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I am trying to calculate the number density of electrons (number of electrons/m^3) for a white dwarf, knowing these parameters :

  • the mass and radius of the white dwarf (therefore its density (kg/m^3))
  • the electronic fraction : fe = 0.5

I am a bit struggling with the latter notion and with the role it plays in the formula we are trying to establish.

Can somebody give me an easy way to link all these parameters to get the number density of electrons?

(I tried many approaches but none of them was convincing. By searching the web, I found a formula using the mass of the proton, which I did not really understand.)

Thanks by advance!

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There are the same number of electrons as protons.

And half the mass is in the form of protons (the other half is neutrons) This is given by the electronic fraction. If the density of the matter is $\rho$, the density of protons' mass is $0.5\rho$ kg/m³.

So if the mass of proton is 1.67e-27 kg, then the number of protons per cubic metre which is $0.5\rho/(1.67\times 10^{-27})$ and the number of electrons is the same.

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    $\begingroup$ "> 9/10 of the atoms, by number, is neutronless hydrogen" Not in white dwarfs. $\endgroup$
    – Leos Ondra
    Commented Jan 11 at 8:21
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    $\begingroup$ @LeosOndra Sorry, you're right of course. I'll delete my comment before it gets more upvotes (sorry, James K). $\endgroup$
    – pela
    Commented Jan 11 at 13:31

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