# Free Energy of a Simple Quantum System

Tags:
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

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.