A more complex explanation of the difference between core and valence electrons can be described with
atomic orbital theory. In atoms with a single electron the energy of an orbital is determined exclusively by the principal quantum number
n. The
n = 1 orbital has the lowest possible energy in the atom. For large
n, the energy increases so much that the electron can easily escape from the atom. In single electron atoms, all energy levels with the same principle quantum number are degenerate, and have the same energy. In atoms with more than one electron, the energy of an electron depends not only on the properties of the orbital it resides in, but also on its interactions with the other electrons in other orbitals. This requires consideration of the
ℓ quantum number. Higher values of
ℓ are associated with higher values of energy; for instance, the 2p state is higher than the 2s state. When
ℓ = 2, the increase in energy of the orbital becomes large enough to push the energy of orbital above the energy of the s-orbital in the next higher shell; when
ℓ = 3 the energy is pushed into the shell two steps higher. The filling of the 3d orbitals does not occur until the 4s orbitals have been filled. The increase in energy for subshells of increasing angular momentum in larger atoms is due to electron–electron interaction effects, and it is specifically related to the ability of low angular momentum electrons to penetrate more effectively toward the nucleus, where they are subject to less screening from the charge of intervening electrons. Thus, in atoms of higher
atomic number, the
ℓ of electrons becomes more and more of a determining factor in their energy, and the principal quantum numbers
n of electrons becomes less and less important in their energy placement. The energy sequence of the first 35 subshells (e.g., 1s, 2s, 2p, 3s, etc.) is given in the following table [not shown?]. Each cell represents a subshell with
n and
ℓ given by its row and column indices, respectively. The number in the cell is the subshell's position in the sequence. See the periodic table below, organized by subshells. ==Atomic core==