Physicist: There’s no reason for electrons not to fill sub-shells past “f”, it’s just that they don’t need to. By the time the atomic number (which is the number of protons or electrons) is large enough to need a new kind of orbital you’ve got a very unstable element on your hands: element 121, “unbiunium”.
Electrons fill shells in a weird order as the atomic number increases. A good way to think of the way an electron hangs out around an atomic nucleus is as a “standing wave”. Thinking of an electron as being like a planet in orbit leads to all kinds of problems. But while a standing wave on a guitar or cello string is pretty straight forward (take a look), standing waves in two and three dimensions are more complex. The math behind standing waves in a (symmetrical) 3-d situation is called “spherical harmonics“.
Most of the energy of an electron’s orbital is determined by what shell it’s in, N=1,2,3… However, there’s also energy tied up in the weird shapes of the electrons’ sub-shells (denoted by s, p, d, f) and that makes things more complicated than just looking at N. The math behind calculating the amount of energy for a particular orbital is stunningly nasty. However, very luckily, the order of orbitals from least energy to most is kinda simple.
The “kinda simple” order in which these shells fill up is responsible for the kinda simple structure of the periodic table. If you feel like tracing it out yourself, these are the basic rules for all of chemistry (relax chemists, your secrets are safe).
The chemical properties of an element are mostly due to the number of electrons in the s and p sub-shells, and the different types hold different numbers of electrons: 2 in s, 6 in p, 10 in d, 14 in f, and so on (increasing by 4 each time). The lines on the periodic table loop around when the s and p sub-shells are filled. For example: helium (1s), neon (1s+2s+2p), argon (1s+2s+2p+3s+3p), etc. The reason that the rows of the periodic table get longer is that the electrons have more sub-shells to fill.
The first atom that would need a “g” orbital would be element 121. However, the largest found so far is 118 (so close!). For comparison, uranium is element number 92. This is all a bit of a moot point however. The higher the atomic number, the less stable the element is. The half-life of element 118 is about 1/1000 of a second, and 121′s is probably shorter.
Generally speaking, the processes used to create new elements are energetic enough (hot enough) that the atoms are formed in an ionized state. In order to fill up all of their shells and sub-shells, atoms need to be in a relatively cool environment. “Cool” as in “colder than plasma”. So to get an electron to settle into a “g” sub-shell you’d need to create element 121 or higher and then, before all of it radioactively decays into lighter elements (which has a way of ionizing everything nearby), you need to get it cooled off and electrically neutral. Then, before you can say “Nobel please”, it’s gone.