Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #4 Key
57 Points
Total
I. Time and Length Scales
1
1. The velocity of an electron inside of an atom is roughly 100 of the speed of light.
(a) Compute the classical momentum at this velocity.
= = (9.1
Chem 3060 Quantum Chemistry & Spectroscopy Problem Set #1 Solutions
Copyright: Michael D. Morse
I. Matter Waves
1. The properties of molecular-scale entities challenge our classical intuition. For this problem,
we will compare the properties of an electro
Chem 3060 Quantum Chemistry & Spectroscopy Copyright Michael Morse
Problem Set # 4 Solutions
I.
Time Dependence
1. We are accustomed to thinking of the ammonia molecule, NH3, as a trigonal pyramidal
molecule which possesses a permanent electric dipole mom
Chem 3060 Quantum Chemistry & Spectroscopy
Copyright Michael Morse
Problem Set # 6 Due Wednesday, November 2
1. A particle of mass moves in a spherical box of radius r0. The particles position is best described
using the spherical polar coordinates (r, ,
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set # 7 Solutions
1. Which of the following wavefunctions satisfy the requirement that the wavefunction must change sign
when two indistinguishable fermions are exchanged? [This is an example of a questio
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set # 5 Due Friday, October 9
1.
The particle on a ring model is suitable as a very crude model for the -electron system in
benzene. Since benzene has 6 -electrons, they will fill the m = 0, m = 1, and m
Chem 3060 Quantum Chemistry & Spectroscopy Problem Set #2 (copyright: Michael D. Morse)
Due Wednesday, September 7 at the beginning of class
I. Time and Length Scales
1. For the following wavelengths, determine whether the radiation is in the microwave, i
Additional Term Symbol Problems - Solutions:
1. An excited configuration of the carbon atom is 1s2 2s2 2p1 3p1. How many states are contained in
this configuration?
A straightforward way to do this is to use the formula #states =
!
!
!
, and apply it to e
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set # 8 Due Monday, November 23
1.
How many states are contained in a
(a).
2p1 3d1 configuration?
The 2p orbital can hold 6 electrons, so N=6. However, only one electron is present, so
n=1. Likewise, the
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #1 Key
Graded
5 pts
I. Time and Length Scales
1. For each of the following systems, determine the order-of-magnitude value for the size of the system (in
SI units of length, meters). For example, a la
Chem 3060 Quantum Chemistry & Spectroscopy Copyright Michael Morse
Problem Set # 3 Due Wednesday, September 14
I. Time and Length Scales
1. The position of an electron in an atom is known to within 2 (this value is the standard deviation, or
x). Using Hei
58 Points
Total
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #3 Key
I. Time and Length Scales
1. (a) Calculate the de Broglie wavelength (in m) for the following objects:
Graded
14 pts
(1 pt ea on (a),
4pts for (b)
The de Broglie wavelength may
35 Points Total
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #6 Key
(3 pts ea)
I. Time and Length Scales
1. The NIST WebBook is a wonderfully useful resource for chemists.
It provides many of the basic
structural, thermodynamic, and spectroscopi
67 Points Total
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #5 Key
+ up to 2 bonus
points
I. Time and Length Scales
Graded
8 pts
1. The particle-in-a-box energies are quantized. We often claim that such quantization is irrelevant on the
macrosc
59 Points Total
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #7 Key
I. Time and Length Scales
1. Determine ballpark numbers for the spacing between (a) electronic, (b) vibrational, and (c) rotational
transitions.
Electronic 10,000s of cm-1
6 Poi
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #14 Key
40 Points Total
I. Time and Length Scales
1. Pigments work by selectively absorbing certain wavelengths of light.
6 Points
(3 ea)
(a) Estimate the wavelength of light (in nm) absorbed by blue
40 Points Total
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #11 - Key
I. Time and Length Scales
1. In lecture, we saw that a superposition of two energy eigenstates will oscillate at a certain frequency. For
a superposition of the ground and fi
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #12 Key
50 Points Total
I. Time and Length Scales
1. Determine the approximate vibrational frequency for each of the following functional groups:
(a) O-H stretches
3600 cm-1
(b) C-H stretches
3000 cm-
41 Points
Total
Chem 3060 Quantum Chemistry & Spectroscopy
Problem Set #2 - Key
I. Time and Length Scales
1. For the following types of radiation, determine the corresponding (approximate) wavelength, in
nanometers.
Graded
18 pts
(2 pts ea,
4 pts for part