# Do electron really experience any repulsive force while attracted by proton compared to positron?

I read up that the reason 2 electrons with same energy states can be binded to the first orbital of a necleus is due to one electron having positive spin half and another having negative spin half allowed by Pauli exclusion principle, then I wonder how do an electron tell the difference between a proton and positron? Also I am not exactly sure why electrons don't repel each other while in the first orbital and can I safely rule out that the electrogmatic force is cancelled out in the first orbital since one or two electrons don't make any difference?

• There are no positrons in normal atoms. Do you consider something exotic like positronium en.wikipedia.org/wiki/Positronium? – atarasenko Jan 29 '19 at 6:21
• @atarasenko: no, I am comparing electron-positron annihilation and hydrogen atom. Because electron in both case experiences an attractive forces but in the case of hydrogen atom something is acting like a force to prevent the electron from colliding with the proton... I like to know more about this force. – user6760 Jan 29 '19 at 6:35
• Electron cannot fall on a proton because of uncertainty principle: if it is confined in a ball of radius $r$, its momentum is $\sim\hbar/r$, and kinetic energy is $\sim \hbar^2/mr^2$. The potential energy grows slower (as $1/r$). More info here physics.stackexchange.com/questions/20003/… – atarasenko Jan 29 '19 at 6:46
• It is not clear what you are asking. What do you mean by electrons "telling the difference between a proton and positron"? It is possible for an electron and a positron to not annihilate and form positronium – ACuriousMind Jan 29 '19 at 18:46

This is only approximately true. Heuristically, each electron is distributed spherically symmetrically, and so has apprx' vanishing electric field inside the sphere, so it's felt by the other electron less then the nucleus is. This sounds very strange, but it kinda works. If it was exact, then we would expect the ionization energy of Helium to be twice that of Hydrogen. In reality it's $$\frac{24.6 \, \rm{eV}}{13.6 \, \rm{eV}}\approx 1.8$$.