polyelectronic atoms reading: zumdahl 12.10-12.13 outline: –spin –the aufbau...
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Lecture 18: Polyelectronic Atoms
• Reading: Zumdahl 12.10-12.13
• Outline:– Spin– The Aufbau Principle– Filling up orbitals and the Periodic Table
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H-atom wavefunctions• The Coulombic potential can be generalized:
e-
P+r
V (r) Ze2
r Z
• Z = atomic number (= 1 for hydrogen)
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H-atom wavefunctions• If we solve the Schrodinger equation using this potential, we find that the energy levels are quantized:
En Z 2
n2
me4
802h2
2.178x10 18J
Z 2
n2
• n is the principle quantum number, and ranges from 1 to infinity.
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Orbitals
Quantum Numbers and Orbitals
n l Orbital ml # of Orb.
1 0 1s 0 12 0 2s 0 1
1 2p -1, 0, 1 33 0 3s 0 1 1 3p -1, 0, 1 3
2 3d -2, -1, 0, 1, 2 5
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Spin
• Further experiments demonstrated the need for one more quantum number.
• Specifically, some particles (electrons in particular) demonstrated inherent angular momentum.
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Spin (cont.)
• The new quantum number is ms (analagous to ml).
• For the electron, ms has 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 use the hydrogen-atom orbital nomenclature to discuss in which orbitals the electrons reside.
• This is an approximation (and it is surprising how well it actually works).
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The Aufbau Principal (cont.)• When placing electrons into orbitals in the
construction of polyelectronic atoms, we use the Aufbau Principle.
• This principle states that in addition to adding protons and neutrons to the nucleus, one simply adds electrons to the hydrogen-like atomic orbitals
• Pauli exclusion principle: No two electrons may have the same quantum numbers. Therefore, only two 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.)• Orbital configurations …
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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.)
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The Aufbau Principal (cont.)• What is the radial distribution for different orbitals?
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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 modern periodic 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 valence electrons.
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The Aufbau Principal (cont.)
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Summary
• Electrons go into hydrogen-like orbitals to construct polyelectronic atoms.