How to Calculate Average Atom Separation in the Sun's Core?

[lycraa]

Homework Statement

in part 1 i used the Saha equation to calculate that the hydrogen in the center of the sun was fully ionized (given temperature and central electron density). part 2 says:

Re-examine the result by computing the average separation of atoms at the center of the sun knowing the radius of the first Bohr orbital.




I'm a little lost here. this would be no problem if i was given the atom density, but I'm not sure how to deal with the electron density

 

[cepheid]

Homework Statement

in part 1 i used the Saha equation to calculate that the hydrogen in the center of the sun was fully ionized (given temperature and central electron density). part 2 says:

Re-examine the result by computing the average separation of atoms at the center of the sun knowing the radius of the first Bohr orbital.




I'm a little lost here. this would be no problem if i was given the atom density, but I'm not sure how to deal with the electron density

How many electrons are there per atom, for hydrogen? What does that tell you about the number density of hydrogen atoms, given the number density of electrons?

 

[lycraa]

well, for NON ionized hydrogen, you would have only one electron. meaning that the number density would be the same as the electron density. So would i be right in saying then, that if the average separation i found using the electron density equals 2* bohr radius, i would have mostly non ionized hydrogen?

 

[cepheid]

well, for NON ionized hydrogen, you would have only one electron. meaning that the number density would be the same as the electron density.

I'm not sure why you have "NON" in all caps. I mean, if you take hydrogen and ionize it, you're still going have equal numbers of protons and electrons. Extra electrons don't just appear out of nowhere.

So would i be right in saying then, that if the average separation i found using the electron density equals 2* bohr radius, i would have mostly non ionized hydrogen?

I'm sorry, but I don't know the answer to that. On the one hand, this does seem to be the tree up which this problem is barking, by having you reconsider your previous result, and showing that these supposedly "free" electrons don't have much room to move around. On the other hand, I had always thought that the solar core consisted of charged particles, especially since people always talk of the fusion reaction consisting of free protons combining together to form helium nuclei. Besides, although those electrons may, on average, have a mean free path that is not much larger than the orbital of a bound electron, they are still too energetic to remain bound, which would have me lean more towards the ionized picture. EDIT: Remember that I said that I just don't know for sure.

 

[paranormal]

I would approach this problem by first reviewing the Saha equation and its assumptions to ensure its applicability in this situation. I would also consider any potential sources of error or uncertainties in the calculation.

Next, I would look into the relationship between electron density and atom density in the sun's core. While the electron density may not be directly given, it can potentially be estimated or inferred from other physical properties of the sun, such as its mass and temperature.

Once the electron density is determined, I would use the first Bohr radius to calculate the average separation of atoms in the sun's core. This value can then be compared to the size of the sun's core to assess the validity of the previous calculation using the Saha equation.

Additionally, I would also consider the potential effects of other factors such as temperature and pressure on the ionization of hydrogen in the sun's core. These factors may impact the average separation of atoms and should be taken into consideration in the analysis.

In conclusion, as a scientist, I would carefully review the assumptions and limitations of the Saha equation and consider other factors that may influence the ionization of hydrogen in the sun's core. By examining the results from different perspectives and taking into account all relevant factors, a more comprehensive understanding of the ionization of hydrogen in the sun can be achieved.