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Electron in metal - Coggle Diagram

- - - - however, the electronic contribution is only 1% of this, Drude model fails to predict C for metal
  - - - however, from the experiment, the graph shown is as below:
- - - - Plots of N(E) versus E for two temperatures:
        
        Plot of the electron distribution function versus energy in ametal at T = 0 K and T = 300 K
        
        At T = 0 K, all levels below the Fermi energy are filled and all levels above the Fermi energy are empty
        
        At 300 K, a small fraction of the free electrons are excited above the Fermi energy.
- - - - electrons are modelled as a Fermi gas, a gas of particles which obey the quantum mechanical Fermi-Dirac statistics
      - free electron model gave improved predictions for the heat capacity of metals, however, it was unable to explain the existence of insulators
    - - utilize Pauli’s exclusion principle.
      - Electrons cannot all be in the lowest energy state, since this would violate the Pauli Principle.
    - - The Free Electron Gas
    - - Cube with volume, V = L3
      - E is the total energy of the system. The square of the wave function ( *) is equal to the probability of finding the particle at a particular region of space.
    - - 1D
      - 3D
      - energy of an electron in 3D free space:
      - Energy of moving particles follows a square law relationship:
    - - relation of for free electron
    - - Fermi radius kF given by
        
        where V is the volume equal to V = L3
      - energy of a free electron with Fermi radius kF
    - - The surface of the Fermi sphere represent the boundary between occupied and unoccupied k states at absolute zero for the free electron gas.