Exam 1
Monday
September 26, 2016
Chapters 7-10
Chapter 10
Molecular Structure
The Born-Oppenheimer Approximation
In determining molecular orbitals, we assume that the kinetic and potential
energies associated with the atomic nuclei can be mathematically s
In a rotational motion, a particle travels in a circle so we need to think in terms of its
position in radians, mass in moments of inertia, velocity in radians/sec and and
momentum as angular momentum
Moment of
Inertia
I = mr2
How much
torque is
required
Franck-Condon Principle
Related to the Born-Oppenheimer Approximation, but applies to transitions
between electronic states during spectroscopy.
The nuclei are much more massive than electrons, so electronic transitions take
place faster than the nuclei c
Useful Information
Imageoffluorescenceinvarioussized
CadmiumSelenideQuantumDots
Dr.D.Talapin,UniversityofHamburg
Question: Which vial contains the smallest
diameter dots?
Chapter 9
Atomic Structure and Spectra
One of the key pieces of evidence in favor of
Recall, Solving the Schrodinger Equation for the Hydrogen Atom
Note: for Hydrogen
Atom energy is
proportional to the
Z2/n2 term
We call n the principal quantum number.
Orbitals with the same value of n form a
shell.
Another important difference
between th
Vibrational Spectra
V(x) = kx2
X = R-Re
Harmonic
Oscillator
Approximation
BornOppenheimer
Approximation of
MO energy
V(x) = kx
X = R-Re
2
But we can describe the potential V(x) by
expanding V(x) as a Taylor Series about the
point x = 0
0
A constant; set
V
Setting Up the Hamiltonian Operator for the Hydrogen Atom
The Schrodinger Equation for a Hydrogen Atom
Important-the potential energy depends only on r
Note: The Laplacian contains the angular dependence and must be expressed in
spherical polar coordinate
Exam 1
Monday
September 26, 2016
Chapters 7-10
Grotrian Diagrams
Notice: Most of the
spectroscopic
transitions are
between p orbitals
and s orbitals, and
there are no
transitions between s
orbitals
PHYSICAL CHEMISTRY: QUANTA, MATTER, AND CHANGE 2E| PETER
Setting Up the Hamiltonian Operator for the Hydrogen Atom
The Schrodinger Equation for a Hydrogen Atom
Important-the potential energy depends only on r
Note: The Laplacian contains the angular dependence and must be expressed in
spherical polar coordinate
Quantum Theory of Motion
Translational Motion
The "particle in a box" problem
Concept of quantization of energy imposed by spatial constraints
tunneling
Vibrational Motion
The harmonic oscillator problem
Model for vibrational motion of bonds and mo
CH301 Worksheet 8 Answer Key: Gases
1. What do we assume about ideal gases? What is the ideal gas law? Give the units for each
variable.
Ideal gases are infinitely small, hard spheres that do not interact with each other. They are
essentially "blind" to o
LECTURE 24: ENTROPY THE TRUTH BEHIND SPONTANEITY
We have defined spontaneity through G:
If G = () Reaction is spontaneous
If G = (+) Reaction is non-spontaneous
And we have seen that reactions can occur:
Whether a reaction is endothermic or exothermic.
Welcome to Chem 3300
Physical Chemistry:
Quantum Mechanics, Spectroscopy, and Kinetics
Michael P. Stone
Professor of Chemistry
SC 5524
michael.p.stone@vanderbilt.edu
B.S. University of California, Davis
Ph.D. University of California, Irvine
Post-doc The
Homework set Due September 5
p 311
Problems 7B1, 7B3, 7B5, 7C1, 7C3, 7C5, 7C11
The Schrodinger Equation
7B.1
Why is this important?
Second order differential equation
wavefunction
The Schrodinger
Equation shows us how
to determine the
allowed (quantum)
e
Wavefunctions that are not eigenfunctions of an operator
Another important postulate of quantum mechanics:
The acceptable wavefunctions that are eigenfunctions of any quantum
mechanical operator constitute a complete set of functions
If this is true, then
Normal modes of
vibration for CO2
symmetric stretching mode
A normal mode is an
independent synchronous
motion of atoms or groups of
atoms that is independent of
any other vibrations in the
molecule
anti-symmetric stretching mode
greatest energy
Indicated
Notice the similarity to a rotational spectrum. This is because at high resolution,
we see the effects of molecular rotation in the vibrational spectrum
Why? Analogy to ice skating
Notice her arms?
By moving her arms she can change her
rotational energy l
Chapter 12
Rotational and Vibrational Spectra
Albert Einstein and the concepts of stimulated vs. spontaneous emission of light
is the energy density of radiation at the
frequency of interest; in his research Einstein
assumed the radiation source was a id
Useful Information
1 eV = 1.602 x 10-19 J
c = 2.998 x 108 m/s
h = 6.626 x 10-34 J s
mass of baseball = 142.5 g
1 mph = 0.44704 m/s
Why is the system quantized?
Boundary Conditions !
The Heisenberg
Uncertainty
Principle requires
that a particle
confined to
Chemistry 230 - Quiz 1
September 5, 2001 Tellinghuisen
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1. (12) Obtain dy /dx for: (a) y = eln (2 x);
(b) y = ln [(3x 2 + 4)3]
(
Chemistry 230 - Quiz 6
October 17, 2001 Tellinghuisen
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1. (15) Consider the reaction, N2 + 3 H 2 2 NH 3 (where all components ar
Chemistry 230 - Quiz 5
October 10, 2001 Tellinghuisen
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1. (18) Do just ONE of the following two derivations (a or b): Be sure to
Chemistry 230 - Quiz 4
September 26, 2001 Tellinghuisen
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Note: If you want your paper returned folded (i.e., score concealed), please print your name on the back.
1. (11) The molar heat capacity of many gases can be taken to be a line