- 4 A Derive The Density Of States For The Free Electron Gas In 2d 9 Marks B Using The Fermi Dirac Distribution Fu 1 (32.17 KiB) Viewed 26 times
4. (a) Derive the density of states for the free electron gas in 2D. [9 marks] (b) Using the Fermi-Dirac distribution fu
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4. (a) Derive the density of states for the free electron gas in 2D. [9 marks] (b) Using the Fermi-Dirac distribution fu
4. (a) Derive the density of states for the free electron gas in 2D. [9 marks] (b) Using the Fermi-Dirac distribution function, show that the total energy of the free electron gas in 3D at T = OK is given by 3 U = Ne [Hint: in 3D the density of states is proportional to the square root of the energy. Start by finding the average kinetic energy per electron and then multiply by N to find the energy of the gas.) [10 marks] (c) Repeat this procedure to find the total energy of the 2D free electron gas. [Hint: Start by finding the average kinetic energy per electron and then multiply by N to find the energy of the gas.]
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