# Pchem Homework Solutions

## Chem 3322 -- Physical Chemistry II

## Syllabus

## NEW LECTURE NOTES

Lecture notes, part 1Lecture notes, part 2

Lecture notes, part 3

Lecture notes, part 4

Lecture notes, part 5

Lecture notes, part 6

Lecture notes, part 7

Lecture notes, part 8

## OLD LECTURE NOTES

Lecture notes, part 1Lecture notes, part 2

Lecture notes, part 3

Lecture notes, part 4

Lecture notes, part 5

Lecture notes, part 6

Lecture notes, part 7

Lecture notes, part 8

Lecture notes, part 9

## HOMEWORK / TESTS

Homework #1, due Jan. 22Homework #1 solutions

Homework #2, due Jan. 29

Homework #2 solutions

Homework #3, due Feb. 5

Homework #3 solutions

Homework #4, due Feb. 12

Homework #4 solutions

Homework #5, due Feb. 26

Test #1 solutions

Homework #6, due March 5

Homework #7, due March 21

Test 1 material: the first set of my lecture notes as well as the 4 assigned homework sets

Test #1 formula sheet

Test 1 textbook contents (note: some topics that we did are not in the textbook like the particle in a finite box, tunneling, particle on a ring,...)

Chapter 1: background (blackbody radiation, photoelectric effect, deBroglie hypothesis)

Chapter 2: classical wave equation; separation of variables

Chapter 3: TISE (section 3-1); probability density (sections 3-4 and 3-6); particle in a box (section 3-5); correspondence principle (section 3-6); 3d box (section 3-9)

Chapter 4: TDSE (section 4-4)

Chapter 5: classical harmonic oscillator (section 5-1); link between harmonic oscillator and chemical bond (section 5-3); harmonic oscillator energy levels (section 5-4); harmonic oscillator wavefunctions (section 5-6)

## Quantum dot and STM/STS slides

SWNT from Dinushi

Tent function fit to particle in a box eigenfunctions

The postulates of quantum mechanics

Central force notes

Anharmonic notes, part 1

Anharmonic notes, part 2

Microwave spectroscopy

missing 1

missing 2

missing 3

missing 4

missing 5

missing 6

missing 7

missing 8

missing 9

cos*cos frequencies

IR and Raman, large molecules

Raman slides

Bright Ideas for Chemical Biology

Fluorescence article

metaphysics ppt slides

metaphysics pdf slides

Quantum eraser article from Scientific Amerian

Interaction free measurement article from Scientific Amerian

Engel/Reid: *Appendix A.1* is a review of complex numbers

McQuarrie/Simon: *Mathchapter A* is a review of complex numbers

## McQuarrie/Simon

chapter 1: background to quantum theoryPractice problems: 1-9, 1-11, 1-14, 1-25, 1-34, 1-37, 1-38, 1-39

Mathchapter A: review of complex numbers

Practice problems: A-5, A-6

chapter 2: classical waves

Practice problems: 2-5, 2-16, 2-18

Mathchapter B: probability

Practice problems: B-1, B-2, B-3, B-4, B-5

chapter 3: Schroedinger equation, particle in box (1d and 3d)

Practice problems: 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8, 3-9, 3-11, 3-12, 3-13, 3-14, 3-16, 3-17, 3-19, 3-20, 3-21, 3-23, 3-25, 3-26, 3-27, 3-28, 3-29, 3-30, 3-35

chapter 4: theory

4.4: separation of variables to get time-independent equation

chapter 5: harmonic oscillator (center of mass coordinates), rigid rotor

chapter 6: hydrogen atom

eq. 6.1 -- potential energy

eq. 6.2 -- Hamiltonian operator

eq. 6.6 -- separation of variables is being attempted

eq. 6.8 -- radial equation

eq. 6.10 -- angular eq. -- spherical harmonics

eq. 6.11 -- separation of variables for the angular part

eq. 6.20 -- phi solutions

Table 6.2 -- theta solutions

Table 6.3 -- spherical harmonics

page 206 -- energies

Table 6.5 -- atomic wavefunctions for hydrogenic atoms

page 209-210 -- "s" orbitals

page 213-218 -- "p" and "d" orbitals

Problems: 6.1, 6.3, 6.20, 6.21, 6.22, 6.23, 6.24, 6.25, 6.28, 6.29, 6.32, 6.33, 6.35, 6.36

page 323-324 -- Born-Oppenheimer approx.

page 497 -- rotational and vibrational transitions

Fig. 13.1 -- rotational/vibrational levels for a diatomic in the harmonic oscillator / rigid rotor approx.

eq. 13.11 -- selection rules in harmonic oscillator / rigid rotor approx.

