Schilb 1
Notes 4/17/13
Physical Chemistry 2 with Hedi Mattoussi
The Aufbau Principle
The patterns associated with filling orbitals are easy to understand, but I will take it seriously
since theres a good chance well be asked to do an electron configuratio
Schilb 1
Notes 4/1/13
Physical Chemistry 2 with Hedi Mattoussi
Radial part of the Wavefunction
First we define a few helpful symbols:
The Bohr radius is a physical constant that is approximately equal to the distance between the
proton and the electron in
Schilb 1
Notes 1/28/13
Physical Chemistry 2 with Hedi Mattoussi
Normalization
Normalization in 3D
Cartesian Coordinates:
Polar (spherical) coordinates:
In general, we always look for a solution that is normalized. Thankfully, the S.E. works in such a
way
Schilb 1
Notes 2/25/13
Physical Chemistry 2 with Hedi Mattoussi
Review
The general form for the wavefunction is:
Here, N represents the normalization constant.
A bell-shaped Gaussian Curve looks like
The H stands for Hermite in this case, and the n subscr
Schilb 1
Notes 3/8/13
Physical Chemistry 2 with Hedi Mattoussi
Cylindrical Coordinates:
How do you get from point O to point M using this system?
First, use phi to determine what direction youre leaving the origin on the xy-plane (the +x-axis
counts as ze
Schilb 1
Notes 3/20/13
Physical Chemistry 2 with Hedi Mattoussi
Schrdinger Equation:
We have derived the following from the Sh. Eq. last time:
Equation one is for the rotation on the xy-plane. Equation two is for the rotation around, through,
above, and b
Schilb 1
Notes 2/6/13
Physical Chemistry 2 with Hedi Mattoussi
Expectation Value
The average value of a large series of measurements is given by the expectation value of the
operator . This is only valid if the function is normalized.
If psi is an eigenfu
Schilb 1
Notes 2/8/13
Physical Chemistry 2 with Hedi Mattoussi
Solving a problem using quantum mechanics
1) Define the problem and analyze the total energy:
2) Construct the Hamiltonian (one dimensional):
3) Develop a Schrdinger Equation:
Free translation
Schilb 1
Notes 2/22/13
Physical Chemistry 2 with Hedi Mattoussi
Harmonic Oscillator
In classical mechanics, our oscillator was a mass on a spring.
In Q.M., molecules (namely diatomic molecules or bonds in larger molecules) form springs. This
is vibrationa
Schilb 1
Notes 2/13/13
Physical Chemistry 2 with Hedi Mattoussi
Tunneling
We left off on tunneling. We learned that even if the particle lacks the energy to beat the potential
barrier, it still has a small chance of being found on the other side.
Ive mark
Schilb 1
Notes 2/27/13
Physical Chemistry 2 with Hedi Mattoussi
Normalization of H.O. Wavefunctions
That equation is a shortcut to finding the normalization constant. Unlike the particle in a box, this
normalization constant can be found by plugging and c
Schilb 1
Notes 3/4/13
Physical Chemistry 2 with Hedi Mattoussi
Rotational Motion Review
This is a review where Ive copied and pasted most of it from day 2 notes. After all weve been
through this stuff should be a breath of fresh air.
Were looking at a mas
Schilb 1
Notes 2/20/13
Physical Chemistry 2 with Hedi Mattoussi
We left off on 2D rectangular potential:
Solving for energy:
If the lengths are the same, we get square potential:
There are nodes at the edges because they are the infinite potential boundar
Schilb 1
Notes 3/22/13
Physical Chemistry 2 with Hedi Mattoussi
Energy:
For the Schrdinger Equation that we saw for a particle rotating around on a fixed sphere, we
said that the Sh. Eq. is simplified to be in a form involving the Legendre:
Simplify.
Mult
Schilb 1
Notes 1/18/13
Physical Chemistry 2 with Hedi Mattoussi
Capacitor
The electric field strength of a capacitor is equal to the electric potential divided by the distance
between the two plates.
