Agreat success of drude was in explaining the wiedemann franz law, which states that the ratio of the electrical and thermal conductivities of metals is proportional to temperature. was drude's success a fluke (a coincidence)? give your answer via a few bullet points. (b) the fermi wavelength for metals is of order angstroms. semiconductors on the other hand, have much longer fermi wavelengths (of order tens of nanometers) why is this? how would you change the fermi wavelength of a semiconductor? provide brief explanations in each case (c) write down a general expression for the electron density in terms of the density of states and the fermi-dirac distribution function for a one-dimensional carbon nanotube (d) millions of dollars are spent to enable a scanning-tunneling microscope (stm) tip to be used to place phosphorous atoms into perfect arrays. there is in the array, no no disorder substitutions, and no dislocations imperfections, no vacancies, no at room temperature, electrical measurements show that the perfect atomic arrays have the same order of resistance as a regular bit of cheap, old metal. briefly explain why this is so. (e) a metal worker notices a correlation between the melting temperature of a metal and its coefficient of thermal expansion. for example, the melting temperatures of copper, aluminium, and indium are: 1218°c, 981 °c, and 156°c respectively their coefficients of thermal expansion are 16.6, 22, and 33 (in units of 10-6 m/m k). briefly explain the microscopic origin of this correlation.