Saha equation partition function for Argon?

In summary, the question is about the degeneracy of states for an Argon atom with one missing electron, and how it affects the partition function. The Saha equation is used to calculate the partition function, but different sources use different formulas for the ionization state. While in principle, all possible excited states should be included, in practice only the ground state is often sufficient. This is also true for hydrogen, and it is a normal assumption to make the "degenerate versus unimportant" distinction in the calculation of the partition function. It is loosely based on astronomy and astrophysics, as the Saha equation is used in solar spectroscopy.
  • #1
randombill
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This question is in regards to the degeneracy of states for an Argon atom with just one missing electron. For hydrogen the problem of finding the partition function depends on finding the the ionized state of hydrogen divided by the non-ionized state...

(please see Saha equation -> en.wikipedia.org/wiki/Saha_ionization_equation where
they use gi+1/ gi but most books use the following)

gi/ ga where ga for hydrogen is 2 because of the number of spins for a proton (I guess) but what about Argon's ga partition, would this require trying to find all the possible configurations (or degenerate states) down to the core (ground state)?
 
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  • #2
Hi randombill,

Is this related to astronomy somehow? If not, I can move it to the appropriate forum.

Thanks.
 
  • #3
randombill said:
This question is in regards to the degeneracy of states for an Argon atom with just one missing electron. For hydrogen the problem of finding the partition function depends on finding the the ionized state of hydrogen divided by the non-ionized state...

(please see Saha equation -> en.wikipedia.org/wiki/Saha_ionization_equation where
they use gi+1/ gi but most books use the following)

gi/ ga where ga for hydrogen is 2 because of the number of spins for a proton (I guess) but what about Argon's ga partition, would this require trying to find all the possible configurations (or degenerate states) down to the core (ground state)?
It sounds like you are asking if the partition function for the one-electron-removed Argon should include only the ground state, or all possible excited states. In principle, the latter, but in practice, the former is often all you need. The same can be said about the Argon without the missing electron-- all its excited states should be included too, but might not need to be. This is even true of hydrogen-- if you want to find the probability that a given hydrogen atom will be ionized, then you need to include all the excited states in the non-ionized hydrogen. But we generally would not bother to do that, and indeed the classical Saha equation doesn't do that. The reason is, the energy levels are usually either closely enough spaced that we can consider them to be degenerate with the ground state, or far enough spaced that the Boltzmann factor we'd associate with those states would make their contributions too small to matter. The only time we run into problems is when there are spacings that are of order kT, and in that case we must incude all such states explicitly in the partition function, and not just in some degenerate g factor. I don't know the energy levels of Argon well enough to say at what kT this could be a concern, so you'd have to check on that, but it is a normal assumption to make the "degenerate versus unimportant" distinction and just call it a g instead of a full partition function.
 
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  • #4
Drakkith said:
Hi randombill,

Is this related to astronomy somehow? If not, I can move it to the appropriate forum.

Thanks.
It's loosely based on astronomy, actually mostly astrophysics, I assume you know that the Saha equation is used for solar spectroscopy, albeit not for argon gas. Its fine if you move it but I cannot see an other category that would fit this question better which is why I choose this forum.
 
  • #5
Ken G said:
It sounds like you are asking if the partition function for the one-electron-removed Argon should include only the ground state, or all possible excited states. In principle, the latter, but in practice, the former is often all you need. The same can be said about the Argon without the missing electron-- all its excited states should be included too, but might not need to be. This is even true of hydrogen-- if you want to find the probability that a given hydrogen atom will be ionized, then you need to include all the excited states in the non-ionized hydrogen. But we generally would not bother to do that, and indeed the classical Saha equation doesn't do that. The reason is, the energy levels are usually either closely enough spaced that we can consider them to be degenerate with the ground state, or far enough spaced that the Boltzmann factor we'd associate with those states would make their contributions too small to matter. The only time we run into problems is when there are spacings that are of order kT, and in that case we must incude all such states explicitly in the partition function, and not just in some degenerate g factor. I don't know the energy levels of Argon well enough to say at what kT this could be a concern, so you'd have to check on that, but it is a normal assumption to make the "degenerate versus unimportant" distinction and just call it a g instead of a full partition function.

Alright, I'll just use the model for hydrogen then with the ionization energy for Argon with a single electron missing from the outer shell, thanks!
 
  • #6
randombill said:
It's loosely based on astronomy, actually mostly astrophysics, I assume you know that the Saha equation is used for solar spectroscopy, albeit not for argon gas.

Well, I know now! :biggrin:
 

1. What is the Saha equation for Argon?

The Saha equation for Argon is a mathematical equation that describes the ionization of Argon gas at a specific temperature and pressure. It relates the number of ionized Argon atoms to the number of neutral Argon atoms in a gas mixture.

2. How is the partition function calculated for Argon using the Saha equation?

The partition function for Argon can be calculated using the Saha equation by taking into account the ionization energy of Argon and the temperature and pressure of the gas mixture. The equation takes into account the relative energies of different ionization states of Argon and calculates the probability of each state being occupied.

3. What is the significance of the Saha equation for studying Argon gas?

The Saha equation is important for studying Argon gas because it helps us understand the behavior of the gas under different temperature and pressure conditions. It also allows us to predict the ionization state of Argon and the relative abundance of neutral and ionized Argon atoms in a gas mixture.

4. Can the Saha equation be applied to other elements besides Argon?

Yes, the Saha equation can be applied to other elements besides Argon. It is a general equation that can be used to study the ionization of any gas mixture as long as the ionization energy and other relevant parameters are known.

5. How does the Saha equation account for the effect of temperature and pressure on Argon gas?

The Saha equation takes into account the effect of temperature and pressure on Argon gas by incorporating them into the equation. As the temperature and pressure of the gas mixture change, the ionization state of Argon also changes, and the Saha equation allows us to calculate this change and understand its impact on the gas mixture.

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