Why atom shells can only hold specific numbers of electrons

[mikewday]

I am looking for a fairly simplistic answer to why different "shells" in atoms can only hold a specific number of electrons. There is so much based on valence electrons and how many electrons make a full shell but, do we know why atoms "seek" a full outer shell? It seems like there should be a pretty simple answer but, I have had a hard time finding information. I appreciate any help or insight.

 

[Useful nucleus]

I can read two questions in your post and I will attempt a brief answer here. More info can be found in any introductory quantum mechanics (or Physical chemistry) text.

(1) The number of electrons that can fill a shell (or a subshell) emerges naturally from the solution of shrodinger equationn.
(2) Closed shells are favored as this minimizes the energy of the atom.

 

[tiny-tim]

hi mikewday!

… why atoms "seek" a full outer shell?

you mean, why eg does sodium like to buddy-up with chlorine, why isn't it happy just to be itself?

simple answer: it is happy when it's on its own

but when there's a nearby chlorine atom, the energy level is lower if they share an electron, so they hang around together, and have more energy for doing other things than if they stayed solo ​