An electron orbital is a region around an atomic nucleus (not seen) in which one or a pair of electrons is most likely to exist. The gold area is where an electron has a positive wavefunction, and the red area is where the wavefunction is negative. The 5gz4 (or 5gzzzz) orbital is part of the 5g shell, which contains nine orbitals in total. The 5g shell is not full in any element in its normal (ground) state, but electrons may occupy 5g orbitals when the atom is excited, for instance by radiation of the correct wavelength.
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