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Free Energy of a Simple Quantum System

  1. Nov 21, 2017 #1
    1. The problem statement, all variables and given/known data
    A quantum system has three energy levels, ##-0.12 ~\rm{eV}##, ##-0.20 ~\rm{eV}## and ##-0.44 ~\rm{eV}## respectively. Three electrons are distributed among these three levels. At a temperature of ##1727^o \rm{C}## the system has total energy ##-0.68 ~\rm{eV}##. What is the approximate free energy of the system?


    2. Relevant equations
    At temperatures higher than ##0~K## electrons occupy higher energy levels.


    3. The attempt at a solution
    Since the temperature of the system is ##>>0~k##, electrons will occupy higher energy levels.
    The energy levels might look like as follows
    Untitled3.png
    The system has a total energy $$E=-0.68~\rm{eV}$$
    Which can be obtained if two electrons are in the third energy level and one in the first energy level : $$2\times (-0.12\rm{eV})+(-0.44\rm{eV})=-0.68~\rm{eV}$$

    Assuming free energy refers to the ground state energy of the system, it is
    $$2\times (-0.44~\rm{eV})+(-0.12~\rm{eV})\approx -1.0~\rm{eV}$$

    Any other explanation possible?
     
  2. jcsd
  3. Nov 26, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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