Problem Set 1. Due Jan. 20 in class.
1. Math practice: evaluate the following:
sin( x )
x
2 ikx
e
f.
x 2
a.
b.
(
2 sin( x )
x 2
x eikx
g.
x
c.
)
cos(k x )
x
d.
h. eikx x
i. Prove
2 cos(k x )
x 2
e.
1
= i
i
eikx
x
(18 pts)
Note: ii = 1
b. sin( x )
Ans
Chem 344 - 1st Hour Exam
Wednesday, Sept. 26, 2012, 2-2:50 PM, 230 SES
Closed book exam, only pencils and calculators permitted. No Computers, no sheets, just you! Put
all of your work in the answer book. If you need extra graph paper we have it. Use of a
Problem Set 10. Due Apr. 13 in class
1. In class, we derived that the angular momentum of light imparts a l = 1 selection rule for hydrogen
atom transitions. However, I didnt specify what n was. I can tell you that n cannot be 0. Why?
m e4
Hint: the energ
Problem Set 2. Due Jan. 27 in class.
1. The Maxwell-Boltzmann Distribution v is:
3
mv 2
m
2 2kT
4 v2
v
e
2k T
Lets rewrite the same as a function of energy, which is E = mv2 . This is a very easy two-step
process; first, wherever you see a v in the
Graphs:
Graph 1: The absorbance of pH 13.89 of trial 1:
Graph 2: The inverse Absorbance of pH 13 of trial 1:
Graph 3: The Average Kobs
versus the concentration of each solution
Graph 4: The Absorbance of pH 13.89, Trial 2
Graph 5: The Absorbance of pH 13.
Problem Set 5. Due Feb. 24 in class.
x
1. Math practice! Operate on e using the operator
1
1
1
x + 2 2
x x x
x x x
(6 pts)
Hint: Its an eigenfunction.
Answer. Starting with the first operation on the left (the derivative) and note the operation on the
Problem Set 8 Due Mar. 16 in class
. This operator is for
i
rotational wavefunctions; the angle spans from 0 to 2. Also, every rotational wavefunction is 0 at =0
and =2.
(8 pts)
1. Prove that the following operator for angular momentum is Hermitian: lz
1
There are no donuts coming sorry
Chemistry 344 Final Exam, May 4, 2016 Version
MY NAME IS:
Extra Credit#1
1. Multiple Choice, circle your answer.
My Grade will be:
a)
b)
(1 pt)
c)
2. True and False! IN 6 (out of 8), explain why one of the statements is
Problem Set 4. Due Feb. 10 in class.
1. Which of the following functions are eigenvectors of the momentum operator p x
a. kx
b. cos(kx)
c. eikx
d. eikx e ikx
e. e kx
2
?
i x
(10 pts)
Answers:
kx
k and this is not-ok.
i x
cos(k x )
ik sin(k x ) , so
Problem Set 6. Due Mar. 2 in class.
1. In the particle-in-a-half-baked-well
problem, you see that the wavefunction
decayed exponentially into the barrier when
E<V as shown on the left. Now the
question is- what do you think happens if
the right barrier wa
Chemistry 344 Exam #2, Mar. 18, 2016 Version
1
Dont Panic
MY NAME IS:
Extra Credit#1
1. Multiple Choice, circle your answer.
You are:
d) 4-LOCO
(1 pt)
a) rotating
e) a lizard
b) vibrating
c) a hydrogen atom
f) a lizard described by a wavefunction
True and
Chemistry 344 Exam #1, Feb. 12, 2016 Version
1
Dont Panic
MY NAME IS:_
Extra Credit#1
1. Multiple Choice, circle your answer.
You are:
a) moving at the speed of light
d) a differential equation
b) unable to fit inside this box!
e) left circularly polarize
Problem Set 9. Due Apr. 6 in class
1. When solving the spherical harmonic problem, we solved for in spherical coordinates as shown
below:
2 2 I E sin 2
m 2 ll 1 sin 2 where l is the
sin sin m
2
principal rotational quantum number and m is the z-c
Chemistry 344 Exam #3, Apr. 22, 2016 Version
1
Dont Panic
MY NAME IS:
Extra Credit#1
1. Multiple Choice, circle your answer.
I am going to
d) fight crime
a) solve the Schrdinger equation
e) call myself Dr. Chicken
(1 pt)
b) be a docter
True and False! One
Problem Set 3. Due Feb. 3 in class. Its my Moms birthday!
