Problem Set 7

CHM 3411, Dr. Chatfield, Spring 2009

Due: Fri. Mar. 6

 

Suggested Discussion Question (Chapter 10): 5, 7, 8.  Suggested Exercises (Chapter 10, all (b)):  7, 8, 9, 11, 13, 14, 15.

 

This problem set explores term symbols (Ch. 10) and valence bond theory (Ch. 11).  The material for the questions on valence bond theory will be covered in class on Monday, March 2.  Note that two additional problems, 5 and 6, are included at the bottom in this new version of the problem set.  Since these were added after Wednesday evening, they will not be required to be turned in.  However, you should do them, and the solutions will be posted.

 

1. For an atom with two electrons, a complete wave function can be written as the product of a spatial function and a spin function.  Consider the following two spatial functions, i and ii, for the Li+ ion.  The first is for the ground state, the second for some of the excited states.  Note that 1s(1) is shorthand for “electron 1 in a 1s orbital,” i.e. y1s(1).

 

i)  1s(1)1s(2)            (ii) [1s(1)2s(2) – 1s(2)2s(1)]

 

(a) Determine the spin functions needed to combine with the spatial functions in order to give wave functions that are antisymmetric with respect to the interchange of any two electons, and write the corresponding complete wave functions.  Which spatial function corresponds to a singlet, and which to a triplet, and why?

 

(b) What would the ground state energy be in the absence of electron repulsion?  Will the actual energy be higher or lower?

 

2. Atkins Exercises (Chapter 10): 16b, 17b, 18b, 19b

 

3. Atkins Problem 10.5.  Note: the answer in the back of Atkins contains an error.  It should be obvious.

 

4. A state in the term 3D3 is described by the wave function y.   Consider the eigenvalue equation     where  is one of the operators listed below and w is the corresponding eigenvalue.  For each operator below, give the value of w.  (You may assume Russell-Saunders coupling to be valid.  If w has several possible values, list them all.)

 

            (a)    (b)    (c)   (d)    (e)    (f)

 

5. Consider acetylene, C2H2, in the context of valence bond theory.

(a) Determine the hybridization of the carbons, and draw a picture of the molecule in which the orbitals and the s and p bonds are identified.

(b) Show that the hybrid orbitals (their form is given in the text) are orthogonal.

 

6. Atkins Problem 11.21.