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 g
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
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 i
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
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 leavi
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. Equatio
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 va
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 dimension
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 bond
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
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, thi
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
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 th
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
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.
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 differ
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 tempe
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 assumptio
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
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
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,
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
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 elect
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 t
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 vec
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 oper
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. O
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.
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
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
mathemati