1. In class I mentioned that light has two natural forms- right and left circularly polarized. This comes
about because light has angular momentum, specifically = 1, where is the angular momentum
q
Problem Set 7. Due Mar. 9 in class
1. For the problem of the free wave
hitting a barrier, we determined that
reflection is related to:
B k1 k 2
. Since
=
A k1 + k 2
2mE
, and E is a positive
number, then k1 is real. However, if E<V, then:
2m(E V )
2m(V E
Chem344 QUIZ #7.
1. Please identify the following H-atom radial wavefunctions (4 of them) using the
following possible 5 states: 1s, 2s, 2p, 3p, 3d:
a). This is a 1s because
0 at r =0 and there are
no nodes.
c). This is a tricky one, because it
can either
Problem Set 2. Due Jan. 25 in class.
1. The Maxwell-Boltzmann Distribution v is:
3
2
m v
m
2 2 R T
2
4 v
v
e
2R T
Lets rewrite the same as a function of energy, which is E = mv2 . This is a very easy two-step
process; first, wherever you see a v i
Problem Set 4. Due Feb. 10 in class.
1. Which of the following functions are eigenvectors of the momentum operator p x
a. kx
b. cos(kx)
c. eikx
d. eikx e ikx
e. e kx
2
?
i x
(10 pts)
Answers:
kx
k and this is not-ok.
i x
cos(k x )
ik sin(k x ) , so
Problem Set 3. Due Feb. 1 in class.
1. More math practice. You know from HW 1 that sin(x) =
using the imaginary form. Hint: cos(x) =
Answer:
eix +eix
2
eix eix
2i
. As such, please solve
.
(5 pts)
e ikx e ikx
sin(k x) 1 e ikx e ikx
1
ikeikx ikeikx k
x
Problem Set 1. Due Jan. 18 in class.
You will need to use the following integral identities:
c
e
ax2
0
c
x e
2 ax2
0
1
x
erf (c a )
2 a
dx
16a 3
2
x 2 e ax x
1
2
1
2
e
0
3
x e
1
x
2 a
2
e ax x
ax2
0
c2
1 c c 2 a
erf ca 2
e
2a
a
ax2
1
dx
Problem Set 11. Due Star Date 66783.9
1. What is the half-time of a first order reaction A products?
(
pts)
kt
Answer: Plug in [A] = [A]0 into the rate equation [A] [A]0 e kt which gives 1 2 [A]0 [A]0 e
1
2
kt
1
which turns into: 1 e 2 . Now take the
Problem Set 10. Due Apr 17 in class
1. We have talked a lot about the parabolic or harmonic potential: V 1 2 k f x 2 (where kf is the spring
constant or bond strength and x is the displacement from equilibrium). Its a good starting point for
2
2
understan
Problem Set 5. Due Feb. 27 in class
Vibrational wavefunction tunneling:
1. In class, we discovered that there is ~8% probability that a bond in the lowest vibrational state will
stretch beyond its allowed energy. Lets do the same for the first excited sta
Problem Set 9. Mostly Review. Due Apr. 10 in class.
1. Absorption of light is not instantaneous- if it was, then there would be no conservation of energy or
momentum. The timescale of absorption can be estimated from the time-energy uncertainty principal:
Chem 344 2nd Hour Exam
Wednesday, Oct. 28, 2009, 2-3:45 PM
Closed book exam, only pencils and calculators permitted. No Computers, no sheets, just you.
Put all of your work in the answer book. If you need extra graph paper we have it. Use of a
calculator
Chem 344 - 2nd Hour Exam
Wednesday, Nov. 7, 2012, 2-2:50 PM, 230 SES
Closed book exam, only pencils and calculators permitted. No Computers, no sheets, just you. Put all
of your work (and answers!) in the answer book. If you need graph paper we have it. U
Chem 344 1st Hour Exam
Wednesday, Sept. 23, 2009, 2-3 PM
Closed book exam, only pencils and calculators permitted. No Computers, no sheets, just you.
Put all of your work in the answer book. If you need graph paper we will provide it. Use of a
calculator
Friday, Nov. 14, 2008, 2-3 PM
Closed book exam, only pencils and calculators permitted. No Computers. Put all of
your work in the answer book. You may have one sheet of paper, 8.5x11 with anything
written on it, nothing more allowed. If you compute things
Chem 344 Final Exam
Wednesday, Dec. 10, 2008, 6-? PM (230 SES)
Closed book exam, only pencils and calculators permitted. You may bring and use one 8 1/2 x 11"
paper with anything on it. No Computers. Put all of your work in the answer book. If you need
gr