Download Slide 1

PHYSICS 420
SPRING 2006
Dennis Papadopoulos
LECTURE 22
More Atom Building
n  1, 2,3, K
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.
l  0,1, 2, K n  1
There are a total of n subshells, each
specified by an angular momentum quantum
number
, and having an angular
momentum of
l
v
L  l  l  1 h
Fig. 8-6, p.267
Fig. 8-7, p.272
Orbiting electrons form a current loop which give rise to a magnetic field.
Magnetic moment of a current loop:
  iA
current
area
enclosed
by current
loop
Since the current is defined as the direction of
flow of positive charge, the orientation of the
magnetic moment will be antiparallel to the
angular momentume of the electron and can be
found using the right hand rule.
The current loop of the orbiting electron sets up a magnetic dipole which
behaves like a bar magnet with the north-south axis directed along .
Kepler’s Law of areas: A line that
connects a planet to the sun sweeps out
equal areas in equal times.
v
2m
 2 r 
 A
2
L  mvr  m 
r


r

2
m



 
T
T


T 
A
v
v
L
A

T 2m
i
q
T
q v
e v
  iA 
L
L
2m
2m
v
Remember that the z component of angular
momentum is quantized in units of h so the magnetic
dipole moment is quantized as well:
z  
e
eh
Lz  
ml    B ml
2me
2me
d 2
2


m
l   
2
d
where
e
B 
eh
 9.274 1024 J/T
2m
The Bohr magneton
Magnetic dipole tends to want to
align itself with the magnetic field
but it can never align due to the
uncertainty principle!
Torque exerted:
v
v
  B
L

t
l  ml  l
1
s
2
There are a total of 2l  1 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.
v
3
S  s ( s  1) h 
h
2
Chemical properties of an atom are determined by the least tightly
bound electrons. VALENCE ELECTRONS
Factors:
•Occupancy of subshell
•Energy separation between the subshell and the next higher
subshell.
Pauli Exclusion Principle
•
To understand atomic spectroscopic data for optical frequencies,
Pauli proposed an exclusion principle:
No two electrons in an atom may have the same set of
quantum numbers (n, ℓ, mℓ, ms).
•
It applies to all particles of half-integer spin, which are called
fermions, and particles in the nucleus are fermions.
The periodic table can be understood by two rules:
1) The electrons in an atom tend to occupy the lowest energy levels
available to them.
2)
Pauli exclusion principle.
s shell
l=0
Helium and Neon
and Argon are
inert…their outer
subshell is closed.
p shell
l=1
Beryllium and magnesium not inert even
though their outer subshell is
closed…why??
Alright, what do we add next???
Uh-oh…3d doesn’t come next…why???
Fig. 9-16, p.324
orbiting electron “sees”
net charge of +e…like
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”,
2s state more tightly bound since it
has a nonzero probability density
inside the 1s shell and “sees” more
of the nuclear charge.
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.
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.
Order of filling, then, is not what we naively
expect. The degree of charge screening plays
a BIG role.
4s comes BEFORE 3d…
…and apparently 5s comes before 4d, and 6s comes before 5d…
The term with the maximum multiplicity lies lowest in energy.
Also, mutual
repulsion
forces
electrons to
higher energy
states.
Note the filling of
aligned spins before
“doubling up”.
Hund’s rule
Lanthanide series (or “rare earths” due to low abundance)
Actinide series
Stick them at the bottom to keep things from getting too awkward.
The Periodic Table
Inert Gases:
• Last group of the periodic table
• Closed p subshell except helium
• Zero net spin and large ionization energy
• Their atoms interact weakly with each other
Alkalis:
• Single s electron outside an inner core
• Easily form positive ions with a charge +1e
• Lowest ionization energies
• Electrical conductivity is relatively good
Alkaline Earths:
• Two s electrons in outer subshell
• Largest atomic radii
• High electrical conductivity
The Periodic Table
Halogens:
• Need one more electron to fill outermost subshell
• Form strong ionic bonds with the alkalis
• More stable configurations occur as the p subshell is filled
Transition Metals:
• Three rows of elements in which the 3d, 4d, and 5d are
being filled
• Properties primarily determined by the s electrons, rather
than by the d subshell being filled
• Have d-shell electrons with unpaired spins
• As the d subshell is filled, the magnetic moments, and the
tendency for neighboring atoms to align spins are reduced
The Periodic Table
Lanthanides (rare earths):
• Have the outside 6s2 subshell completed
• As occurs in the 3d subshell, the electrons in the 4f
subshell have unpaired electrons that align themselves
• The large orbital angular momentum contributes to the
large ferromagnetic effects
Actinides:
• Inner subshells are being filled while the 7s2 subshell is
complete
• Difficult to obtain chemical data because they are all
radioactive
• Have longer half-lives
The ionization energies are
periodic…
If you are filling shells in order
of successively higher energies,
why does this happen??
Z2
En  13.6 2 eV
n
The atomic radius is surprisingly
constant. Why does is not scale
with the number of electrons?
E1  (ke2 / 2ao )( Z 2 /1) ; 24 KeV
Fig. 9-17, p.325
E[ K
Continuous + line spectrum,
Cut-off at maximum exciting electron
energy