What

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Whats coming up???

• Oct 25 The atmosphere, part 1 Ch. 8
• Oct 27 Midterm No lecture
• Oct 29 The atmosphere, part 2 Ch. 8
• Nov 1 Light, blackbodies, Bohr Ch. 9
• Nov 3,5 Postulates of QM, p-in-a-box Ch. 9
• Nov 8,10 Hydrogen and multi e atoms Ch. 9
• Nov 12,15 Multi-electron atoms Ch.9,10
• Nov 17 Periodic properties Ch. 10
• Nov 19 Periodic properties Ch. 10
• Nov 22 Valence-bond Lewis structures Ch. 11
• Nov 24 Hybrid orbitals VSEPR Ch. 11, 12
• Nov 26 VSEPR Ch. 12
• Nov 29 MO theory Ch. 12
• Dec 1 MO theory Ch. 12
• Dec 2 Review for exam

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• We can split the hydrogen wavefunction into two
• Y(x,y,z) ? Y(r,q,j) R(r) x Y(q,j)

Depends on angular variables
Depends on r only
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• The solutions have the same features we have seen
  already
• Energy is quantized
• En - R Z2 / n2
• - 2.178 x 10-18 Z2 / n2 J n 1,2,3
• Wavefunctions have shapes which depend on the
  quantum numbers
• There are (n-1) nodes in the wavefunctions

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• Because we have 3 spatial dimensions, we end up
  with 3 quantum numbers
• n, l, ml
• n 1,2,3, l 0,1,2 (n-1) ml -l, -l1,
  0l-1, l
• n is the principal quantum number gives energy
  and level
• l is the orbital angular momentum quantum number
  it gives the shape of the wavefunction
• ml is the magnetic quantum number it
  distinguishes the various degenerate
  wavefunctions with the same n and l

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• En - R Z2 / n2
• - 2.178 x 10-18 Z2 / n2 J n 1,2,3

degenerate
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Probability Distribution for the 1s wavefunction
Maximum probability at nucleus
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A more interesting way to look at things is by
using the radial probability distribution, which
gives probabilities of finding the electron
within an annulus at distance r (think of onion
skins)
max. away from nucleus
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90 boundary Inside this lies 90 of the
probability
nodes
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P-orbitals
Node at nucleus
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The result (after a lot of math!)
Node at s 2!!
Nodes at f, q 0 !!
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The Boundary Surface Representations of All Three
2p Orbitals
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A Comparison of the Radial Probability
Distributions of the 2s and 2p Orbitals
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A Cross Section of the Electron Probability
Distribution for a 3p Orbital
Spatial nodes and Angular nodes!
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Nodes at f, q 0 !!
Nodes at s 0 and 4
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The Boundary Surfaces of All of the 3d Orbitals
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Representation of the 4f Orbitals in Terms of
Their Boundary Surfaces
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The Radial Probability Distribution for the 3s,
3p, and 3d Orbitals
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Another quantum number!
Electrons are influenced by a magnetic field as
though they were spinning charges. They are not
really, but we think of them as having spin up
or spin down levels. These are labeled by the
4th quantum number ms, which can take 2 values.
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This 2-valued electron spin can be shown in an
experiment
In silver (and many other atoms) there is one
more spin up electron than spin down or vice
versa. This means that an atom of silver can
interact with a magnetic field and be deflected
up or down, depending on which type of spin is in
excess.
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In multi-electron atoms things change, because
of the influence of electrons which are already
there
Remember the energies are lt0
The degenerate energy levels are changed somewhat
to become
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THE MULTI-ELECTRON ATOM ENERGY LEVEL DIAGRAM
Remember the energies are lt 0
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THE PAULI PRINCIPLE
No two electrons in the same atom can have
the same set of four quantum numbers (n, l, ml ,
ms).
An orbital is described by three quantum numbers,
Then each electron in a given orbital
must have a different ms
HOW MANY ELECTRONS IN AN ORBITAL?
each orbital may contain a maximum of two
electrons, and they must have opposite spins.
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ELECTRONIC CONFIGURATIONS
THE BUILDING-UP PRINCIPLE.
GROUND STATE
lowest energy electronic configuration
assign electrons to orbitals one at a time
Electrons go into the available orbital of lowest
energy.
Electrons are placed in orbitals according to the
Pauli Principle.
A maximum of two electrons per orbital.
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THE AUFBAU (BUILDING-UP) PRINCIPLE
electrons are added to hydrogen-like atomic
orbitals in order of increasing energy
The electron configuration of any atom or ion....
can be represented by an orbital diagram
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ORBITAL DIAGRAM
Hydrogen has its one electron in the 1s orbital
1s 2s 2p H
1s1
?
both occupy the 1s orbital
Helium has two electrons
Pauli principle
with opposite spins
1s 2s 2p He
?
?
1s2
1s 2s 2p He
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ORBITAL DIAGRAM
Hydrogen has its one electron in the 1s orbital
1s 2s 2p H
1s1
?
Helium has two electrons
both occupy the 1s orbital
Pauli principle
with opposite spins
1s 2s 2p He
?
?
1s2
helium ground state
Helium can also exist in an excited state such as
1s 2s 2p He
?
1s12s1
?
Now onto the next atoms
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Lithium has three electrons, so it must use the
2s orbital Beryllium has four electrons, which
fill both the 1s and 2s orbitals Borons five
electrons fill the 1s and 2s orbitals, and begin
to fill the 2p orbitals. Since all three are
degenerate, the order in which they are filled
does not matter.
1s 2s 2p Li 1s22s1
1s 2s 2p Be 1s2 2s2
1s 2s 2p B 1s22s22p1
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CARBON Z6
A CHOICE
1s 2s 2p C 1s22s22p2
OR
1s 2s 2p C 1s22s22p2
How can we decide?????
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HUNDS RULE
FOR THE GROUND STATE
ELECTRONS OCCUPY DEGENERATE ORBITALS SEPARATELY
THE SPINS ARE PARALLEL
SO FOR CARBON THE GROUND STATE IS
1s 2s 2p C 1s22s22p2
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ENERGY LEVEL DIAGRAM FOR A MULTI-ELECTRON ATOM
BROMINE ELECTRONIC CONFIGURATION
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Ar 4s23d104p5
??
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The idea of penetration explains why the 3d
orbitals lie higher in energy than the 4s.
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The valence electron configuration of the
elements in the periodic table repeat
periodically!
Every element in a group has
the same valence electron configuration!