What is Fermi energy? given the number of electrons and (L)

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SUMMARY

The discussion revolves around calculating the Fermi energy for 5.5E22 free electrons confined in a one-dimensional potential barrier of length 3.2 Å. The key point is the necessity to relate the number of electrons (N) to the volume (V) to determine the charge density (n). The confusion arises from the application of this relation, which is typically valid in three dimensions, while the problem specifically addresses a one-dimensional scenario. The distinction between potential barriers and wells is also highlighted as a critical aspect of the problem.

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  • Understanding of Fermi energy and its significance in solid-state physics.
  • Knowledge of charge density calculations in quantum mechanics.
  • Familiarity with potential barriers and wells in one-dimensional systems.
  • Basic principles of electron confinement in quantum mechanics.
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  • Study the derivation of Fermi energy in one-dimensional systems.
  • Learn about the implications of charge density in quantum mechanics.
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  • Investigate the application of three-dimensional electron density relations in various contexts.
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u061926
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hi every body

question is :
Consider that 5.5E22 free electrons are confined in a potential barrier of length 3.2A . find its Fermi energy ?the main point is that i was confident about the answer of question .. but the doctor said it is wrong .. he said i should use the relation between the number of electrons (N) to the volume (V) to get the density of charge(n) .. Even we learned that this relation used only in 3 dimensions and the question was about potential barrier which is one dimension which means that N=2n and n is fermi level and N is the number of conduction electrons .. am really con fused
 
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Perhaps the doc expected you to interpret the problem for 3D.
As written, it is not well worded.. i.e. particles may be confined in potential wells, not barriers.
 

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