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I have a question regarding the White Dwarf radius formula given on wikipedia, in terms of what units I am supposed to use and what expected values of one variable would be.

https://en.wikipedia.org/wiki/White_dwarf#Mass%E2%80%93radius_relationship

Listed here.

I think I have everything working, and used the right units I think (I used the eV-s version of the reduced plank constant, kg for electron mass, and of course kg-m-s2 for gravitational constant, kg for mass of the star), but I am not sure how to get the elctrons per unit mass.

So, for instance, I have a hypothetical star of 0.4 solar masses, just for a way to test the formula. But I can't get the right answer for the formula unless I know how many electrons per unit mass there are. So how exactly is this decided upon? What is a reasonable range for this value?

Like, for instance, I put in a thousand and get a radius of 1515331.7009 metres or 1515.3317 kilometres or 0.0021 solar radii. Which I know is too small, as lower mass White Dwarves should be more massive.

47.5047 seems to line up with the Radius approximation of 0.01(M)^-1/3. So would that actually be closer to the right answer? Edit: I got units wrong there, it is actually closer to 2998.8042. Not 47.5047. My mistake.

Just, please help me with finding what the values should be for electrons per unit mass. I am most confused by this condundrum.

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  • $\begingroup$ See astronomy.stackexchange.com/questions/22494/… For many small nuclei there is 1 electron for two nucleons eg Carbon 12 has 6 electrons. $\endgroup$
    – James K
    Commented Dec 4, 2023 at 0:07
  • $\begingroup$ @JamesK That doesn't seem what it is asking for here. it is asking for electrons per unit mass, not electrons per nucleus. And putting in two for that just gets out a white dwarf of only 48 metres in radius, which is definitely very, very off from the reality. It most definitely a much higher number. But it also does not seem like moles are an accurate measure either as using anything to do with moles makes the radius way too high. So it is somewhere between those, which does not narrow it down much, sadly. $\endgroup$
    – DanceroftheStars
    Commented Dec 4, 2023 at 4:17
  • $\begingroup$ What do you mean with 'eV-version of the planck constant'? You have to use the same units for everything. $h=6.62607015 × 10^{-34}m^2 kg / s$. You cannot add 12 apples and 1kg of oranges to get 13 kg of fruit salad. This said, 0.5 is a good first guess for electrons per unit mass $\endgroup$
    – planetmaker
    Commented Dec 4, 2023 at 7:37
  • $\begingroup$ And please always give the units for your numbers. It helps you as much as the reader. 47000 is no measure of size, nor is 115000. However 47000km might be. If you plug in numbers into an equation, plug in the units, too. If you don't get the expected units, check your inputs and/or conversions $\endgroup$
    – planetmaker
    Commented Dec 4, 2023 at 8:13
  • $\begingroup$ Checkout reference 40 cited just above equation for units. N is $\beta/m_p$ with $\beta$ about 0.5. $\endgroup$
    – eshaya
    Commented Dec 4, 2023 at 14:03

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