Fermi Energy & Calculation of Fermi Energy

 Fermi Energy & Calculation of Fermi Energy

[ 1 ] Fermi Energy :

 

- Fermi Energy Is Defined As The Energy Of The Topmost Filled

  Level In The Ground State Of N Electrons.

- As Given In Equation The Fermi Energy Can Be Given As

  𝜀𝐹 = (ℏ^2/2m) (𝑛𝐹π/L)^2

- The Fermi Energy Is A Concept In Quantum Mechanics Usually

  Referring To The Energy Difference Between The Highest And

  Lowest Occupied Single-Particle States In A Quantum System Of

  Noninteracting Fermions At Absolute Zero Temperature.

- In A Fermi Gas, The Lowest Occupied State Is Taken To Have

  Zero Kinetic Energy, Whereas In A Metal, The Lowest Occupied

  State Is Typically Taken To Mean The Bottom Of The Conduction

  Band.

 

[ 2 ] Calculation Of Fermi Energy :

 

- Suppose A Given Metal Contains N Free Electrons. We Can

  Calculate Its Fermi Energy By Filling Up Its Energy States.

- At T=0, Starting From 𝜀 = 0, All Quantum States Upto 𝜀 = 𝜀𝐹 

   Are Filled. That Is

- This Is The Expression For The Fermi Energy Of A Metal At T=0,

   The N/V Is The Density Of Free Electrons.

- Thus, The Fermi Energy Is Independent Of The Size Of Metal.

   Fermi Energy Can Be Written In Terms Of Fermi Temperature

   Defined As  𝜀𝐹  = ktf,Where K Is The Boltzmann’s Constant.

 

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