Geometrical Multiplication of a vector by a scalar.
Positive scalar: The direction is unchanged, the length is multiplied by the scalar.
Negative scalar: The direction is reversed, the length is multiplied by the magnitude of the scalar.
Geometrical Subtr
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 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 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 4/19/13
Physical Chemistry 2 with Hedi Mattoussi
Magnetic Moment:
What happens when a magnetic moment and a magnetic field interact?
A magnetic moment in a magnetic field has a potential energy:
This is similar to what we have learned in th
Schilb 1
Notes 4/3/13
Physical Chemistry 2 with Hedi Mattoussi
Atomic Orbitals and their Energies
1) All of the energies given by the above equation are negative. They refer to the bound states of
the atom, in which the energy of atom is lower than that o
Schilb 1
Notes 2/15/13
Physical Chemistry 2 with Hedi Mattoussi
Motion in two dimensions
Let us consider a particle in a box like a particle confined in a 2D potential well. The particles
wavefunction now depends on two variables. It still obeys the Sh. E
Schilb 1
Notes 4/5/13
Physical Chemistry 2 with Hedi Mattoussi
The S-orbitals (1s, 2s, 3s, 4s, 5s)
For such orbitals, we have:
As the shell number n increases, the spatial extension of finding the electron away from the
center increases, i.e. the radius o
Schilb 1
Notes 4/10/13
Physical Chemistry 2 with Hedi Mattoussi
Review
We left off on the radial distribution function:
The function p(r) starts at zero, climbs up, but then eventually heads down to zero at infinity.
Between these points there must have b
Schilb 1
Notes 2/11/13
Physical Chemistry 2 with Hedi Mattoussi
The instructor answered questions about the homework and specifically explained the last
problem about operators. He hasnt uploaded the solutions yet at the time of writing this, but he
will
Schilb 1
Notes 4/15/13
Physical Chemistry 2 with Hedi Mattoussi
There was a small review of the p-orbitals, but weve seen enough of that.
The d-Orbitals:
There are five d-orbitals in each d-subshell.
As done for the p-orbitals, we can combine pairs of the
Schilb 1
Notes 1/25/13
Physical Chemistry 2 with Hedi Mattoussi
The Schrdinger Equation
It introduced the notion of wavefunction associated with the electron and proposed a new
equation for the electron motion that replaces the classical Newtons equation.
Schilb 1
Notes 4/12/13
Physical Chemistry 2 with Oliver Steinbock
Regardless of where we left off on Wednesday, today were starting with some new material:
Multi-electronic atoms:
An atom with two electrons would have this Hamiltonian:
That last term (ele
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 2/27/13
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 2/1/13
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
Schilb 1
Notes 2/4/13
Physical Chemistry 2 with Hedi Mattoussi
In general,
Hermitian Operators
A Hermitian operator is one for which the following relation is true:
This holds true for the momentum operator, the second derivative operator, and the x-hat p
Schilb 1
Notes 3/25/13
Physical Chemistry 2 with Hedi Mattoussi
Spin:
Key experiment: Stern-Gerlach (1921)
I found this picture online:
I dont think it matters which pole of the magnet is on top or bottom. The indentations are what
are important and I bel
Electric Circuits
1 Volt = 1Joule/Coulomb
1 Ampere = 1Coulomb/s
e = 1.602*10-19 Coulombs
Current = Potential/Resistance ()
Kirchoffs Laws:
1. Current flowing into a node = current flowing out of node
2. Sum of voltage drop in a loop is 0.
Resistors add se
Spectroscopy
= Frequency (# cycles per second), Hertz(Hz) or s-1
Quantification from luminescence experiments:
Fluorescence;
Remember that this gives energy per photon!
1mol photons = 1 einstein ; 6.022*1023 photons/einstein
Chemicals are colored b/c the