Max Born:
*
( x) ( x)dx = Probability of e- between x and x+dx
2
= probability density
2
=
*
2
dx = probability
2
d = the probability in the volume element d
d = dxdydz
In spherical polar coordinates:
d=s d
r i d
nr d
2
The probability of finding
Heisenberg Uncertainty Principle
If the electron bound to two atoms is a wave we cannot specify the
electrons exact position and velocity/momentum at the same time.
1
pq
2
h
xmv
4
h
xp
4
p = cfw_< p > < p >
2
2 1/ 2
x = cfw_< x > < x >
2
2 1/ 2
Hei
The de Broglie Duality of Matter
E= mc2 (Einstein); E =h (Planck)
Photon momentum P =mv =mc
Photoelectric effect = particle
Diffraction = wave
h
c
p=
; = ,
c
h
=
mv
h
p = = mv
Electron is both a wave because it has wavelength,
and also a particle because
15
Impurities in semiconductors
15.1 Bohrs hydrogen atom model
Shallow impurities are of great technological importance in semiconductors since they determine
the conductivity and the carrier type of the semiconductor. Shallow impurities are defined as
im
Problem: If the wavefunction of an electron is proportional
to e-r/b, where b is a constant and r is the distant from the
nucleus, calculate the relative probabilities of finding the
electron inside a region of volume 1.0 pm3 located at a)
the nucleus, b)
Chem 131A Homework
Week 5
1. [12.1(b)] Calculate the zero-point energy of a harmonic oscillator consisting of a rigid CO
molecule adsorbed to a metal surface by a bond of force constant 285 N m1.
8.31021 J
2. [12.5(b)] Locate the nodes of the harmonic osc
Chem 131A Discussion
Week 5
1. Discuss the physical origin of a) quantization of energy for a particle confined to motion inside a
one-dimensional box, and b) quantum mechanical tunneling.
a) In quantum mechanics, particles are said to have wave chara
Chemistry 131A Credit by Examination
Sample questions
1. The kinetic energy of a proton is 1 eV. Find the magnitude of its velocity.
2. Two electrons are initially at rest and separated by a distance of 10-6 m. They
accelerate due to their mutual
Chem 131A Week 0 Homework
1.4b) Draw Lewis (electron dot) structures of (a) O3, (b) CIF3+, (c) N3
1.6b) Use VSEPR theory to predict the structures of (a) H2O2, (b) FSO3, (c) KrF2, (d) PCl4+
2.3b) Consider a harmonic oscillator with B=0; relate the total e
Chem 131A Homework
Week 9
1. [19.1(a)] The classical picture of an electron is that of a sphere of radius r = 2.82 fm. On the
basis of this model, how fast is a point on the equator of the electron moving? Is this answer
plausible?
2. [20.1(b)] What are t
Chem 131A Discussion
Week 10
1. Describe and account for the variation of first ionization energies along Period 2 of the
perdiodic table. Would you expect the same variation in Period 3?
2. A series of lines in the spectrum of neutral Li atoms rise
Chem 131A Homework
Week 9
1. [19.1(a)] The classical picture of an electron is that of a sphere of radius r = 2.82 fm. On the
basis of this model, how fast is a point on the equator of the electron moving? Is this answer
plausible?
The speed of rotation i
Chem 131A Homework
Week 10
1. [E23.2(b)] Suppose that a molecular orbital has the (unnormalized) form 0.727 + 0.144.
Find a linear combination of the orbitals and that is orthogonal to this linear combination
and determine the normalization constants
Chem 131A Homework
Week 8
1. [17.1(b)] Calculate the ionization energy of the Li2+ ion.
2. [17.3(b) The wavefunction for the 2s orbital of a hydrogen atom is (2 /0 ) /20 .
Determine the normalization constant .
3. [18.1(b)] What is the orbital angular mom
Chem 131A Discussion
Week 8
1. Discuss the separation of variables procedure as it is applied to simplify the description of a
hydrogenic atom free to move through space.
See textbook Section 17.1 and Justification 17.1
2. List and discuss the signif
Chem 131A Discussion
Week 3
1. Use Eulers formula to show that
1
cos() = ( + )
2
Write an equivalent expression in terms of exponential functions for sin().
sin() =
1
( )
2
2. Determine which of the following functions are eigenfunctions of the inversion
Chem 131A Homework
Week 6
1. [14.1(b)] The rotation of a molecule can be represented by the motion of appoint mass moving
on the surface of a sphere with angular momemtum quantum number = 2. Calculate the
magnitude of its angular momentum and the possible
Chem 131A Discussion
Week 4
1. Convert each of the following photon wavenumbers into a wavelength, and energies in J and eV:
a) 10 cm1; b) 1500 cm1; c) 15000 cm1; d) 25000 cm1; e) 40000 cm1. Identify the region of
the electromagnetic spectrum for each as
Chem 131A Homework
Week 4
1. [9.3(b)] Calculate the energy separations in joules, electronvolts, and as a wavenumber
between the levels (a) = 3 and = 1; (b) = 7 and = 6 of an electron in a one-dimensional
nanoparticle modeled by a box of length 1.5 nm.
(a
Chem 131A Homework
Week 1
1.
[4.1(b)] Calculate the size of the quantum involved in the excitation of (i) and molecular
vibration of period 3.2 fs; (ii) a balance wheel of period 1.0 ms. Express the results in joules and
kJ/mol.
= = /
(i) 0.21 aJ or 125
Chem 131A Homework
Week 2
1. [5.3(b)] An un-normalized wavefunction for an electron in a carbon nanotube of length is
sin(2/). Normalize this wavefunction.
2 1/2
=( )
2. [5.5(b)] What is the probability of finding the electron between = /4 and = 3/4?
= 0
Chem 131A Discussion
Week 6
1. Describe the variation of the separation of the vibrational energy levels with the mass and force
constant of the harmonic oscillator.
=
where
!
=
and ! is the force constant, m is the mass.
2. Discuss the phys
Chem 131A Discussion
Week 2
1. Show that the Planck distribution collapses to the Rayleigh-Jeans law in the long wavelength
!
!
!
!
limit. Recall that ! = 1 + + ! + ! + .
As increases, / decreases, and at very long wavelength / 1. Hence we can
expan
Chem 131A Discussion
Week 7
1. Describe the vector model of angular momentum in quantum mechanics. What features does it
capture? What is its status as a model?
See lecture notes or textbook. A vector can be used to represent angular momentum. The
ve
Chem 131A: Quantum Principles
Week 7
1. Show that the moment of inertia for rigid rotor can be written as I = r2 , where r = r1 + r2
(the fixed separation of the two masses) and is the reduced mass.
2. The J = 0 to J = 1 transition for carbon monoxide (12
Chem131A Final Exam Information
1. The final exam takes place on Friday, December 10th in ELH 100 from
8:00am 9:50am.
2. The exam will cover all material contained in chapters 1-5 of the book
with emphasis on chapters 4 and 5. Concepts related to chapters
Contrast mechanism for resolving
organic molecules with
tunnelling microscopy
J. K. Spong*, H. A. Mizesr, L. J. LaComb Jrili,
M. M. Doveki, J. E. Frommer* & J. 5. Foster*
* lBM Research Division, Almaden Research Center, San Jose,
California 95120, USA
T
Winter 2010
Chem 130 B
Practice Questions and Problems for Midterm Exam
1. Where does classical theory fail in blackbody radiation, at short or long wavelengths? How do
we know it is incorrect?
2. Where does Plancks blackbody radiation fail at?
a. Short w