One electron accelerated by an electric potential of on
Schilb 1
Notes 1/23/13
Physical Chemistry 2 with Hedi Mattoussi
Bragg Diffraction Review
The signal coming from rays 1 and 2 interfere because they have a phase difference that derives
from the difference in optical paths:
Constructive interference occurs
Schilb 1
Notes 1/14/13
Physical Chemistry 2 with Hedi Mattoussi
As a review, were working with black-body radiation at a certain temperature.
Here, three curves are drawn to show three different temperatures. Higher temperatures mean
that the peak intensi
Schilb 1
Notes 1/16/13
Physical Chemistry 2 with Hedi Mattoussi
Heat capacity
Monatomic solid:
Perfect gas:
At lower temperatures, the value has been found experimentally to go down.
Plancks assumptions
Plank proposed an interpretation based on:
The radia
Schilb 1
Notes 1/11/13
Physical Chemistry 2 with Hedi Mattoussi
Energy is by definition the capacity to do work. However, when it succumbs to entropy it loses
its ability to do macroscopic work.
That is the energy associated with motion, but there is also
Schilb 1
Notes 1/9/13
Physical Chemistry 2 with Hedi Mattoussi
Rotational Motion
A rotation of a particle around a central point is described by an angular moment.
The angular frequency is related to speed and the inertia is related to mass.
Example:
A po
Schilb 1
Notes 1/7/13
Physical Chemistry 2 with Hedi Mattoussi
These notes use equation editor extensively and not everyone has their software working
correctly.
If you cannot see the above equation, you may need a later version of Microsoft word.
If any
Schilb 1
Notes 3/18/13
Physical Chemistry 2 with Hedi Mattoussi
Spherical Coordinates:
Ill spare you from another review of this. We left off on the laplacian.
For Cartesian coordinates:
For spherical coordinates:
This symbol is called the legendrian and
Schilb 1
Notes 3/27/13
Physical Chemistry 2 with Hedi Mattoussi
Chapter 9
Atomic Structure:
We will use quantum mechanics to describe the electronic structure of an atom, like the
arrangement of electrons around the nucleus. The hydrogen atom has one elec
Schilb 1
Notes 3/1/13
Physical Chemistry 2 with Hedi Mattoussi
The particle in a boxs energy uses this equation:
A particle in a spherical cavitys energy uses this equation:
And then HO seems to use this one:
In order to modify the energy of the particle
Schilb 1
Notes 3/6/13
Physical Chemistry 2 with Hedi Mattoussi
Reminder:
Both real and imaginary parts of this function have nodes.
QM Angular Momentum Operator:
The equation editor doesnt allow a vector arrow and a circumflex simultaneously. Just assume
Schilb 1
Notes 2/1/13
Physical Chemistry 2 with Hedi Mattoussi
Postulate 3
The measurement of a physical parameter or observable will give a result that is only an
eigenvalue of the corresponding operator .
Postulate 4
Heres something else the Hamiltonian
Schilb 1
Notes 3/29/13
Physical Chemistry 2 with Hedi Mattoussi
Setting up the Schrdinger equation:
The Schrdinger equation for the system (nucleus and electron) can be separated into two
equations. One is for the center of mass of the whole atom and the
CHM 4410_01
HW6
1. Calculate S when a diatomic molecule at 10 C and 1.00 bar in a container of 0.450
dm3 is allowed to expand to 0.900 dm3 and is simultaneously heated to 75 C.
Assume ideal behavior.
2. Calculate S for the same changes in temperature and
CHM 4410-01!
HW5
1. Using the formal thermodynamic definitions for the constant-pressure and constantvolume heat capacities, derive a general expression for Cp - Cv. Note: a general
expression is one that would work for a non-ideal gas as well as an ideal
CHM 4410_01
HW 7
1. The Helmholtz Energy represents the maximum work that can be done by a system. Explain
this statement using the mathematical expression for the Helmholtz Energy. (Hint: a
mathematical justification is not needed.
2. Provide a mathemati