# Homework Help: Free Energy of a Simple Quantum System

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1. Nov 21, 2017

### VSayantan

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

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. Nov 26, 2017

### PF_Help_Bot

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