Fig. 13.2 -- rotational / vibrational spectrum

Fig. 13.4 -- beyond the harmonic approx.

page 521 -- active and inactive vibrational motions

page 531-532 -- rigid rotor selection rules

page 533-534 -- harmonic oscillator selection rules

Problems: 13.1, 13.2, 13.3, 13.5, 13.7, 13.8, 13.9, 13.11, 13.12, 13.34

## Chem 332: Physical Chemistry II (Spring 2013)

**Course Description:** Elementary quantum theory; atomic electronic structure; molecular structure and spectra; bonding theory

**Prerequisites:** Math 220 and Chem 331, each with a grade of C or better

**Class Schedule:** MWF 9:10-10:00 am in Fulmer 150 (note the room change)

**Textbook:**__Physical Chemistry,__ T. Engel and P. Reid, 3rd ed. (Prentice Hall, 2012)

## Navigation Links:

## Notices/Announcements:

**Final Exam is graded - all scores are now posted. Tentative final grades are also posted and will be finalized on Zzusis on Friday.**

## Staff and Office Hours:

**Instructor:**

** ** Prof. Kirk Peterson

Office: Fulmer 104B (335-7867)

** Office Hours: **Tues, 4-5pm, Fri, 2-3pm (or by appointment)

** E-mail:**kipeters@wsu.edu

**Class Web Page (this site):**

http://tyr0.chem.wsu.edu/~kipeters/Chem332/

## Grading:

points | |

3 hour exams | 600 |

homework | 150 |

final exam | 250 |

total | 1000 |

**Grading Scale:**

85 - 100%: A

80 - 84.9: A-/B+

70 - 79.9: B

65 - 69.9: B-/C+

59 - 64.9: C

56 - 58.9: C-

50 - 55.9: D

< 50% : F

**Notes:** Cheating of any kind will not be tolerated. This includes the inappropriate use of solution manuals for homework sets, as well as the usual forms of copying, etc.

__Note that homework is not a group project__.

At the discretion of the instructor, the grading scale may be curved downwards, but never upwards.

## Tentative Schedule of Lecture Topics

- Historical Background (blackbody radiation, photoelectric effect, atomic line spectra, Bohr hydrogen atom, de Broglie waves, Heisenberg Uncertainty Principle)
- Classical and Quantum Waves (classical wave equations, Schrödinger equation, operators, Postulates of Quantum Mechanics)
- Quantum Mechanics of Model Systems (free particle, particle in a box, particle on a ring, simple harmonic oscillator)
- Angular Momentum (operators, spherical harmonics)
- Vibrational and Rotational Spectroscopy of Diatomic Molecules
- The Hydrogen Atom (overview of solutions, wave functions and orbitals)
- Many Electron Atoms (He atom, electron spin, antisymmetry of the wavefunction, Slater determinants)
- Coupling of Angular Momentum in Atoms (term symbols, atomic spectroscopy)
- Approximation Methods (variation technique, perturbation theory)
- Homonuclear Diatomic Molecules (the molecular Hamiltonian, Born-Oppenheimer approximation, solutions for H
_{2}^{+}, molecular orbitals) - Molecular Structure of Polyatomic Molecules (hybridization, MO theory, Hückel method)

## Homework

- Problem Set 1 (due at beginning of class, Wednesday, Jan. 16th); solutions here
- Problem Set 2 (due at beginning of class, Friday, Jan. 25th); solutions here
- Problem Set 3 (due on Friday, Feb. 1st); solutions here
- Problem Set 4 (due on Friday, Feb. 15th); solutions here
- Problem Set 5 (due on Wednesday, Feb. 27th); solutions here
- Problem Set 6 (due on Wednesday, March 6th); solutions here
- Problem Set 7 (due on Wednesday, March 27th); solutions here
- Problem Set 8 (due on Friday, April 5th); solutions here
- Problem Set 9 (due on Monday, April 15th); solutions here

### General notes on homework assignments

(1) Show all work in order to get credit - this includes major unit conversions too (partial credit will be given, but only if I can figure out what you actually did)

(2) Use full precision for fundamental constants and masses - the data should dictate the final precision and not your rounding of known constants

(3) All final answers should have appropriate units noted

(4) Be aware of significant figures in your final result (but don't go crazy on them)(5) No hand-drawn graphs! Please minimize the use of your calculator's solver button as well as Wolfram Alpha

## Exam Solutions

## Class Resources

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Last revised (more or less): January 2, 2013

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## Comments