¡Bienvenido(a), Cogujada! No te preocupes por tu inglés, está muy bien.

a

_{0} is a constant independent of the element, usually and here supposedly too. The most important effect is that more protons attract all electrons nearer to the nucleus. The rest, electrostatic repulsion AND fermion nature, is only a correction.

So, I would say too: F has a smaller 2d orbital than Li.

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You mentioned shielding. If wanting such a detailed description (which is necessary to get meaningful figures), the idea of "orbitals" should be refined. Shielding is in fact only an attempt to keep the relatively manageable orbitals of the hydrogen atom, with one electron. This attempt tries to describe electrons as almost independent, a bit as if an inner electron had a distribution little altered by the outer ones, and as if an inner electron acted globally on an outer electron. Such attempts are useful, but they are formally wrong, and they need much unjustified numerical tinkering before they give meaningful figures.

Take the

electrostatic repulsion. An electron has the same charge magnitude as a proton, and the distances are about an atomic radius too. So the interactions are very strong. If you find one electron in a small volume within an atom, finding an other electron in that small volume is very improbable. That is, if p

_{1} and p

_{2} are individual probabilities for electrons 1 and 2, taken as mean values over the positions of the other electrons, then the probability of finding both electrons in the same small volume is less than p

_{1}×p

_{2}. This means that ψ(r

_{1}, r

_{2}) can't be written as ψ(r

_{1})×ψ(r

_{2}). ψ(r

_{1}, r

_{2}, ...) should be solved at once, but this is rarely done, and only for few electrons, since no algebraic solution exists, and computers stop at very few electrons. So, simplified methods are used.

I wrote "if" an electron is in a small volume, not "when". By definition of an orbital, it's independent of time. ψ(r

_{1}, r

_{2}, ...) has a component as exp(iωt), and everything else is static. |ψ| is completely independent of time. This is a bit abstract, some meditation is useful here.

ψ(r

_{1}, r

_{2}) ≠ ψ(r

_{1})×ψ(r

_{2}) is called quantum entanglement

https://en.wikipedia.org/wiki/Quantum_entanglementit's the usual situation for nearly all particles on Earth.

There is more. Fermions, including electrons, have by nature an

antisymmetric wave function ψ(r

_{1}, r

_{2}, ...). One consequence is "two electrons with antiparallel spin per orbital", but the consequences reach much farther. The wave function is antisymmetric for all electrons, including on different orbitals, which constraints the shape of the orbitals. Have a look there

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/helium.htmlwith two electrons on different orbitals of a helium atom, the energy levels depend on the alignment of the spins, because the spin is a component of antisymmetry, so it changes the shape of the possible wave functions. The effect on energy is not at all explainable by magnetic interaction.