1. The Drude model requires two material-dependent parameters, n and 7. For a given material, they...

 

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1. The Drude model requires two material-dependent parameters, n and 7. For a given material, they can be systematically extracted from data. Note that 7 can depend on temperature. The goal of this problem is to find the parameters for silver and gold and to use them to find physical properties. (a) Find appropriate transport data from published sources and extract n and 7. You may work at a fixed temperature, To, of your choice. Do cite your sources. (b) Using the extracted values of n and 7, find the plasma frequencies of silver and gold. (Bonus: compare your answers with experimentally obtained values for the plasma frequencies). (c) Where do these frequencies fall within the spectrum of light? Interpret your answer in terms of the colour of silver and gold. 2. Construct a cube with its centre at the origin. (a) Construct the 'dual' of the cube, i.e., the object which has the face-centres of the cube as its vertices. Argue that this is a regular octahedron. (b) Identify all possible rotations and reflections that leave the cube invari- ant. Write these operations explicitly by labelling the vertices of the cube as A, B, C, etc. Show that the dual object is also left invariant by each symmetry operation. Argue that the converse is also true all symmetries of the dual are also symmetries of the cube. Bonus question: show that the cube has Se symmetry a six-fold rotation followed by a mirror operation about a plane perpendicular to the axis. (Hint: construct the cube with one vertex at the origin and the body diagonal along 2. Apply a six-fold rotation about the z direction.) 1. The Drude model requires two material-dependent parameters, n and 7. For a given material, they can be systematically extracted from data. Note that 7 can depend on temperature. The goal of this problem is to find the parameters for silver and gold and to use them to find physical properties. (a) Find appropriate transport data from published sources and extract n and 7. You may work at a fixed temperature, To, of your choice. Do cite your sources. (b) Using the extracted values of n and 7, find the plasma frequencies of silver and gold. (Bonus: compare your answers with experimentally obtained values for the plasma frequencies). (c) Where do these frequencies fall within the spectrum of light? Interpret your answer in terms of the colour of silver and gold. 2. Construct a cube with its centre at the origin. (a) Construct the 'dual' of the cube, i.e., the object which has the face-centres of the cube as its vertices. Argue that this is a regular octahedron. (b) Identify all possible rotations and reflections that leave the cube invari- ant. Write these operations explicitly by labelling the vertices of the cube as A, B, C, etc. Show that the dual object is also left invariant by each symmetry operation. Argue that the converse is also true all symmetries of the dual are also symmetries of the cube. Bonus question: show that the cube has Se symmetry a six-fold rotation followed by a mirror operation about a plane perpendicular to the axis. (Hint: construct the cube with one vertex at the origin and the body diagonal along 2. Apply a six-fold rotation about the z direction.)

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