For 3D free electron gas, the density of states counts the number of degenerate electron states dn per energy interval dE around a given energy E as g(E): = dn dE 3 (2m₂)2V 1 E2 2π²ħ³ At absolute zero temperature, N electrons can fill up all low lying energy levels (following Pauli exclusion principle) up to a given energy level E called Fermi energy. From the density of states, what is the relation between the total electron states N below a given energy E? Use this result to show that the Fermi energy EF is given by - - 2010 (307² M)³ ħ² 3π²N\3 EF 2me V
For 3D free electron gas, the density of states counts the number of degenerate electron states dn per energy interval dE around a given energy E as g(E): = dn dE 3 (2m₂)2V 1 E2 2π²ħ³ At absolute zero temperature, N electrons can fill up all low lying energy levels (following Pauli exclusion principle) up to a given energy level E called Fermi energy. From the density of states, what is the relation between the total electron states N below a given energy E? Use this result to show that the Fermi energy EF is given by - - 2010 (307² M)³ ħ² 3π²N\3 EF 2me V
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Transcribed Image Text:For 3D free electron gas, the density of states counts the number of degenerate electron states dn per
energy interval dE around a given energy E as
g(E):
=
dn
dE
3
(2m₂)2V 1
E2
2π²ħ³
At absolute zero temperature, N electrons can fill up all low lying energy levels (following Pauli exclusion
principle) up to a given energy level E called Fermi energy.
From the density of states, what is the relation between the total electron states N below a given
energy E? Use this result to show that the Fermi energy EF is given by
- - 2010 (307² M)³
ħ²
3π²N\3
EF 2me V
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