1. ZnS crystallizes with the space group, with a= 3.8227(1) Å and c = 6.2607 Å
a)Draw projections of the unit cell along the  and  directions.
b) Show (1 2 10) and (0003) planes on the projections.
c) Calculate the 2θ angles at which diffraction from the (1 2 10) plane will occur for no monochromated CuKα radiation.
2. A phase diagram of the Gd-Bi binary system is presented below. You need to grow crystals of GdBi2 from the self-flux. How would you do it? What composition and temperatures would you use and why?
3. The crystals of MoO2 can be grown by chemical vapor transport with I2. The growth direction is from 900º C to 700º C. Explain the growth direction in terms of the thermodynamic parameters, K, ΔH, ΔS.
4. Derive the ground term for Dy³+ and calculate its effective magnetic moment in units of μB. Assume that a compound containing Dy³+ can be fully magnetized with a strong magnet. What magnetic moment per Dy³+ in units of μB can you achieve? Explain your answer.
5. Using the Drude theory of metals, derive the velocity of conduction electrons in n-doped Si at 20º C (electron concentration is 10²º cm-³).
Calculate the average velocity of conduction electrons in the same Si according to the free electron model, assuming that EF = 1.12eV. By comparing the two velocities, would you predict the two theories to give relatively similar values for electrical conductivity?
Note: Within the free electron model, the average energy of electrons is