Rutgers Camden -- Department of Chemistry
Chem 345 – Fall 2010
Exam 2 –answer key
Section 1- Concepts and Definitions (50% 5 points each)
1) Give two examples of a hydrogenic atom other than hydrogen (H):
Any atom with only 1 electron: Li2+ ; atom X(atomic # -(atomic # + 1))+
2) The Born-Oppenheimer approximation allows us to select an internuclear separation in a
molecule and then to solve the Schrödinger equation for the electrons at that nuclear separation.
This can be illustrated with a molecular potential energy curve like the one shown below. In this
diagram what does the bottom of the well represent? The point where the dotted lines intersect.
Equilibrium separation of nuclei
1
3) The figure below has three distinct energy levels corresponding to bound species. The ionization
study which led to the creation of the figure obtained binding energies of 15, 5, and 1eV. Assign
the appropriate binding energy to the appropriate n-level.
4) Consider the bonding between two atomic orbitals, one is s and the other p. Circle the
figure which results in a greater bonding interaction between the two.
2
5) The ground state term symbol for a carbon atom is 3P0 (1s22s22p2). The excited state
term symbols for the excited-state electron configuration 1s22s22p13d1 are 3P, 3D, 3F, 1P,
1
D, 1F. Using the table below mark whether a given transition is allowed, if it is
forbidden indicate why by checking the appropriate box.
6) The orbital approximation allows us to rewrite the right side of the expression below
(complete the expression)
7) Draw a vector diagram(s) which represents spin-orbit coupling.
3
8) For the two states depicted to the right of the ground state correctly label each as either
singlet or triplet.
9) Illustrate two molecular orbital diagrams arising from the interaction of atomic s orbitals,
one representing a non-polar and the other a polar molecule.
4
10) Molecular orbitals are composed of linear combinations of atomic orbitals as depicted
below. Write out the probability density expressions for the bonding and antibonding
combinations of the atomic orbitals A and B (denoting which is which). Circle the
difference between the two expressions.
5
Section 2- Problems (45%)
1) (10 points) Show how the energy of a 2p orbital of a hydrogenic atom changes due to
spin-orbit coupling in terms of the spin–orbit coupling constant, A. Determine the values
and sketch an energy level diagram.
2) (10 points) In a particular photoelectron spectrum using 22.00 eV photons, electrons
were ejected with kinetic energies of 10.00 eV, 8.25 eV, and 5.50 eV. Sketch an energy
level diagram for the species, showing the ionization energies of the three identifiable
orbitals.
-I1 = -12.00 eV
-I2 = -13.75 eV
-I3 = -16.50 eV
6
3) (10 points) Using Hückel theory and the determinant below determine the MO energies
for ethene
4) (15 points) What are the possible term symbols for the following electron
configurations?
i.
ii.
iii.
i.
[Ne]3s2
1s22s13s1
1s22s22p2
[Ne]3s2
closed shell l=0 and L=0 so term is 1S
ii.
1s22s13s1
2 s electrons l=0 and L=0;
S = s1+s2 and |s1-s2| = 1, 0
so terms are 1S0 3S1
iii.
1s22s22p2
2 p electrons l=1 and L=2,1, 0;
S = s1+s2 and |s1-s2| = 1, 0
J=L+S, L+S-1, |L-S| = 3,2,1,0
so terms are 3D3 3D2 3D1 1D2 3P2 3P1 3P0 1P1 3S1
7
Section 3- Scientific Impact (5%)
Oxygen and nitrogen are two of the major components of the atmosphere as well as critical
components for all biological system. Both elements exist as diatomic gases (X2) within the
atmosphere. O2 is a reactive species which is often involved in oxidation. This process leads to
the formation or rusts and is a major influence in the general aging and weather of natural and
synthetic materials. Additionally O2 species can be transformed into radical species relatively
easily, leading to even greater reactivity. In contrast diatomic nitrogen, N2, is almost completely
unreactive under standard condition in a manner similar to the noble gases. Due to this N2 is
used most often as a preservation or preventing agent, with its primary function to prevent
reactive species from reaching a substrate.
1) (2 points) What is the bond order for:
a) O2 :1/2(8-4) = 2
b) N2 : 1/2(8-2) = 3
2) (3 points) The formation of the radical O2.- involves the addition of an electron. What
MO level would this electron be in? Be as specific as possible, you may draw your
answer or simply write down the proper designation.
Antibonding pi (Atkins, p. 385)
8