Why is this statement false? The arrangement of the orbitals is the same in a multielectron atom and a single-electron atom.

Question

Why is this statement false?

 

The arrangement of the orbitals is the same in a multielectron atom and a single-electron atom.

 

The website's answer:

The arrangement of the orbitals in a multielectron atom is different from the arrangement in a single-electron atom owing to the electron-electron repulsions in a multielectron atom. In the case of a single-electron atom, the orbitals in a given principal shell have the same energy. However, in the case of a multielectron atom, the orbitals in a given principal shell have different energies.

 

What exactly is a multielectron atom and a single-electron atom? Isn't Hydrogen technically the only atom that will only have one electron? Or are they talking about valence electrons?

Answer 1

Suppose an atom of a multi-electron element is ionized to the point where it is left with only one electron.  At that point, it is a one-electron atom.  Mathematically, its electron orbitals are computed the same way as for the hydrogen atom, using quantum mechanics relations, but with +Ze instead of +e for the nuclear charge, where Z = atomic number of the element and +e = proton charge.  Use of Ze instead of e in the quantum mechanics relations will give different results for the ion shell energies compared to hydrogen, to the extent that the results depend on the nuclear charge.  (As an approximation, the higher nuclear mass will have negligible impact, but it can be accounted for too.)  When they talk about one-electron atoms, they mean hydrogen and any heavily ionized atom that is left with only one electron.