Name:
Chem 3322 test #1 out of 40 marks, given on Feb. 14, 2014
I want complete, detailed answers to the questions. Show all your work to get full credit.
Data:
The Schrdinger time dependent equation is, for (x, t)
o
i
2
2 (x, t)
(x, t)
=
+ V (x)(x, t)
t
Chem 3322 homework #2 solutions, out of 17 marks
Problem 1 10 marks
Suppose we have a wavefunction
(x, t) = 1 (x)eiE1 t/ + 2 (x)eiE2 t/
(1)
with E1 = E2 . Write down an expression for the probability density corresponding to this
wavefunction and reduce i
Chem 3322 homework #2 solutions out of 32 marks Problem 1 4 marks Consider the operator d d ^ A=x - x dx dx (1)
What does this operator do to a function f (x)? Based on your answer, express this operator in a simpler form. Solution:
^ Af (x) =
d d - x f (
Problem 1 20 marks
For the harmonic oscillator with potential energy V(:c) = kx2/2 = mw2x2/2) we showed
that the (unnormalized) ground state wavefunction is 1/)(Lr) = 6"2
with or : mw/Zh.
a) 10 marks Sketch the potential energy7 the ground state wavefunct
Chem 3322 homework #3 due Feb. 6, 2015
Problem 1 particle in a box
Consider a particle in a one-dimensional box of length L in its lowest energy (ground)
stationary state. Calculate the probability that the particle is
a) in the left half of the box
b) in
Name:
Chem 3322 test #1 solutions, out of 30 marks
I want complete, detailed answers to the questions. Show all your work to get full credit.
indenite integral :
sin2 (ax)dx =
x sin(2ax)
2
4a
(1)
The Schrdinger time dependent equation is, for (x, t)
o
i
2
Name:
Chem 3322 test #1 out of 40 marks, given on Feb. 14, 2014
I want complete, detailed answers to the questions. Show all your work to get full credit.
Data:
The Schrdinger time dependent equation is, for (x, t)
o
i
2
2 (x, t)
(x, t)
=
+ V (x)(x, t)
t
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Advantages of Raman: can use any photon
wavelength you want. If you use visible light:
1. can avoid absorption of light by H2O, CO2, etc.
2. can use optical microscopy to focus with a
spatial resolution better than 0.01 mm. This is
called Raman microscope
Anharmonicity
In real molecules, highly sensitive vibrational
spectroscopy can detect overtones, which are
transitions originating from the n = 0 state for
which n = +2, +3,
Overtones are due to anharmonicity. A good
approximation of realistic anharmonic
Particle in a box : Quantum Dots
The color of light emitted by a semiconductor material
is determined by the width of the energy gap
separating the conduction and valence energy bands.
In bulk semiconductors, this gap width is fixed by the identity
(i.e.
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Chem 3322 homework #9 due April 24, 2015
Problem 1
The vibrational frequency of I2 is 208 cm1 . At what temperature will the population in
the rst excited state be half of the ground state?
Problem 2 vibrational populations
The force constants for H2 and
Chem 3322 homework #9 solutions, out of 36 marks
Problem 1 5 marks
The vibrational frequency of I2 is 208 cm1 . At what temperature will the population in
the rst excited state be half of the ground state?
Solution:
We know that, since there is no degener
Chem 3322 homework #8 solutions, out of 15 marks
Problem 1 15 marks
Relative to the n = 0 vibrational level of the ground (X) electron state of
79
Br2 , the
vibrational levels (n) of the excited (B) state have energies (in cm1 ) as follows: (the table
is
Chem 3322 homework #7 out of 27 marks
Problem 1 9 marks
The spacing between vibrational energy levels is substantially larger than the spacing
between (low-lying) rotational energy levels, which itself is substantially larger than the
spacing between tran
Chem 3322 homework #8 due April 17, 2015
Problem 1 Vibrational Energy Levels
Relative to the n = 0 vibrational level of the ground (X) electron state of
79
Br2 , the
vibrational levels (n) of the excited (B) state have energies (in cm1 ) as follows: (the
Chem 3322 homework #7 due April 10, 2015
Problem 1 Rigid Rotor / Harmonic Oscillator
The spacing between vibrational energy levels is substantially larger than the spacing
between (low-lying) rotational energy levels, which itself is substantially larger
Chem 3322 homework #3 solutions, out of 37 marks
Problem 1 9 marks
Consider a particle in a one-dimensional box of length L in its lowest energy (ground)
stationary state. Calculate the probability that the particle is
a 3 marks) in the left half of the b
Chem 3322 homework #1 solutions, out of 34 marks
Problem 1 16 marks
a 4 marks) Show that u(x, t) = sin(kx t) satises the classical wave equation by
directly using the function sin(kx t) in the wave equation.
Solution:
For this problem we need the chain ru
Chem 3322 homework #2 due Jan. 29, 2016
Problem 1 10 marks
Classical physics predicts that there is no stable orbit for an electron moving around a
proton. What criterion did Niels Bohr and/or Louis de Broglie use to dene special orbits
that he/they assum
Chem 3322 homework #3 solutions, out of 10 marks
Problem 1 5 marks
The electrons in benzene can be approximated as particles on a ring. Calculate the
diameter of this electron ring if it is assumed that a transition occurring at 250.0 nm
corresponds to an
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Course Syllabus
Course Information
(course number, course title, term, any specific section title)
PHYSICAL CHEMISTRY II - CHEM-3322-001 2015S
MWF 9:00am 9:50am GR 3.420
Professor Contact Information
(Professors name, phone number, email, office location,