CHE 110A
CHEM 110A
Page 1 of 5
Name_KEY_
Introduction to Physical Chemistry
Mid Term 1
Student Name: _KEY_
Student ID: _
Exam Instructions:
This is a closed exam. no books, notes or additional papers permitted
Do not open the exam until instructed
Usef
CHE 110B !"#$
Homework 1
1. Express the Hamiltonian operator for a hydrogen molecule in atomic units.
2. Determine the normalized wave function for _=c1(1sA 1sB)
3. Show that
HAA = HBB = - + J
and that
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Chem 110A
Equations
2 nx
sin
L L
2 d 2 k 2
Harmonic Oscillator: H
x
2 dx 2 2
1/
4 x 2 /2
0 x e
n 2 2h2 n 2 h 2
En
2mL2
8mL2
mm
1 2
m1 m2
Particle in a 1D box: n x
3 1/ 4
4
x 2 /2
1 x
xe
1/ 4
with
2
2 x 2 x 2 1e x /2
4
p x i
x
3D:
p
= -
Homework 2
CHE110A 2013
1. Evaluate the following average values for the ground state of the Harmonic
Oscillator
(a)
(b )
(c)
(d )
<x>
<p>
<x2>
<p2>
For this problem use wavefunctions and notation
2. For a harmonic oscillator of effective mass 1.33 1025
Homework 4
CHE110A 2013
1. Using the method of making a microstate table show that the term symbols
arising from a configuration with two d electrons in the same level, 3d2 for
example are 1S, 1D, 3P 3F and 1G. Would your answer have been different for
CHE110A 2013
Homework 3
1. a. Calculate the energy of electron at ground state in J and (o=8.854x10-12 C2/N
m2 )
b. Supposed that 2 electrons are at the distance 3 amstron. Calculate the
potential energy between them in J (k=1/4o, o=8.854x10-12 C2/N m2
CHE110A 2013
Homework1
1. Use uncertainty principle of Heisenberg to determine the uncertainty of
position and velocity for 2 following situations:
a. Electron moves in atom with velocity v = 3.106 m/s, me = 9.1.10-31 kg
b. A bullet having mass of 1 gra