CH511 Problem Set 1

due: 10:00 AM Tues Oct 15

1.    Determine the value of r where the RDF of a 2p_z orbital is a maximum.

2.    Prove that the electron probability function for a ground state N atom has spherical symmetry, i.e. show that the sum of a p_x, p_y and p_z orbital has no angular dependence.

3.   (counts as two problems) Madelung constants can be derived by calculating a summation of coulombic interactions, each term in the series indicates all the interactions for a specific ion-ion distance.  For each term, the sign (from anion or cation), the total number of interactions, and interaction distance needs to be determined.  The notes have a simple example for the infinite linear chain.

Derive the first 20 terms (arising from 20 shortest distances) for determining the Madelung constant of CsCl.  For each term, indicate the number of interactions, the sign, and the distance in terms of the lattice parameter a.  To accomplish this, apply symmetry and permutations to (xyz) coordinates, do not try to use drawings or models.

4.     After solving the above problem, what can you conclude about the convergence of this constant. Are 20 terms sufficient to determine which structures are most stable in terms of lattice enthalpy?

5.     Ternary compounds (with 3 elements) often have structures closely related to the common structure types we will discuss for binary compounds.  Describe the structures, and relations to simple binary structures, for both K₂PtCl₆ and NaFeO₂.

6.     Show that the ionic compound CaCl (s), which does not exist, would be thermodynamically unstable with respect to disproportionation.