Lecture 3
The first is the experiment of Joseph John Thomson, who first demonstrated that atoms are
actually composed of aggregates of charged particles. Prior to his work, it was believed that
atoms were the fundamental building blocks of matter. The fir
Molecular geometry and coordinates
Consider a diatomic molecule AB. Imagine fixing this molecule at a very specific spatial
location, as shown below:
Figure 1:
In order to locate the molecule so specifically, we would need to give the
coordinates of each
Molecules with an odd number of electrons
The octet can only work for molecules with an even number of valence electrons. While this
covers most cases, there are a few molecules that have an odd number of electrons. As an
example, consider the molecule NO
Covalent bonding and Lewis structures
Covalent bonds involve the sharing of electrons between two atoms. What do `shared'
electrons actually look like? Below are shown electron density plots of an H molecule at
four different separations between the atoms
Energetics of ionic bonding
Consider the KF molecule. K has a low ionization energy and can act as an electron donor
according to the reaction:
F has a high electron affinity and can accept an electron according to the reaction:
so that
just the sum of
kJ
Electron affinity
The electron affinity measure the ability of a neutral atom to gain an electron, as described by
the reaction:
The electron affinity,
is defined to be the negative of
for this reaction:
can be either positive or negative. If
, attachment
In this part of the course, we will set aside quantum mechanics briefly and discuss the socalled classical theory of chemical bonding. In our crude classical picture, electrons are
viewed as point particles that move in stable classical orbits determined
Hartree-Fock theory
For the helium atom, what happens if we try to use a product form as a `guess' wave
function? Ignoring spin for the moment, we take as a guess of the solution for the groundstate wave function
Then we know from problem set #4 that the
Electron spin
The quantum numbers
are not sufficient to fully characterize the physical state of the
electrons in an atom. In 1926, Otto Stern and Walther Gerlach carried out an experiment that
could not be explained in terms of the three quantum numbers
Physical character of the wave functions
Recall that a classical electron has a stable orbit around the nucleus when we neglect
electromagnetic radiation effects. The wave functions
of the electron are,
therefore, called orbitals. However, do not confuse
The Schrdinger equation for the hydrogen atom and hydrogen-like cations
So what does it look like? The Schrdinger equation for single-electron Coulomb systems in
spherical coordinates is
This type of equation is an example of a partial differential equati
The quantum hydrogen atom
Now that we have introduced the basic concepts of quantum mechanics, we can start to apply
these concepts to build up matter, starting from its most elementary constituents, namely
atoms, up to molecules, supramolecular complexes
Particle in a three-dimensional box
Generalization of the results for a two-dimensional square box to a three-dimensional cubic
box is straightforward. Since we live in a three-dimensional world, this generalization is an
important one, and we need to be
Particle in a two-dimensional box
A quantum particle of mass
that is zero if
in a two-dimensional square box by a potential energy
and
energy is entirely kinetic because
where
and
and infinite otherwise. Inside the box, the
, so the classical energy is
ar
General Chemistry II & Lab
CHEMUA 126
SAMPLE EXAM 1
(WITH ANSWERS)
Note: It is best if you start with the version
"without answers".
Spring 2012
Prof. Halpin
Page 1 of 19 tlntul' It points)
7) (nnsitltr the hydrogen hitlitlcs. HF. Hfl. HBr.':tnd HI.
:1! (
Pauling's method
Recall the Mulliken's method was based on the arithmetic average of the first ionization
energy
and the electron affinity
. Both of these energies are properties of individual
atoms, hence this method is appealing in its simplicity. Howev
Overview of molecular quantum mechanics
Using quantum mechanics to predict the chemical bonding patterns, optimal geometries, and
physical and chemical properties of molecules is a large and active field of research known as
molecular quantum mechanics or
The hydrogen molecule ion
The hydrogen molecule ion H is the only molecule for which we can solve the electronic
Schrdinger equation exactly. Note that it has just one electron! In fact, there are no multielectron molecules we can solve exactly. Thus from
Lecture 2
Research in chemistry proceeds along two directions: Experimental and theoretical.
Experimental chemistry is the science of observation. We pose a question to nature, carry out
the corresponding experiment, and observe the outcome. What happens
Lecture 1
Let us begin our study of chemisty with a simple question:
What is chemistry?
Chemistry is about structure: Specifically, it is the study of the stable structures or chemical
bonding patterns that can be formed by bringing atoms into specific sp
A word about time dependence in quantum mechanics
Recall that the Schrdinger equation
yields the allowed energies and corresponding amplitude (wave) functions. But it does not
tell us how the system evolves in time. It would seem that something is missing
A simple model of a chemical bond: A particle in a one-dimensional box
In this section, we will consider a very simple model that describes an electron in a chemical
bond. This is the so-called particle in a box model. We imagine a particle strictly confi
Lecture 6
Predicting energy levels and probabilities: The Schrdinger equation
In the last lecture, we saw that the Bohr model is able to predict the allowed energies of any
single-electron atom or cation. However, the Bohr model is, by no means, a general
Measuring spectra: The Beer-Lambert law
The figure below shows the experimental setup for taking a spectrum:
Figure: Schematic of the experimental setup needed to record a spectrum.
Radiation from a source is passed through a monochromator, which filters
Coulomb's Law
Given two charged particles with charges
and
, there is an interaction between them
that behaves as follows: Since charge can be positive or negative, opposite charges attract
each other and like charges repel each other. The strength of the
Heisenberg's uncertainty principle
If particles cannot be assigned well-defined positions and momenta, then how are these two
quantities related for a quantum particle? The fact that particles do not follow well-defined
paths means that there must be a li
Sum over paths picture (Online only)
Let us now consider an alternative explanation of the double-slit experiment, however, due to
Richard Feynman (who, by the way, was born in Queens!). This explanation is published in
his 1965 book, Quantum Mechanics an
The photoelectric effect
The photoelectric effect was explained by Albert Einstein in 1905. When light impinges on a
metal surface, it is observed that for sufficiently high frequency light, electrons will be
ejected from the surface as shown in the figur
Lecture 4
In the late 19th and early 20th centuries, the science of physics and the prevailing view of the
universe changed in a truly profound manner. The change was instigated by a series of key
experiments that could not be rationalized within the exis
Overview of organic chemistry
Organic chemistry is the study of carbon and its compounds. Because of carbon's unique
position in the periodic table (second period, group IV), it is able to form a very large number
of stable compounds due to its size and a