# If a system is made of 3 atoms with no degeneracy with energy levels

## Main Question or Discussion Point

if a system is made of 3 atoms with no degeneracy with energy levels of fro example 0, e, 2e

would it be safe to say that the system only has three microstate or will it be 2^3 microstates.

if it is 2^3 can you please explain why?

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It's 3 microstates. and won't be 8 anyway, it may be 6 "configurations" not microstates as follows:

classical mechanics says that it's 6=3x2x1 different configurations, because the particles would be distinguishable, like if you have 3 numbered balls in 3 different boxes, and you want to count how many configurations are possible.

Quantum mechanics says that particles like electrons are not distinguishable, therefore you have less configurations by N!, and so you only have 1 possible configuration, and yet three microstates. This gives the rise to Gibbs paradox, you can find something about that in Wikipedia.

good luck :)

thankyou veryy much

Welcome :)

if a system is made of 3 atoms with no degeneracy with energy levels of fro example 0, e, 2e

would it be safe to say that the system only has three microstate or will it be 2^3 microstates.

if it is 2^3 can you please explain why?

Each atom can be in three states. To specify the state of the three atom system means telling in which of the three state each individual atom is, so there are 3^3 = 27 microstates for the three atom system.

TheDestroyer's explanation is wrong and on the indistinguishability issue he is misleading, because if we talk about atoms that can be in certain energy level, we are usually talking about a system in which the atoms are in some position and the energy level refers to the electronic states only.

If you have a system in which you have three atoms in a box and the state refers to the complete quantum state that includes the translational motion, then depending on whether the atoms are Bosons or Fermions, can they be in the same state or not. Also, permuting te atoms does not yield a new state. But for system in which you have 3 atoms in 3 posible states, you can't divide by factorial 3 to take that into account, as you can easily see by writing down all the states.