Chem 455 Fall 2012 Homework 5 due Mon Oct 29 5:00pm (in box 65 on 3rd floor)
1. Tunneling. An electron with energy 0.200 eV runs into a potential step of height 3.50 eV. What is the
penetration depth of the electron?
The penetration depth is 1/K, with
. F
Chem 455 Fall 2012 Homework 6 due Mon Nov 5 at 5:00pm (in box 65 on 3rd floor)
1. Oscillator. The energy eigenstates of the harmonic oscillator are described by wavefunctions that
contain the Hermite polynomials,
. Using
,
, and the recursion
relationship
Chem 455 Spring 2015 Homework 3 due Mon Apr 20 5:00pm (in box 71 on 3rd floor)
1. Orthonormal. Given two functions 0 () = 0 , 1 () = 1 + 1 , determine the values for the
coefficients and that make the functions orthonormal over the interval 0 +1. Hint: Fo
Chem 455 Spring 2015 Homework 6 due Mon May 11 at 5:00pm (in box 71 on 3rd floor)
Go to Links on the course website to get a table of isotope masses.
1. Oscillator. The vibrations of 14N2, dinitrogen, can approximately be described with a Morse potential
Chem 455 Spring 2015 Homework 6 due Mon May 11 at 5:00pm (in box 71 on 3rd floor)
Go to Links on the course website to get a table of isotope masses.
1. Oscillator. The vibrations of 14N2, dinitrogen, can approximately be described with a Morse potential
Chem 455 Spring 2015 Homework 4 due Mon Apr 27 5:00pm (in box 71 on 3rd floor)
1. 1D box. Lycopene is the main pigment in tomatoes. It features a conjugated system extending over
21 bonds (colored in red) that accommodates 11 electron pairs. A solution of
Chem 455 Fall 2012 Homework 3 due Mon Oct 15 5:00pm (in box 65 on 3rd floor)
()
1. Operators. Consider the operator
. Two eigenfunctions of this operator are
()
and
, where m is a real number. (A) Show that each has the eigenvalue
(they are degenerate).
Chem 455 Fall 2012 Homework 1 due Mon Oct 1 in class
1. Energy units. The atomic unit of energy is the hartree (symbol Eh); its value is 27.211385 eV. How
much is this in kJ/mol and in J?
2. Energy units. One of the vibrational modes (the asymmetry stretc
Chem 455 Fall 2012 Homework 5 due Mon Oct 29 5:00pm (in box 65 on 3rd floor)
1. Tunneling. An electron with energy 0.200 eV runs into a potential step of height 3.50 eV. What is the
penetration depth of the electron?
2. Tunneling. Consider an electron wit
Chem 455 Fall 2012 Homework 3 due Mon Oct 15 5:00pm (in box 65 on 3rd floor)
()
1. Operators. Consider the operator
. Two eigenfunctions of this operator are
()
and
, where m is a real number. (A) Show that each has the eigenvalue
(they are degenerate).
Chem 455 Fall 2012 Homework 2 due Mon Oct 8 5:00pm (in box 65 on 3rd floor)
The first six problems are intended to help you review some math prerequisites we need in this course.
You can find summaries in the Math Appendix of the textbook. In addition to
Chem 455 Fall 2012 Homework 7 due Fri Nov 9 5:00pm (in box 65 on 3rd floor)
1. Angular momentum. Using the definitions of the operators , and in Cartesian coordinates,
compute the commutator [ ].
For this type of operator calculations, it helps to imagine
Chem 455 Fall 2012 Homework 6 due Mon Nov 5 at 5:00pm (in box 65 on 3rd floor)
1. Oscillator. The energy eigenstates of the harmonic oscillator are described by wavefunctions that
contain the Hermite polynomials,
. Using
,
, and the recursion
relationship
Chem 455 Spring 2016 Homework 2 due Mon Apr 11 5:00pm (in box 68 on 3rd floor)
The first eight problems are intended to help you review some math prerequisites we need in this
course. You can find summaries in the Math Appendix of the textbook. In add
Chem 455 Fall 2013 Final 11 Dec 2013
Name, or student number _
Wait until instructed to start.
All necessary constants and nontrivial integrals are provided in the attached reference sheet.
Problem
1
2
3
4
5
6
7
8
9
10*
Points total
15
15
10
10
15
15
15
1
Chem 455 Spring 2012 Midterm 2 11 May 2012
Name, or student number _
Wait until instructed to start.
All necessary constants and nontrivial integrals are provided in the attached reference sheet.
Problem
1
2
3
4
5
6
7
Points total
20
15
10
10
15
15
15
100
Chem 455 Spring 2015 Homework 2 due Mon Apr 13 5:00pm (in box 71 on 3rd floor)
The first eight problems are intended to help you review some math prerequisites we need in this course.
