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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?

user6760
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"...then I wonder how do an electron tell the difference between a proton and positron?"

It doesn't really. 2 electrons can be bound to a positron. The proton doesn't repel the electrons, it's just that they cannot annihilate, even when they spatially overlap, in contrast with a positron.

If protons and electrons could annihilate to a photon the way positrons and electrons do, then by crossing symmetry a proton could decay into a positron by emitting a photon, in which case protons would be unstable and we would not find them abundantly in nature. You could also think of this inability to annihilate as a consequence of approximate Baryon number conservation and Lepton number conservation.

"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?"

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 $\frac{24.6 \, \rm{eV}}{13.6 \, \rm{eV}}\approx 1.8$.

Tal Sheaffer
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