Core-level

Core electrons are the electrons in an atom that are not valence electrons and therefore do not participate in bonding. The number of valence electrons of an element can be determined by the periodic table group of the element. With the exception of the transition metals in groups 3-12 and the Lanthanide and Actinide series, the number of valence electrons ranges from 0-8 electrons. All the non-valence electrons for an atom of that element are considered core electrons. Core electrons are tightly bound to the nucleus. Therefore, unlike valence electrons the core electrons play a secondary role in chemical bonding and reactions by screening the positive charge of the atomic nucleus from the valence shell of electrons. In transition metals, the distinction between core and valence electrons is less distinct with electrons in the highest d-shell acting more like valence electrons than core electrons.

A more complex explanation of the difference between core and valance electrons can be described with atomic orbital theory.

In atoms with a single electron the energy of an orbital is determined exclusively by the principle 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, 2p, 3d, etc.) is given in the following table. 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.

...
Wikipedia