Fermi Distribution of Energy Levels

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SUMMARY

The discussion focuses on calculating the energy difference between two electron energy levels using the Fermi-Dirac distribution. The occupation probabilities are given as ¼ for the first level and ¾ for the second level. The calculation involves applying the Fermi-Dirac distribution formula, resulting in an energy difference of ΔE = kBT ln(20/7), which equals approximately 1.0498 kBT. The importance of including the chemical potential in the distribution is also noted.

PREREQUISITES
  • Fermi-Dirac distribution formula
  • Understanding of thermal energy (kBT)
  • Basic logarithmic functions
  • Concept of electron energy levels
NEXT STEPS
  • Study the derivation of the Fermi-Dirac distribution formula
  • Explore the role of chemical potential in statistical mechanics
  • Learn about thermal energy calculations in semiconductor physics
  • Investigate applications of Fermi distribution in solid-state physics
USEFUL FOR

Physicists, materials scientists, and students studying statistical mechanics or semiconductor physics will benefit from this discussion.

lvuongt
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Based on Fermi distribution, if there are two electron energy levels with occupation possibility of ¼ and ¾, respectively, calculate energy difference between these two levels.
 
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lvuongt said:
Based on Fermi distribution, if there are two electron energy levels with occupation possibility of ¼ and ¾, respectively, calculate energy difference between these two levels.
Hello, Did you tried an attempt for obtaining a solution? I advice you to start from Fermi-Dirac distribution formula! Write down the formula and each terms present in the formula, then you knwo what to do next,
Cheers, Rajini
 
Sorry forgot to put my attempt,

P(E)=1eE/kBT−1 ------------(1) from eq. 1, P(E1)=1/4 and P(E2)=3/4 E1=kBTln(5) E2=kBTln(7/4) hence DeltaE=E1−E2=kBTln(20/7)=1.0498 kBT

I was sure if this answer was okay since the distribution include the chemical potential as well.
 

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