Lecture 1 Notes: Atom Composition
(a) Assumptions underlying the Bohr atom
(1)
Atoms can exist in stable states without radiating. The states have
discrete energies En, n = 1, 2, 3,., where n = 1 is the lowest energy
state (the most negative, relative to
Lecture 6 Notes: Transitions
m
Yl
Y ,l
m
l 0, 1, 2,.
,lmm
2l 1 l m !
4 l m !
Y2
4 1 2
0
5
3
Y
1
2
1
2
16
1
0
3cos2 1
1
cos
15 2
Y1
2
4
3
1
2
i
sin cose
8
1
1
Y
im
H Efor the rigid rotor problem.
1
0
m
Pl
m
Y
cose
2
m 0,1, 2, 3,. l
Yl s are the eigenfu
Lecture 3 Notes: Deviation Values
xi x
th
xi x
Deviation of i
Average deviation from average value <x>
xi x
But for particle in a box,
xi x 2
0
Square of deviation of i
value <x>
xi x 2
x
2
xi x 2
Note
measurement from average value <x>
th
measurement fr
Lecture 2 Notes: Uncertainty Principle
Consequences (II)
x p !
2
x
Heisenberg Uncertainty Principle
Consider diffraction through a single slit
x
D
s
peak-null
distance
l
light,
D
s
l
D l
s
Now consider a beam of electrons with de Broglie wavelength . Th
Lecture 4 Notes: Experiment
Success
Consider the rotation of two particles at a fixed distance R from one another:
r r R
1
2
m1
m1r1 m2 r2center of mass (COM)
r1
r2
COM
m2
These two particles could be an electron and a proton (in which case wed be
looking
Lecture 7 Notes: MO Vectors
+
For the simple case of the one-electron bond in H2 we have seen that using the
LCAO principle together with the variational principle led to a recipe for
computing some approximate orbitals for a system that would be very dif
Lecture 10 Notes: Magnetic Fields
Just as IR spectroscopy is the simplest example of transitions being induced by lights oscillating
electric field, so NMR is the simplest example of transitions induced by the oscillating magnetic
field. Because the stren
Lecture 9 Notes: Equilibrium Bonds
As weve emphasized many times in this course, within the Born
Oppenheimer approximation,
Harmonic
the nuclei move on a potential
Approximation
energy surface (PES)
R
A + B separated atoms
determined by the electrons.
For
Lecture 5 Notes: Commutation
Relations
2
Since L and Lz commute, they share common eigenfunctions. These functions are
extremely important for the description of angular momentum problems they
determine the allowed values of angular momentum and, for syst
Lecture 8 Notes: Polyatomic Molecules
In general, the vast majority polyatomic molecules can be thought of as
consisting of a collection of two-electron bonds between pairs of atoms. So the
qualitative picture of and -bonding and antibonding orbitals that