Consider a 2D gas of free electrons confined to a square with area A = L² a) Determine the state density g(e) of the gas. What is the energy dependence of this space density? b) Determine the fermi energy Ef of the gas given by the number of particles N and the surface area A. Show that at temperature T = 0 K the average energy of the electrons is EF/2.
Consider a 2D gas of free electrons confined to a square with area A = L² a) Determine the state density g(e) of the gas. What is the energy dependence of this space density? b) Determine the fermi energy Ef of the gas given by the number of particles N and the surface area A. Show that at temperature T = 0 K the average energy of the electrons is EF/2.
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![Consider a 2D gas of free electrons confined to a square with area A = L
a) Determine the state density g(e) of the gas. What is the energy dependence of
this space density?
b) Determine the fermi energy Ef of the gas given by the number of particles N
and the surface area A. Show that at temperature T = 0 K the average energy of the
electrons is EF/2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f9411d4-b052-4158-b8b0-2a2b51a7f8e3%2F406f1964-7168-4e7c-bfcc-87b84ad76ec4%2Fcl4eofm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a 2D gas of free electrons confined to a square with area A = L
a) Determine the state density g(e) of the gas. What is the energy dependence of
this space density?
b) Determine the fermi energy Ef of the gas given by the number of particles N
and the surface area A. Show that at temperature T = 0 K the average energy of the
electrons is EF/2.
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