Question 1 The Fermi energy of metallic gold is 5.53 eV. a) Calculate the Fermi temperature of gold and, hence, lustify

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Question 1 The Fermi Energy Of Metallic Gold Is 5 53 Ev A Calculate The Fermi Temperature Of Gold And Hence Lustify 1 (475.19 KiB) Viewed 43 times

Question 1 The Fermi energy of metallic gold is 5.53 eV. a) Calculate the Fermi temperature of gold and, hence, lustify the applicability of the degenerate (le at OK) electron gas model to gold at 273 K. Use diagrams in your answer showing schematically the distribution of the electrons at OK and 273 K. (6 marks) b) Show that the total number of electrons contained in a volume of gold at OK can be written as an integral of the density of states. Use this result to estimate the number density and the average energy Ew of the free electron gas in gold at 300 K. The density of states of the free electron gas is 8(E)= *** (2me). (9 marks) c) Obtain an expression for the pressure P of the free electron gas as a function of its Fermi energy and electron number density if P = (2E/3V) and Els the total internal energy of the gas and is the volume. Estimate the value of Pfor metallic gold at 273 K. (10 marks)