One of these problems will be graded (10 points)

1. LiF has the NaCl structure (fcc) and a lattice parameter of 4Å. A study determines that the binding energy is given by,

Where,

a. Using this information, calculate the value of the constant A in Joules.

b. Calculate U at the equilibrium position r_o.

2. Calculate the Madelung constant for the two dimensional array below:

- + - + - + -+

+ - + - + - + -

- + - + - + -+

+ - + - + - + -

- + - + - + -+

+ - + - + - + -

- + - + - + -+

a. Calculate the contribution to the Madelung constant for each successive shell. Start with the smallest square about the central ion, and follow with the second smallest, third smallest and so on….

b. Add each contribution as follows:

i. first square

ii. first + second

iii. first + second + third

c. Does the constant calculated in bi - iii oscillate about a given number? Converge toward a given number? What does your answer tell you about the calculation: for example, Is this crystal "too small"? Comment briefly.

3. Atomic orbitals and structure. The diamond structure is shown in Figure 24 and 25, Chapter 1 in Kittel. In class it was mentioned that this structure comes about because the atomic configuration of carbon adopts a sp³ hybrid orbital configuration. Graphite, on the other hand, exhibits sp² hybridization.

Use this information to explain the hexagonal structure of graphite. Use the following steps as guidelines:

a. C is a sp element. How many valence electrons does C have?

b. Which orbitals do not hybridize when the sp² orbitals are formed?

c. Make a sketch of the structure.

4. Do problem 7, page 93 in Kittel.

5. Example 6.1 in DePodesta shows how to calculate the coefficient of the 1/r¹² term in the Lennard-Jones potential for the fcc structure. Calculate it for the coefficient of the 1/r⁶ term.