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CHM 3411
Final Exam
April 25th, 2005
There are seven problems on this exam. Do all of the problems. Show your work.
1) The following question is concerned with the total intensity of light emitted by an ideal blackbody.
a) Consider an ideal blackbody at some initial temperature T1. What new value for temperature
would be required to double the total intensity of light emitted by the ideal blackbody? Give your answer
in terms of T1 and/or other constants.
b) The total intensity of emitted light for a particular ideal blackbody emitter is 0.2846 J/cm2.s.
What is the temperature (in K) of this ideal blackbody?
2) Consider the operator Ô = - (2/2m) (d2/dx2). Determine under what conditions, if any, each of the
following functions is an eigenfunction of the operator Ô. For cases where the function is an eigenfunction,
give the corresponding eigenvalue.
a) f(x) = cos(ax) ; a  0
b) f(x) = exp(ax2) ; a  0
c) f(x) = sin(ax) + cos(bx) ; a  0, b  0
3) The potential energy for a particle in a sphere, which corresponds to a particle trapped within a sphere, is
V(r) = 0 ; 0  r  r0
V(r) =  ; r > r0
The wavefunctions that are solutions for the above system within the sphere may be written as follows
n,,m (r,,) = Rn,(r) Ym(,)
r  r0
 = 0, 1, 2, ..., (n-1)
n = 1, 2, 3, ...
m = 0, 1, 2, ..., 
where Rn,(r) is the radial part of the solution and Ym(,) are the spherical harmonics.
a) What is the boundary condition that applies to the above system at r = r 0? Briefly justify your
answer.
b) One radial function that is a solution to the above system is
R(r) = C sin(r/r0)
where C is a normalization constant. Find the value for C that makes R(r) a normalized radial wavefunction.
4) The wavefunctions that are solutions to the particle in a box TISE discussed in class are
n(x) = (2/L)1/2 sin(nx/L)
=0
0xL
n = 1, 2, 3, ...
x < 0 or x > L
Find the following.
a) <p2> for the n = 3 solution to the particle in a box.
b) The value for the following two integrals, which are related to the intensity of transitions
between states of the particle in a box.
i) 0L 2 x 3 dx
ii) 0L 2 x 4 dx
Note that the x that appears in between the two wavefunctions in the above integrals is the operator for
position.
5) The lowest energy electron configuration for the phosphorus atom is [Ne]3s 23p3.
a) What is the term symbol corresponding to the ground state for a phosphorus atom? Include the
appropriate value for J.
b) If an electron is promoted from a 3p to the 4s orbital the electron configuration for phosphorus
becomes [Ne]3s23p24s1. The possible combinations of ML and MS that correspond to this electron
configuration are given below. Based on this, give all of the term symbols corresponding to this electron
configuration, and rank them in order from lowest energy to highest energy. You do not have to give the
possible values for J for the various states.
ML\MS
2
1
0
-1
-2
3/2
1
1
1
1/2
1
3
4
3
1
- 1/2
1
3
4
3
1
- 3/2
1
1
1
6) A KrF eximer laser operates at a wavelength  = 249.1 nm.
a) A particular KrF laser produces 8.5 nsec light pulses with an average energy of 5.68 mJ per
pulse. How many photons are produced per light pulse?
b) Consider a molecule of 35Cl2, initially at rest and in the v" = 0, J" = 0 state. The molecule
absorbs one photon from the above laser and dissociates to form two 35Cl atoms. What is the value for v,
the velocity, for the 35Cl atoms produced by the above photodissociation process? The following
information may be of use to you in doing this problem.
m(35Cl) = 34.969 amu
D0(35Cl2) = 239.3 kJ/mole
7) Consider the molecule NS (nitrogen monosulfide).
a) Give the term symbol corresponding to the ground electronic state of NS. Note that NS is
isoelectronic with NO, and that the correct ordering for the valence molecular orbitals for this molecule are
given in Figure 14.30, page 425 of Atkins.
b) The value for the vibrational constant for 14N32S is e = 1220.0 cm-1. What value is expected
for e for 14N33S?
c) Since NS has an odd number of electrons it will exhibit an esr spectrum. At what magnetic
field strength (in Tesla) will peaks occur (at low resolution) in an esr spectrometer operating at a frequency
 = 14550. MHz (1 MHz = 106 s-1).
d) How many peaks do you expect in the esr spectrum of 14N32S? Justify your answer.
e) How many peaks do you expect in the esr spectrum of 14N33S? Justify your answer.
The following information may be of use to you in doing this problem.
m(14N) = 14.0031 amu
m(32S) = 31.9721 amu
m(33S) = 32.9715 amu
I(14N) = 1
I(32S) = 0
I(33S) = 3/2