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Elements in the 3rd period and below can have more than an octet because they can access their d orbital electrons, while other elements without d orbital electrons (in period 2, such as C,N,O) cannot, therefore restricting them to only having 8 electrons.
The elements that can have more than 8 valence electrons have orbitals principal quantum number of at least 3 (n=3) so they have access to the d orbitals (d orbitals only start appearing from n=3). So, they can put the extra electrons in the d orbital. This explains why oxygen and nitrogen are not able to have more than 8 valence electrons since they don't have access to the d orbitals (n=2) while sulfur, a period down, does.
The energy between the 3d and 4s orbitals is not very big, so the d-orbitals can take in additional e- to give an expanded octet. In the first and second periods of the periodic table, no d-orbital exists, but starting with the third period, the d-orbital is present and can accomodate additional e-.
Atoms that are in the 4th period and below are the ones that are able to exceed the octet rule because they have access to their 3d orbitals. The energy difference between the 3d and 4s orbital is much smaller in comparison to other orbitals.
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