Boltzman Equation: Exploring the Probability of Atomic Levels in Stars

[shirin]

Hi
When the temprature of star increases so that KT>>E_i(E_i as the energy of level i), Boltzmann equation states that the probability of finding atoms in every level is equal. Does this really happen or some other facts may prohibit this?

 

[Ken G]

Yes, that really happens all the time, if by "every level" you just mean "both the upper and lower levels of the transition that has energy E_i". It almost sounds like you are asking if the atom is as likely to be found in any possible level for that atom, and that only happens when all the energies are << kT, including the ionization energy. When that's true, there's very little chance of finding that atom in the first place-- it will be ionized.

If your question is just about the upper and lower levels of some particular transition in an atom that takes much more energy than that to ionize, then it happens all the time that the atom will be almost equally likely to be in the upper or lower level. For example, much of the radio spectrum deals with observing transitions whose energies are much less than kT, and as a result, the lower and upper level populations are very close, and this produces a great deal of stimulated emission and completely alters the nature of the radio brightness.

By the way, some imagine that when E_i << kT, we should expect the upper level population to be greater than the lower, but you are correct that this is not the case.

 

[shirin]

So assume that a star is just composed of neutral Helium atoms. As the temprature of the star T goes to infinity, Boltzmann equation states that the probability of finding helium atoms in each level of transition is equal, but in fact the temprature is so high that the atoms are ionized and we can't find them in tranition states of netral helium,because they are ions. Did I understand it correctly?
Now can we say that according to Boltzmann equation these ions may be found in all of excitation states equally?

 

[Ken G]

Yes, they'll be in all their excitation states equally, if there were atoms in excitation states, which there would actually be very few of, because the vast majority would be ionized. Indeed, the reason they'd be ionized is that the ionization states count among the equally-populated excitation states, and there are vastly more of them, so the atom ionizes.