Why are excited state populations so rare in the sun despite tiny energy cost?

[zezima1]

My book calculates the ratio of probability to find an atom in an excited state vs finding it in the ground state in the sun and gets approx 1/10⁹.
Essentially this must mean that the ratio of the multiplicities of the system must also be equal to this, i.e.:

$\Omega$2/$\Omega$1 = 1/10⁹

How can this be possible? Say you excite the atom. The energy that the surroundings in the sun loses is tiny compared to its total energy. So shouldn't the two multiplicities be approximately the same?

 

[mathman]

There is something very confusing about your question. There are few (if any) atoms in the sun. Just about everything is fully ionized.

 

[zezima1]

It's in the sun's atmosphere.

 

[mathman]

It's in the sun's atmosphere.

I am not sure what you mean by the sun's atmosphere, since it is entirely in a gaseous or plasma state. The surface is close to 6000 K. I presume everything is highly ionized, but I am no expert on the subject.

 

[zezima1]

Then say its somewhere, where everything is not ionized. This has no relevance for my question, which is about the conceptual understanding of the Boltzmann distribution!

 

[Modulated]

Essentially this must mean that the ratio of the multiplicities of the system must also be equal to this

Really? This would imply that every energy level is equally likely to be filled, which I hope seems unlikely. So what difference between the ground and the excited state haven’t you taken into account?