Lecture 3 Notes
B. A. Rowland
53750/53760
Coulomb’s Law
Charged particles (protons [+] and electrons []) can exert a force between each other
known as
electrostatic forces
. A knowledge of electrostatics is very helpful in chemistry,
as one can explain things like dipoles in water, ionic bonds, and ionization energies,
amongst others. Remember the expression:
opposites attract
. This is true in
electrostatics, as oppositely charged particles (think one proton and one electron) will
exert an
attractive
force on one another. The converse of the above statements is also
true:
likes repel
. Similarly charged particles (think two protons or two electrons) will
exert a
repulsive
force upon each other. We can write expressions for attractions and
repulsions,
Attractions (proton/electron) Repulsions (proton/proton and
electron/electron)
Where
r
is the distance between the two charged particles in questions. You would write
a
V(r)
expression for each
pair
of charged particles.
Practice Problem:
Write expressions for the electrostatic interactions in the lithium
atom.
The Hamiltonian
The Hamiltonian is the operator appearing as
H
in Schrödinger’s equation. It has the
form
The first term is a second derivative, and represents the
kinetic energy
of the wave
function. The second term is a
potential energy
term. This is where we customize the
Hamiltonian for each system of interest (for atoms, we will put attractive and repulsive
Coulomb terms
V(x)
, for the Particle in a box,
V(x)
= 0), thus generating the appropriate
Schrödinger equation.
Practice Problem
: Which (neutral) atom will have 6 electronelectron repulsion terms in
V(x)
?
Particle in a Box
There are three types of motions atoms and molecules may undergo. There are
translations
(movement through space),
rotations
, and
vibrations
. The particle in the box is the model
2
2
ˆ
( )
d
H
V x
dx
ψ
ψ
ψ
=
+
1
( ) ~
V r
r
1
( ) ~
V r
r

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for quantum translations—basically, how does an object with waveparticle duality (think
electrons) move through space in a confined potential? We will explicitly model the
wave through Schrödinger’s equation.
The set up for the particle in the box is simple. Basically, a “particle” is placed in a
canyon with infinitely high walls (to prevent the particle from leaving the box). The
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 Spring '07
 Fakhreddine/Lyon
 Chemistry, Electron, Proton, Hydrogen atom

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