# CHM 501

### Homework 3

#### Due April 4, 2016

1. The repulsive term in the lattice energy equation can be assigned to be an exponential function of the form E_{rep} = Ce^{–r/d*} (this is the Mayer repulsion). Use this function and derive a lattice energy equation similar to the Born-Lande equation used in class.

2. Estimate ΔH°_{f} for the hypothetical compound KBr_{2}. Cite your sources for data you use in your calculation. Use the lattice energy equation you derived in question 1 with d* = 34.5 pm. Assume that KBr_{2} has the same structure as CaBr_{2} and that the ionic radii are similar for two cations.

3. The group 14 atoms (C (diamond), Si, Ge, and α-Sn) have the following band gaps: 5.4 eV, 1.1 eV, 0.67 eV, and 0.08 eV, respectively, and the following room temperature electrical conductivities, 10^{–6} S/cm, 10^{–5} S/cm, 10^{–2} S/cm, and 10^{0} S/cm, respectively. Are these two data sets consistent? Why or why not? What underlying periodic property (or properties) drives these trends?

Answers