Why is the Schrödinger equation so much simpler to solve for electrons in atoms like H and He+ than for Na or even B+?


a.The strong force and Coulomb forces are nearly in balance for the smaller atoms.
b.The electrons in larger atoms affect each other by Coulomb repulsion.


c. Nuclear charge is distributed in significantly larger volume in larger atoms and therefore the Coulomb force is diminished on the electrons.
d.Gravity affects each electron of larger atoms more, making the approximation of only Coulomb potential grossly inaccurate.
e. More principal quantum numbers are allowed for all electrons in the larger atoms.



The Coulomb potential field that is approximated as the only one affecting the electron in the cases with one electron around the nucleus gets far more complicated with the addition of even one more electron. The Schrödinger equation becomes very difficult to process.

Physics & Space Science

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