Section 1- Concepts and Definitions (50% 5 Points Each)

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

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.

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, 1D, 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.

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.

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.

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.

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. [Ne]3s2

ii. 1s22s13s1

iii. 1s22s22p2

i. [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

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)