<p>There are the same number of electrons as protons.</p>
<p>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 <span class="math-container">$\rho$</span>, the density of protons' mass is <span class="math-container">$0.5\rho$</span> kg/m³.</p>
<p>So if the mass of proton is 1.67e-27 kg, then the number of protons per cubic metre which is <span class="math-container">$0.5\rho/(1.67\times 10^{-27})$</span> and the number of electrons is the same.</p>

CC BY-SA 4.0
2024-01-11T08:21:50.470Z
"> 9/10 of the atoms, by number, is neutronless hydrogen" Not in white dwarfs.
Leos Ondra
CC BY-SA 4.0
2024-01-11T13:31:24.063Z
@LeosOndra Sorry, you're right of course. I'll delete my comment before it gets more upvotes (sorry, James K).
pela
CC BY-SA 4.0
2024-01-10T22:25:50.747Z
2024-01-10T22:25:50.747Z
James K
<p>I am trying to calculate the number density of electrons (number of electrons/m^3) for a white dwarf, knowing these parameters :</p>
<ul>
<li>the mass and radius of the white dwarf (therefore its density (kg/m^3))</li>
<li>the electronic fraction : fe = 0.5</li>
</ul>
<p>I am a bit struggling with the latter notion and with the role it plays in the formula we are trying to establish.</p>
<p>Can somebody give me an easy way to link all these parameters to get the number density of electrons?</p>
<p>(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.)</p>
<p>Thanks by advance!</p>

<astrophysics><white-dwarf>
How to calculate the number density of electrons?
Jean Pégoud
# How to calculate the number density of electrons?

(Asked by: username_0 on 2024-01-10)

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!

**Tags:** astrophysics, white-dwarf


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## 1 answers

### Answer by username_1 on 2024-01-10. Score: 6 | Accepted answer

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.

> **Comments:**
> **username_2**: "> 9/10 of the atoms, by number, is neutronless hydrogen" Not in white dwarfs.  
> **username_3**: @username_2 Sorry, you're right of course. I'll delete my comment before it gets more upvotes (sorry, username_1).  

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