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In my textbook, examples for the octet rule are only given for up to the third shell.

What about the fourth and fifth shell?

I still get confused over the fact that the $n=3$ shell has 18 electrons yet for chemical purposes atoms seek out 8 electrons. My understanding is that the energy difference between the 3p and 3d orbitals are just so large that it creates a certain stability when the 3p orbital is full. If that is true then things should get messier for the fourth and fifth shells due to more overlapping.

The first shell contains the 1s orbitals. The second shell the 2s and 2p. The third shell the 3s and 3p. What orbitals do the fourth and fifth shells include and how many electrons fill these shells?

Another way of viewing my issue. Take the electronic configuration of Calcium which is 2,8,8,2. There are 2 electrons in the fourth shell. What is the maximum number that can go in that fourth shell before a fifth shell is introduced?

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The shell concept is useful rather for 1-electron hydrogen-like atoms, where energies of ns, np, nd, nf orbitals are all the same ( well, not fully true due the very tine QED effect of interaction of electrons with quantum vacuum ).

For multielectron atoms, energy wise, $\mathrm{nd}$ orbitals from originally nth shell belong now rather to the (n+1)th shell. Similarly, $\mathrm{nf}$ orbitals from originally nth shell belong now rather to the (n+2)th shell.

So the octet rule for the 4th and higher periods have limited applicability for the $\mathrm{s}$ and $\mathrm{p}$ orbitals only for groups 1-2 and 13-18. It is not applicable for transition metals involving partially occupied $\mathrm{d}$ or $\mathrm{f}$ orbitals.

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