<p>The 2 in your equation is the average number of mass units per electron. e.g. totally ionised carbon has 6 electrons and 12 mass units. In your formula, the mass of a proton is used as a mass unit (close enough in this case).</p>

<p>In your second equation $n_e^{-1/3}$ is an approximation for the inter-particle separation. This <em>is</em> an approximation and there is a small numerical factor that would need to be introduced in an accurate treatment.</p>

CC BY-SA 3.0
2017-09-03T21:44:46.210Z
2017-09-03T21:44:46.210Z
ProfRob
<p>I somewhere see that in a white dwarf, we have this equation:</p>

<p>$\rho = 2 N_e * m_p / V = 2 n_e * m_p$</p>

<p>where $N_e$ is the number of particles (in this case e, electrons) and $n_e$ is the number density. and $m_p$ mass is mass of proton. My problem is with the 2 in this equation. why $2 * n_e$ and not just $n_e$?</p>

<p>Also about Electric Potential Energy between a Ion and electron, somewhere said:</p>

<p>$ E = (Z e * 1e) * n_e^{1/3} / (4 \pi \epsilon_0) $ </p>

<p>I don't understand the $n_e$ term. Is the above really a equation or is it an approximation? I think it can't be an equation  because $ne \neq 1/r^3$.</p>

<white-dwarf>
Question about number density of electrons
titansarus
# Question about number density of electrons

(Asked by: username_0 on 2017-09-03)

I somewhere see that in a white dwarf, we have this equation:

$\rho = 2 N\_e \* m\_p / V = 2 n\_e \* m\_p$

where $N\_e$ is the number of particles (in this case e, electrons) and $n\_e$ is the number density. and $m\_p$ mass is mass of proton. My problem is with the 2 in this equation. why $2 \* n\_e$ and not just $n\_e$?

Also about Electric Potential Energy between a Ion and electron, somewhere said:

$ E = (Z e \* 1e) \* n\_e^{1/3} / (4 \pi \epsilon\_0) $

I don't understand the $n\_e$ term. Is the above really a equation or is it an approximation? I think it can't be an equation because $ne \neq 1/r^3$.

**Tags:** white-dwarf

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## 1 answers

### Answer by username_1 on 2017-09-03. Score: 3

The 2 in your equation is the average number of mass units per electron. e.g. totally ionised carbon has 6 electrons and 12 mass units. In your formula, the mass of a proton is used as a mass unit (close enough in this case).

In your second equation $n\_e^{-1/3}$ is an approximation for the inter-particle separation. This *is* an approximation and there is a small numerical factor that would need to be introduced in an accurate treatment.


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