Final Exam

Ml 503/Ch 515                                                                      Dec. 14, 1998

Answer all questions on the paper supplied. Do not repeat the question. Just give a brief but complete answer. There are 100 points on this exam.

1. (10) Identify the orbitals in Figure 1. Some are atomic orbitals and some are molecular orbitals. The x,y,z coordinates are the same for all diagrams. Give as complete a label as possible.



2. (6) Benzene is a compound with six carbon atoms in a ring (cycle). Each carbon has one p electron. Write out the secular determinant equation according to the Hückel approximations. Use only x's, 0's, and 1's inside the determinant.

 

3. (7) A ring of five carbon atoms in a ring, each with one p electron, has the following five solutions to the Hückel secular determinant. x = -2, x = -(5 - 1)/2 (twice), and x = +(5 + 1)/2 (also twice).
• Sketch the energy-level diagram for this species. Label the energy levels. On the vertical axis, show "" and mark it off in 's.
• Use arrows to represent electrons and show the occupancies of these levels.
• What is the pi-electron bond order?

 

4. (7) If an atom has a spin-only magnetic moment of approximately 5.92 Bohr Magnetons, how many unpaired electrons would it have? Show your method.

 

5. (7) Consider the diatomic species C₂.
   • What would be its electronic configuration?
   • What would be its bond order?
    
6. (7) Consider the electronic configuration (t_2g)²(e_g)² for some transition metal ion.
• What tells you that this is not for an octahedral field?
• What tells you that this is not for a tetrahedral field?
• What is the geometry of the field about this ion?
 
7. (8) The cobalt 2+ ion in a tetrahedral field absorbs light at 14,900 cm^-1 (or 1.85 eV).
• What is the value of Dq for this cobalt 2+ ion (in eV)?
• What is the value of this Co²⁺'s CFSE (in eV)?

 

8. (6) Why would the following adopt a z-out tetragonal geometry rather than pure octahedral?
• A d⁷ transition metal ion?
• A d⁸ transition metal ion?
 
9. (7) Unlike radii of the first row transition metal ions in octahedral fields, those in tetrahedral fields change only slightly across the series. However, assume both weak and strong fields occur in tetrahedral fields and predict which electronic configuration might have a maximum radius and which one might have a minimum radius. Base your predictions on the same trends that occur for these ions in octahedral fields. Give your reasoning.
 
10. (7) Suppose that the two first row transition metal ions Mn³⁺ and Fe²⁺ were competing for octahedral and cubic sites in some crystal lattice. Calculate the octahedral/cubic OSSE for both ions and predict which ion would be found in the octahedral sites and which ion in the cubic sites. Give your reasoning.
 
11. (7) Two of the lanthanide elements have anomalous values for their metallic radius. Why doesn't the same effect occur in the first row transition metal series?
 
12. (7) What is the packing fraction (in units of %) for a b.c.c. lattice? Show how it is calculated.
 
13. (7) Answer both parts.
• In the unit cell of a f.c.c. lattice, there are 4 spheres and 4 octahedral sites. How many tetrahedral sites are there in this unit cell?
• If a certain cell of a h.c.p. lattice has 6 spheres (not a unit cell), then how many octahedral sites would it have in that cell?
 
14. (7) In the wurtzite lattice, the Zn²⁺ are said to be located in the tetrahedral sites within a S^2- lattice. If the Zn²⁺ has an ionic radius of 0.74 Å and the S^2- has a radius of 1.84 Å, are the radius ratio rules obeyed? Give your reasoning.