How many empty orbitals do elements have? A student was contemplating a question regarding elements with "no empty valence orbitals." An argument was made that elements all have infinite number of valence orbitals. 


  Every atom basically has an infinite number of shells. The thing is that almost all of those shells are empty (they don’t have electrons in them).


https://van.physics.illinois.edu/qa/listing.php?id=1224

So it is facile to say that, say, the fluoride anion has no empty valence orbitals on the basis of it having 8 valence electrons and the $2n^2$ rule (where n = 2)?
In my view there is an important difference between empty orbitals and empty valence orbital.  There are an infinite number of orbitals, a finite number of filled orbitals, but only one valence orbital.  

The definition of a valence electron is usually something like, "The electrons in the outermost shell are the valence electrons--the electrons on an atom that can be gained or lost in a chemical reaction."  Therefore, a valence orbital would be the orbital holding those electrons.  If the valence orbital is full, it is full; there are no other valence orbitals.

Based on this understanding, it would be correct to say "the fluoride anion has no empty valence orbitals."