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Midterm Exam OPTI 507 October 23, 2007, 11:00 a.m. — 12:30 p.m. 1. Consider a square lattice with lattice constant a and one atom at each site. rad Ty le— 2 —> iy a) (10 points) Sketch the reciprocal lattice and provide the appropriate dimensions and directions (of £ and ). b) (10 points) Sketch the first Brillouin zone on your picture of part (a) and give appropriate dimensions. 2. (10 points) Consider a band with energy given by E(k) = Eo — 2V) cos(ka) What is the electron velocity at k = 1 /2a? 3. (15 points) Draw qualitatively the reflection and transmission spectra of a silver film as a function of a/m, where ap is the plasma frequency. 4. Determine the number of phonon modes for the following cases. In each case, how many are optical and acoustic modes, transverse or longitudinal? a) (5 points) A three-dimensional solid with one atom per unit cell, such as aluminum. b) (5 points) A three-dimensional solid with two dissimilar atoms per unit cell, such as NaCl. c) (5 points) A three-dimensional solid with two identical atoms per unit cell, such as Ge. d) ( points) Describe the motion of the ions in the acoustic phonon and optical phonon cases. e) (5 points) Describe an experimental technique to obtain the phonon-polariton dispersion curve. 
