MB, BE & FD Statistics

  MB , BE & FD Statistics

Statestics : 

Need For Quantum Statistics

- Classical Statistics Due To Maxwell-Boltzmann Explained The Energy And Velocity 

  Distribution Of The Molecules Of An Ideal Gas But It Failed To Explain The 

  Observed Energy Distribution Of Electrons In The So Called ‘Electron Gas’ And

  That Of Photons In The ‘Photon Gas’

 

M.B Statistics :

Classical Statistics Is Generally Known As Maxwell–Boltzmann Statistics.

-      In M.B Statidtics Particales Are Indistinguishable.
-      There Is No Rustication For Particales To Occupy Any State.
-      Volume In Six Dimension (Phase Space ) Is Not Know.
-      Applicable To Ideal Gase Moluculs
-      Most Probable Distribustion Is

Limitations Of Maxwell Boltzmann Statistics

 

-    - Maxwell–Boltzmann Statistics Is Valid Only In The Classical Limit.

- It Applies Well To An Ideal Gas.

- It Also Gives You The Approx Specific Heat For Solids In Temperatures

  High Enough.

- It Fails To Explain Certain Phenomenon Like Photo 

  Electric Effect, Black Body Radiation Etc.

      

      F.D Statistics :

      - It Is Applicable For Identical And Indistinguishable Particles.

- Total Energy And Total Number Of The Particles Of The Entire System Is Constant.

- Spin Of The Particles Should Be Half Integral Spin I.E.1/2,3/2

- Particles Must Obey Pauli’s Exclusion Principle, The Number Of Particles In Each

  Sublevel Will Be One Or More I.E. Gi ≥ Ni .

- Functions Associated With The Particles Should Be Antisymmetric.

- All Particles Which Obey F.D. Statistics Are Known As Fermions (Electron, Proton,

  Neutron, 3He, Neutrino, Muons, All Hyperons (Λ, Σ, Ξ, Ω) Etc).

- Most Probable Distribustion is 

B.E Statestics :

- It is applicable for identical and indistinguishable particles.

- Any number of particles can occupy a single cell in the phase space.

- The size of cell can not be less than h³ where h isPlanck’s constant.

- The number of phase space cells is comparable with the number of particles i.e.,

  occupationind ex,ni/gi=1.

- It is applicable to particles with integral spin angular momentum in units of h/2π. All

  particles which obey B.E. statistics are known as Bosons (photon, phonon, all mesons

  etc).

- The wave function of the system is symmetric under the positional exchange of any

  two particles.

- Total energy and total number of particles of the entire system is constant

   

#MaxwellBoltzmannDistribution 

#FermiDiracDistribution

#BoseEinsteinDistribution 

#StatisticalPhysics 

#QuantumStatistics

#FDStatistics

#M.BStatistics 

#B.EStatistics 

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#B.E

#M.B

#Statistics

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