CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Problem Set 1: Solution Set
Q1.
Part a.)
UV: 10 400 nm
Visible: 400 700 nm
IR: 700 106 nm
Microwave: 106 109 nm
Part b.)
1
Wavenumber/Wavelength Conversion: =
9 nm
1&
m
Example: 106 n
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Exam 1: Solution Set
Q1.
As we derived in the last homework set, the three-dimensional time-independent
Schrdinger equation is the following:
o
(x, y, z) =
2
a
1
2
2
b
nx x
sin
a
1
2
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Exam 1: Solution Set
Q1. (McQ 3-3)1
Eigenfunctions are of the form Af (x) = f (x) where A and (eigenvalue)
are an operator and a constant, respectively. We are asked to nd the eigenval
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Exam 1: Solution Set
Q1.
See McQuarrie page 226, Figure 5.10. To have probability densities outside of the potential well indicates that there is a nonzero probability that
the oscilla
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Problem Set 2: Solution Set
Q1.
Our task is to start with a general form of the classical wave equation, with
separated variables (Eqn 2.5):
1 d2 X(x)
1
d2 T (t)
= 2
X(x) dx2
v T (t) d
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Problem Set 6: Solution Set
Q1.
We want check whether the Legendre Polynomials P0 (x) and P2 (x) are orthogonal. Naturally, we just evaluate the overlap integral.
i j d
where:
1
j = P2
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Problem Set 7: Solution Set
Q1.
We need to look at the change in volume (integral) when changing our radius.
dV
d 4 3
=
r = 4r2 dr
dr
dr 3
which explains the 4 and r2 term that is requ
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Problem Set 9: Solution Set
Q1.
The electronic conguration of Be is: 1s2 s2 so we are assigning two electrons
to two spin (s) orbitals, we only have one possible conguration:
m1
m1
s
0
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Exam 1: Solution Set
Q1.
a.) See Figure 3.2 (page 106) in McQuarrie.
b.) Were going from the rst excited state to the second excited state
of a one dimensional particle in a box. Since
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Problem Set 8: Solution Set
Q1.
HHe
1 2 1
HH =
2
r
1 2
2
2
1
=
+
2
r1 r2 r1 2
Q2.
Part a.)
Sz (r, , ) = ms (r, , )
where
1
1
ms = ., 1, , 0, + , +1, .
2
2
Part b.)
S 2 (r, , ) =
2
s
CHEM 3412: Spring 2013
Instructor: Dr. Christine Payne
TA: Colin Trout
Exam 1: Solution Set
Q1.
Part a.)
The intensity of a laser beam has no eect on the energy of the electrons.
A 400 nm laser contains the same energy electrons regardless of the power
po