You can find summaries in the Math Appendix of the textbook. In additio
Chem 455 Spring 2015 Homework 5 due Mon May 4 5:00pm (in box 71 on 3rd floor)
1. Leaky box. An electron with energy 0.250 eV runs into a potential step of height 1.80 eV. What is
the penetration depth of the electron?
2. Tunneling. Consider an electron wi
Chem 455 Spring 2015 Homework 7 due Mon May 18 5:00pm (in box 71 on 3rd floor)
1. Vibration/rotation. For 1H2H, the equilibrium bond length is 74.14 pm, and the force constant is
575.0 N m-1. (A) Use the rigid rotator-harmonic oscillator approximation to
Chem 455 Spring 2015 Homework 8 due Wed May 23 5:00pm (in box 71 on 3rd floor)
1. Hydrogen atom. The energies of the stationary states of the hydrogen atom can be expressed in
several different ways. Starting from
2
1 2
2
1
= ( 2 )(
) 2
4
40
2
show how
Chem 455 Spring 2015 Homework 7 due Mon May 18 5:00pm (in box 71 on 3rd floor)
1. Vibration/rotation. For 1H2H, the equilibrium bond length is 74.14 pm, and the force constant is
575.0 N m-1. (A) Use the rigid rotator-harmonic oscillator approximation to
Chem 455 Spring 2015 Homework 9 due Mon Jun 1 5:00pm (in box 71 on 3rd floor)
1. Zeeman effect. Calculate the energy splitting, in eV, between the two 1s 2S1/2 (s = 1/2, l = 0, j = 1/2)
states of a hydrogen atom placed in an external magnetic field that i
Chem 455 Fall 2013 Midterm 2 Friday 15 Nov 2013
Name, or student number _
Wait until instructed to start.
All necessary constants and nontrivial integrals are provided in the attached reference sheet.
Problem
1
2
3
4
5
6
7
Points total
20
15
10
10
15
15
1
Chem 455 Spring 2016 Homework 4 due Mon Apr 25 5:00pm (in box 68 on 3rd floor)
1. 1D box. Lycopene is the main pigment in tomatoes. It features a conjugated system extending over
21 bonds (colored in red) that accommodates 11 electron pairs. A solution of
Chem 455A Spring 2016 Midterm 1 20 April 2016
Name, or student number _KEY_
Wait until instructed to start.
All necessary constants, nontrivial equations and integrals are provided in the attached reference sheet.
Problem
1
2
3
4
5
6
7
Points total
20
13
Chem 455 Spring 2015 Homework 1 due Mon Apr 6 at 5pm in box #71 on the third floor
Significant figures (sigfigs): Make sure your result has the correct number of sigfigs! In Chem455, we use
the following convention to indicate the number of sigfigs of phy
If the location of a Helium atom is known within 20 pm, what is the uncertainty in its
velocity?
What kinetic energy would an electron need to reach a penetration depth of
0.5 nm in a barrier of 2eV?
To what depth would a proton of the same energy penetra
Boltzmann distribution
When in an MRI machine, the
protons in the H atoms in your body
can be found with their spin either
parallel or antiparallel to the
magnetic field. Each proton
constitutes a two-level quantum
system with a ground state and an
excite
If the location of a Helium atom is known within 20 pm, what is the uncertainty in its
velocity?
What kinetic energy would an electron need to reach a penetration depth of
0.5 nm in a barrier of 2eV?
To what depth would a proton of the same energy penetra
Problem 1. Consider the one-dimensional harmonic oscillator with potential energy V(:c) = (1/2)ka:2.
(a) (20 points) Calculate [W13].
(b) (10 points) Write down the Heisenberg uncertainty principle for the product of the uncertainties of
the operators V a
Problem 1. (20 points) Calculate the longest and the shortest wavelength observed in the Balmer series
(transitions to the n = 2 state of the hydrogen atom). State your result in units of nanometers (1 nm =
10"9 m).
For m9 n Mansikom 'Hne Que/5H 0[ 6 alw
Homework Set 1 Solutions
Chemistry 455 Section A, Fall 2016
Instructor: Professor Lutz Maibaum
TA: Shushan He, hes8@uw.edu
Problem 1.(Solution) To calculate the dominant wavelength we need the given equation:
hc
max =
(1)
5kB T
To then calculate frequency
Homework Set 4 Solutions
Chemistry 455 Section A, Fall 2016
Instructor: Professor Lutz Maibaum
TA: Shushan He, hes8@uw.edu
Problem 1.(Solution) (P 4.12/15.12) We have the energy eigenvalue for 1-D particle in a box:
h2 n2
(1)
En =
8ma2
1 E by changing onl
Homework Set 2 Solutions
Chemistry 455 Section A, Fall 2016
Instructor: Professor Lutz Maibaum
TA: Shushan He, hes8@uw.edu
Problem 1.(Solution) (P1.3/12.3)
The observed lines are give by:
= RH
1
1
2
2
n1 n
(1)
where n > n1 , and RH = 109677cm1 . We also