Putting%20it%20all%20together

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Putting it all together -or- How to build an atom
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4 quantum numbers needed to specify an
electron's state
The allowed energy levels are quantized much like
or particle in a box. Since the energy level
decreases a the square of n, these levels get
closer together as n gets larger.
There are a total of n subshells, each
specified by an angular momentum quantum number
, and having an angular momentum of

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There are a total of orbitals
within each subshell, these can be thought of as
projections of the angular momentum on the z axis.
The electron has an intrinsic magnetic moment
called spin. The orientation of the angular
momentum vector of this apparent rotation motion
can only have a manitude of ½.
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Putting the pieces together...
z
Moving charges give rise to magnetic fields,
which will then interact. Since the magnetic
moments never align with the z-axis the torque
is never zero.
y
x
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If the orbital angular momentum is zero, you have
to think about how it interacts with the spin, as
some magnetic potential energy will arise from
that interaction.
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Spectrosopic Notation
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The Pauli Exclusion Principle
The total wavefunction must be antisymmetric
for electrons!
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Chemical properties of an atom are determined by
the least tightly bound electrons.

• Factors
• Occupancy of subshell
• Energy separation between the subshell and the
  next higher subshell.

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A pattern starts to emerge
s shell l0
Helium and Neon and Argon are inerttheir outer
subshell is closed.
p shell l1
Beryllium and magnesium not inert even though
their outer subshell is closedwhy??
Alright, what do we add next???
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Uh-oh3d doesnt come nextwhy???
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Charge screening
orbiting electron sees net charge of elike
hydrogen
nucleus charge 3e
closed s shell total charge -2e
Note that for higher orbital angular momentum,
the energy more nearly equals to the
corresponding levels in hydrogen. The more
nuclear charge an electron sees,
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Influence of the radial wavefunction
Note the pulling down of the energy of the low
angular momentum states with respect to hydrogen
due to the penetration of the electric shielding.
2s state more tightly bound since it has a
nonzero probability density inside the 1s shell
and sees more of the nuclear charge.
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Sodium...not what we expect?
Excited state 4s lies lower than 3d!!
The energy separating shells becomes smaller with
increasing n. Electrons in lower angular
momentum states penetrate shielding more, and
thus are more tightly bound. As the energy
levels become closer together, some lower angular
momentum states of higher n may actually have a
lower energy.
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Order of filling, then, is not what we naively
expect. The degree of charge screening plays a
BIG role.
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Now we know where to put the transition metals
4s comes BEFORE 3d
and apparently 5s comes before 4d, and 6s comes
before 5d
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The term with the maximum multiplicity lies
lowest in energy.
Also, mutual repulsion forces electrons to higher
energy states.
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General order of filling shells
Note the filling of aligned spins before
doubling up.
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Alright, so where on the periodic table do we
make room for all of those f orbitals??
Lanthanide series (or rare earths due to low
abundance)
Actinide series
Stick them at the bottom to keep things from
getting too awkward.
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Viola...the periodic table demystified
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Putting the "periodic" in the periodic table
The ionization energies are periodic If you are
filling shells in order of successively higher
energies, why does this happen??
The atomic radius is surprisingly constant. Why
does is not scale with the number of electrons?
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n1
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n2
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n3
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X-ray spectra
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Moseley's law
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For a given multiplicity, the term with the
largest value of L lies lowest in energy.
electrons spend less time near each other, less
coulomb repulsion.
For atoms with less than half-filled shells, the
level with the lowest value of J lies lowest in
energy.